Sample records for rayleigh wave inversions

  1. Rayleigh wave inversion using heat-bath simulated annealing algorithm

    Lu, Yongxu; Peng, Suping; Du, Wenfeng; Zhang, Xiaoyang; Ma, Zhenyuan; Lin, Peng


    The dispersion of Rayleigh waves can be used to obtain near-surface shear (S)-wave velocity profiles. This is performed mainly by inversion of the phase velocity dispersion curves, which has been proven to be a highly nonlinear and multimodal problem, and it is unsuitable to use local search methods (LSMs) as the inversion algorithm. In this study, a new strategy is proposed based on a variant of simulated annealing (SA) algorithm. SA, which simulates the annealing procedure of crystalline solids in nature, is one of the global search methods (GSMs). There are many variants of SA, most of which contain two steps: the perturbation of model and the Metropolis-criterion-based acceptance of the new model. In this paper we propose a one-step SA variant known as heat-bath SA. To test the performance of the heat-bath SA, two models are created. Both noise-free and noisy synthetic data are generated. Levenberg-Marquardt (LM) algorithm and a variant of SA, known as the fast simulated annealing (FSA) algorithm, are also adopted for comparison. The inverted results of the synthetic data show that the heat-bath SA algorithm is a reasonable choice for Rayleigh wave dispersion curve inversion. Finally, a real-world inversion example from a coal mine in northwestern China is shown, which proves that the scheme we propose is applicable.

  2. Rayleigh scattering and nonlinear inversion of elastic waves

    Gritto, R.


    Rayleigh scattering of elastic waves by an inclusion is investigated and the limitations determined. In the near field of the inhomogeneity, the scattered waves are up to a factor of 300 stronger than in the far field, excluding the application of the far field Rayleigh approximation for this range. The investigation of the relative error as a function of parameter perturbation shows a range of applicability broader than previously assumed, with errors of 37% and 17% for perturbations of {minus}100% and +100%, respectively. The validity range for the Rayleigh limit is controlled by large inequalities, and therefore, the exact limit is determined as a function of various parameter configurations, resulting in surprisingly high values of up to k{sub p}R = 0.9. The nonlinear scattering problem can be solved by inverting for equivalent source terms (moments) of the scatterer, before the elastic parameters are determined. The nonlinear dependence between the moments and the elastic parameters reveals a strong asymmetry around the origin, which will produce different results for weak scattering approximations depending on the sign of the anomaly. Numerical modeling of cross hole situations shows that near field terms are important to yield correct estimates of the inhomogeneities in the vicinity of the receivers, while a few well positioned sources and receivers considerably increase the angular coverage, and thus the model resolution of the inversion parameters. The pattern of scattered energy by an inhomogeneity is complicated and varies depending on the object, the wavelength of the incident wave, and the elastic parameters involved. Therefore, it is necessary to investigate the direction of scattered amplitudes to determine the best survey geometry.

  3. Study on Rayleigh Wave Inversion for Estimating Shear-wave Velocity Profile

    T.A. Sanny


    Full Text Available Rayleigh wave or ground roll is a noise in seismic body waves. However, how to use this noise for soil characterization is very interesting since Rayleigh wave phase velocity is a function of compression-wave velocity, shear-wave velocity, density and layer thickness. In layered-medium Rayleigh wave velocity also depends on wavelength or frequency, and this phenomenon is called dispersion. Inversion procedure to get shear-wave velocity profile needs a priori information about the solution of the problem to limit the unknown parameters. The Lagrange multiplier method was used to solve the constrained optimization problems or well known as a smoothing parameter in inversion problems. The advantage of our inversion procedure is that it can guarantee the convergence of solution even though the field data is incomplete, insufficient, and inconsistent. The addition of smoothing parameter can reduce the time to converge. Beside numerical stability, the statistical stability is also involved in inversion procedure. In field experiment we extracted ground roll data from seismic refraction record. The dispersion curves had been constructed by applying f-k analysis and f-k dip filtering. The dispersion curves show the dependence of Rayleigh wave phase velocities in layered media to frequency. The synthetic models also demonstrate the stability and the speed of inversion procedure.

  4. Estimation of near-surface shear-wave velocity by inversion of Rayleigh waves

    Xia, J.; Miller, R.D.; Park, C.B.


    The shear-wave (S-wave) velocity of near-surface materials (soil, rocks, pavement) and its effect on seismic-wave propagation are of fundamental interest in many groundwater, engineering, and environmental studies. Rayleigh-wave phase velocity of a layered-earth model is a function of frequency and four groups of earth properties: P-wave velocity, S-wave velocity, density, and thickness of layers. Analysis of the Jacobian matrix provides a measure of dispersion-curve sensitivity to earth properties. S-wave velocities are the dominant influence on a dispersion curve in a high-frequency range (>5 Hz) followed by layer thickness. An iterative solution technique to the weighted equation proved very effective in the high-frequency range when using the Levenberg-Marquardt and singular-value decomposition techniques. Convergence of the weighted solution is guaranteed through selection of the damping factor using the Levenberg-Marquardt method. Synthetic examples demonstrated calculation efficiency and stability of inverse procedures. We verify our method using borehole S-wave velocity measurements.Iterative solutions to the weighted equation by the Levenberg-Marquardt and singular-value decomposition techniques are derived to estimate near-surface shear-wave velocity. Synthetic and real examples demonstrate the calculation efficiency and stability of the inverse procedure. The inverse results of the real example are verified by borehole S-wave velocity measurements.

  5. Estimating the location of a tunnel using correlation and inversion of Rayleigh wave scattering

    Kasililar, A.; Harmankaya, U.; Wapenaar, C.P.A.; Draganov, D.S.


    The investigation of near-surface scatterers, such as cavities, tunnels, abandoned mine shafts, and buried objects, is important to mitigate geohazards and environmental hazards. By inversion of travel times of cross-correlated scattered waves, due to the incident Rayleigh waves, we estimate the loc

  6. Impact of density information on Rayleigh surface wave inversion results

    Ivanov, Julian; Tsoflias, Georgios; Miller, Richard D.; Peterie, Shelby; Morton, Sarah; Xia, Jianghai


    We assessed the impact of density on the estimation of inverted shear-wave velocity (Vs) using the multi-channel analysis of surface waves (MASW) method. We considered the forward modeling theory, evaluated model sensitivity, and tested the effect of density information on the inversion of seismic data acquired in the Arctic. Theoretical review, numerical modeling and inversion of modeled and real data indicated that the density ratios between layers, not the actual density values, impact the determination of surface-wave phase velocities. Application on real data compared surface-wave inversion results using: a) constant density, the most common approach in practice, b) indirect density estimates derived from refraction compressional-wave velocity observations, and c) from direct density measurements in a borehole. The use of indirect density estimates reduced the final shear-wave velocity (Vs) results typically by 6-7% and the use of densities from a borehole reduced the final Vs estimates by 10-11% compared to those from assumed constant density. In addition to the improved absolute Vs accuracy, the resulting overall Vs changes were unevenly distributed laterally when viewed on a 2-D section leading to an overall Vs model structure that was more representative of the subsurface environment. It was observed that the use of constant density instead of increasing density with depth not only can lead to Vs overestimation but it can also create inaccurate model structures, such as a low-velocity layer. Thus, optimal Vs estimations can be best achieved using field estimates of subsurface density ratios.

  7. Feasibility of waveform inversion of Rayleigh waves for shallow shear-wave velocity using a genetic algorithm

    Zeng, C.; Xia, J.; Miller, R.D.; Tsoflias, G.P.


    Conventional surface wave inversion for shallow shear (S)-wave velocity relies on the generation of dispersion curves of Rayleigh waves. This constrains the method to only laterally homogeneous (or very smooth laterally heterogeneous) earth models. Waveform inversion directly fits waveforms on seismograms, hence, does not have such a limitation. Waveforms of Rayleigh waves are highly related to S-wave velocities. By inverting the waveforms of Rayleigh waves on a near-surface seismogram, shallow S-wave velocities can be estimated for earth models with strong lateral heterogeneity. We employ genetic algorithm (GA) to perform waveform inversion of Rayleigh waves for S-wave velocities. The forward problem is solved by finite-difference modeling in the time domain. The model space is updated by generating offspring models using GA. Final solutions can be found through an iterative waveform-fitting scheme. Inversions based on synthetic records show that the S-wave velocities can be recovered successfully with errors no more than 10% for several typical near-surface earth models. For layered earth models, the proposed method can generate one-dimensional S-wave velocity profiles without the knowledge of initial models. For earth models containing lateral heterogeneity in which case conventional dispersion-curve-based inversion methods are challenging, it is feasible to produce high-resolution S-wave velocity sections by GA waveform inversion with appropriate priori information. The synthetic tests indicate that the GA waveform inversion of Rayleigh waves has the great potential for shallow S-wave velocity imaging with the existence of strong lateral heterogeneity. ?? 2011 Elsevier B.V.

  8. Joint Inversion for Earthquake Depths Using Local Waveforms and Amplitude Spectra of Rayleigh Waves

    Jia, Zhe; Ni, Sidao; Chu, Risheng; Zhan, Zhongwen


    Reliable earthquake depth is fundamental to many seismological problems. In this paper, we present a method to jointly invert for centroid depths with local (distance distance of 5°-15°) Rayleigh wave amplitude spectra on sparse networks. We use earthquake focal mechanisms and magnitudes retrieved with the Cut-and-Paste (CAP) method to compute synthetic amplitude spectra of fundamental mode Rayleigh wave for a range of depths. Then we grid search to find the optimal depth that minimizes the joint misfit of amplitude spectra and local waveforms. As case studies, we apply this method to the 2008 Wells, Nevada Mw6.0 earthquake and a Mw5.6 outer-rise earthquake to the east of Japan Trench in 2013. Uncertainties estimated with a bootstrap re-sampling approach show that this joint inversion approach constrains centroid depths well, which are also verified by independent teleseismic depth-phase data.

  9. Crustal Structure of the Pakistan Himalayas from Ambient Noise and Seismic Rayleigh Wave Inversion

    Li, A.


    The western Himalayan syntaxi is a unique feature resulted from the India-Asia collision and its formation remains poorly understood. To image crustal structure in the western syntaxi, we analyze Rayleigh waves from ambient seismic noise and earthquake data recorded during the Pakistan Broadband Seismic Experiment. The Pakistan experiment included 9 broadband stations with an aperture of ~200 km and operated from September to December in 1992. We compute cross-correlations of ambient noise data on an hourly base and stack all the cross-correlations for 70 days to produce the estimated Green functions. Power spectrum analysis shows that the dominant energy is from 0.15 to 0.25 Hz and from 0.05 to 0.07 Hz, consistent with the well-know background seismic noise. A phase with large amplitude appears at near zero time on almost all stacked cross- correlations and its origin is not clear to us at this moment. Rayleigh waves can be clearly observed for station pairs at the distance of 80 km and larger but are contaminated by the near zero time phase at shorter station spacing. Rayleigh wave phase velocities at periods of 4 to 15 s will be produced from the ambient noise data. Using regional and teleseismic earthquakes, we expect to obtain Rayleigh wave dispersions at periods from 15 to 50 s. The phase velocities from both datasets will be inverted for crustal thickness and shear-wave structure beneath the Pakistan Himalayas.

  10. Influence of gravity waves and tides on mesospheric temperature inversion layers: simultaneous Rayleigh lidar and MF radar observations

    Sridharan, S. [National Atmospheric Research Lab., Chittoor (India); Sathishkumar, S.; Gurubaran, S. [Indian Inst. of Geomagnetism, Tirunelveli (India). Equatorial Geophysical Research Lab.


    Three nights of simultaneous Rayleigh lidar temperature measurements over Gadanki (13.5 N,79.2 E) and medium frequency (MF) radar wind measurements over Tirunelveli (8.7 N,77.8 E) have been analyzed to illustrate the possible effects due to tidal-gravity wave interactions on upper mesospheric inversion layers. The occurrence of tidal gravity wave interaction is investigated using MF radar wind measurements in the altitude region 86-90 km. Of the three nights, it is found that tidal gravity wave interaction occurred in two nights. In the third night, diurnal tidal amplitude is found to be significantly larger. As suggested in Sica et al. (2007), mesospheric temperature inversion seems to be a signature of wave saturation in the mesosphere, since the temperature inversion occurs at heights, when the lapse rate is less than half the dry adiabatic lapse rate. (orig.)

  11. Influence of gravity waves and tides on mesospheric temperature inversion layers: simultaneous Rayleigh lidar and MF radar observations

    Sridharan, S.; Sathishkumar, S.; Gurubaran, S.


    Three nights of simultaneous Rayleigh lidar temperature measurements over Gadanki (13.5° N, 79.2° E) and medium frequency (MF) radar wind measurements over Tirunelveli (8.7° N, 77.8° E) have been analyzed to illustrate the possible effects due to tidal-gravity wave interactions on upper mesospheric inversion layers. The occurrence of tidal gravity wave interaction is investigated using MF radar wind measurements in the altitude region 86 90 km. Of the three nights, it is found that tidal gravity wave interaction occurred in two nights. In the third night, diurnal tidal amplitude is found to be significantly larger. As suggested in Sica et al. (2007), mesospheric temperature inversion seems to be a signature of wave saturation in the mesosphere, since the temperature inversion occurs at heights, when the lapse rate is less than half the dry adiabatic lapse rate.

  12. A method for inversion of layered shear wavespeed azimuthal anisotropy from Rayleigh wave dispersion using the Neighborhood Algorithm

    Huajian Yao


    Seismic anisotropy provides important constraints on deformation patterns of Earth's material.Rayleigh wave dispersion data with azimuthal anisotropy can be used to invert for depth-dependent shear wavespeed azimuthal anisotropy,therefore reflecting depth-varying deformation patterns in the crust and upper mantle.In this study,we propose a two-step method that uses the Neighborhood Algorithm (NA) for the point-wise inversion of depth-dependent shear wavespeeds and azimuthal anisotropy from Rayleigh wave azimuthally anisotropic dispersion data.The first step employs the NA to estimate depthdependent Vsv (or the elastic parameter L) as well as their uncertainties from the isotropic part Rayleigh wave dispersion data.In the second step,we first adopt a difference scheme to compute approximate Rayleigh-wave phase velocity sensitivity kernels to azimuthally anisotropic parameters with respect to the velocity model obtained in the first step.Then we perform the NA to estimate the azi.muthally anisotropic parameters Gc/L and Gs/L at depths separately from the corresponding cosine and sine terms of the azimuthally anisotropic dispersion data.Finally,we compute the depth-dependent magnitude and fast polarization azimuth of shear wavespeed azimuthal anisotropy.The use of the global search NA and Bayesian analysis allows for more reliable estimates of depth-dependent shear wavespeeds and azimuthal anisotropy as well as their uncertainties.We illustrate the inversion method using the azimuthally anisotropic dispersion data in SE Tibet,where we find apparent changes of fast axes of shear wavespeed azimuthal anisotropy between the crust and uppermost mantle.

  13. The Uniqueness of Single Data Function, Multiple Model Functions, Inverse Problems Including the Rayleigh Wave Dispersion Problem

    Menke, William


    We prove that the problem of inverting Rayleigh wave phase velocity functions c( k ) , where k is wavenumber, for density ρ ( z ) , rigidity μ ( z ) and Lamé parameter λ ( z ) , where z is depth, is fully non-unique, at least in the highly-idealized case where the base Earth model is an isotropic half space. The model functions completely trade off. This is one special case of a common inversion scenario in which one seeks to determine several model functions from a single data function. We explore the circumstances under which this broad class of problems is unique, starting with very simple scenarios, building up to the somewhat more complicated (and common) case where data and model functions are related by convolutions, and then finally, to scale-independent problems (which include the Rayleigh wave problem). The idealized cases that we examine analytically provide insight into the kinds of nonuniqueness that are inherent in the much more complicated problems encountered in modern geophysical imaging (though they do not necessarily provide methods for solving those problems). We also define what is meant by a Backus and Gilbert resolution kernel in this kind of inversion and show under what circumstances a unique localized average of a single model function can be constructed.

  14. The Uniqueness of Single Data Function, Multiple Model Functions, Inverse Problems Including the Rayleigh Wave Dispersion Problem

    Menke, William


    We prove that the problem of inverting Rayleigh wave phase velocity functions c( k ), where k is wavenumber, for density ρ ( z ), rigidity μ ( z ) and Lamé parameter λ ( z ), where z is depth, is fully non-unique, at least in the highly-idealized case where the base Earth model is an isotropic half space. The model functions completely trade off. This is one special case of a common inversion scenario in which one seeks to determine several model functions from a single data function. We explore the circumstances under which this broad class of problems is unique, starting with very simple scenarios, building up to the somewhat more complicated (and common) case where data and model functions are related by convolutions, and then finally, to scale-independent problems (which include the Rayleigh wave problem). The idealized cases that we examine analytically provide insight into the kinds of nonuniqueness that are inherent in the much more complicated problems encountered in modern geophysical imaging (though they do not necessarily provide methods for solving those problems). We also define what is meant by a Backus and Gilbert resolution kernel in this kind of inversion and show under what circumstances a unique localized average of a single model function can be constructed.

  15. Seismic Rayleigh Wave Digital Processing Technology

    Jie, Li


    In Rayleigh wave exploration, the digital processing of data plays a very important position. This directly affects the interpretation of ground effect. Therefore, the use of accurate processing software and effective method in the Rayleigh wave exploration has important theoretical and practical significance. Previously, Rayleigh wave dispersion curve obtained by the one-dimensional phase analysis. This method requires channel spacing should be less than the effective wavelength. And minimal phase error will cause great changes in the phase velocity of Rayleigh wave. Damped least square method is a local linear model. It is easy to cause that inversion objective function cannot find the global optimal solution. Therefore, the method and the technology used in the past are difficult to apply the requirements of the current Rayleigh wave exploration. This study focused on the related technologies and algorithms of F-K domain dispersion curve extraction and GA global non-linear inversion, and combined with the impact of Rayleigh wave data acquisition parameters and the characteristics. Rayleigh wave exploration data processing software design and process technology research is completed. Firstly, the article describes the theoretical basis of Rayleigh wave method. This is also part of the theoretical basis of following treatment. The theoretical proof of existence of Rayleigh wave Dispersive in layered strata. Secondly, F-K domain dispersion curve extraction tests showed that the method can overcome the one-dimensional digital processing technology deficiencies, and make full use of multi-channel Rayleigh wave data record information. GA global non-linear inversion indicated that the inversion is not easy getting into local optimal solution. Thirdly, some examples illustrate each mode Rayleigh wave dispersion curve characteristics in the X-T domain. Tests demonstrated the impact on their extraction of dispersion curves. Parameters change example (including the X

  16. Measurement of Rayleigh wave Z/H ratio and joint inversion for a high-resolution S wave velocity model beneath the Gulf of Mexico passive margin

    Miao, W.; Li, G.; Niu, F.


    Knowledge on the 3D sediment structure beneath the Gulf of Mexico passive margin is not only important to explore the oil and gas resources in the area, but also essential to decipher the deep crust and mantle structure beneath the margin with teleseismic data. In this study, we conduct a joint inversion of Rayleigh wave ellipticity and phase velocity at 6-40 s to construct a 3-D S wave velocity model in a rectangular area of 100°-87° west and 28°-37° north. We use ambient noise data from a total of 215 stations of the Transportable Array deployed under the Earthscope project. Rayleigh wave ellipticity, or Rayleigh wave Z/H (vertical to horizontal) amplitude ratio is mostly sensitive to shallow sediment structure, while the dispersion data are expected to have reasonably good resolution to uppermost mantle depths. The Z/H ratios measured from stations inside the Gulf Coastal Plain are distinctly lower in comparison with those measured from the inland stations. We also measured the phase velocity dispersion from the same ambient noise dataset. Our preliminary 3-D model is featured by strong low-velocity anomalies at shallow depth, which are spatially well correlated with Gulf Cost, East Texas, and the Lower Mississippi basins. We will discuss other features of the 3-D models once the model is finalized.

  17. Forward and inverse problems for surface acoustic waves in anisotropic media: a Ritz-Rayleigh method based approach.

    Stoklasová, Pavla; Sedlák, Petr; Seiner, Hanuš; Landa, Michal


    We show that the Ritz-Rayleigh method can be used for calculation of velocity of surface acoustic waves (SAWs) propagating in a general direction of an anisotropic medium of arbitrary symmetry class. The main advantage of this method is that expanding the displacement field of SAW into a fixed functional basis transforms the calculation of SAW velocities into a simple linear eigenvalue problem. The correctness and reliability of the proposed approach are verified on experimental SAW data obtained for generally oriented planes of an indium phosphide single crystal. The same experimental datasets are then used to discuss the invertibility of the method, i.e. the possibility of determination of elastic coefficients from SAW measurements in general directions. It is shown that the SAW data obtained on a single generally oriented plane are sufficient for such an inverse calculation for a cubic material only if they are complemented by measurements of velocities of bulk quasi-longitudinal (qL) waves propagating along the same free surface. Moreover, when the SAW and qL data are available from three almost perpendicular faces of a single specimen, the complete elastic tensor (21 independent constants) can be inversely determined, without considering a priori any symmetry constraints to the material.

  18. Joint inversion of teleseismic and ambient noise Rayleigh waves for phase velocity maps, an application to Iceland

    Harmon, Nicholas; Rychert, Catherine A.


    We present a method for joint inversion of teleseismic and ambient noise Rayleigh wave data for phase velocity maps from 18 to 50 s period. We adapt the two-plane wave method for teleseismic data to include ambient noise phase data. We apply the method to data from Iceland's ICEMELT and HOTSPOT arrays. Checkerboard tests show that the joint inversion improves phase velocity model recovery over methods that use the data sets independently, particularly at 18 s period. The addition of ambient noise data also extends resolution to shallower depths and shorter periods in comparison to previous teleseismic results beneath Iceland. We show there are significant differences in the phase velocity maps from the joint approach in comparison to other approaches, for instance, using only teleseismic data, only ambient noise data, or the mean of the two. The difference in phase velocities in turn affects the resulting shear velocity models. The advantage of the joint inversion is that it produces a single phase velocity map that satisfies both data sets simultaneously. Our phase velocity maps show a transition from low velocities centered beneath the main volcanic centers in Iceland at 18-25 s period, primarily crustal depths, to a low-velocity region that traces the rift zones from the Reykjanes Ridge in the south to the Kolbeinsey Ridge in the north at 29-50 s period, greater depths. These results are consistent with previous studies, although with an extended and improved region of resolution, which extends further into the Atlantic and Arctic Ocean.

  19. Detailed 3-D S-wave velocity beneath the High Lava Plains, Oregon, from 2-plane-wave Rayleigh wave inversions

    Wagner, L. S.; Forsyth, D. W.; Fouch, M. J.; James, D. E.


    The High Lava Plains (HLP) of eastern Oregon represent an unusual track of bimodal volcanism extending from the southeastern-most corner of the state to its current position beneath the Newberry Volcano on the eastern margin of the Cascades. The silicic volcanism is time progressive along this track, beginning some 15 Ma near the Owyhee plateau and then trending to the north east. The timing and location of the start of the HLP coincides with that of the initial volcanism associated with the Yellowstone/Snake River Plain track (YSRP). While the YSRP has often been interpreted as the classic intra-continental hot spot track, the HLP, which trends almost normal to absolute plate motion, is harder to explain. This study uses the 100+ stations associated with the HLP seismic deployment together with another ~100 Earthscope Transportable Array stations (TA) to perform a high resolution inversion for Rayleigh wave phase velocities using the 2-plane-wave methodology of Forsyth and Li (2004). Because of the comparatively small grid spacing of this study, we are able to discern much finer scale structures than studies looking at the entire western U.S. with only TA stations. Preliminary results indicate very low velocities across the study area, especially at upper mantle depths. Especially low velocities are seen beneath the Owyhee plateau and along both the HLP and YSRP tracks. Final details about the exact geometries of these features will help constrain possible scenarios for the formation of the HLP volcanic sequence.

  20. Rayleigh wave modeling: A study of dispersion curve sensitivity and methodology for calculating an initial model to be included in an inversion algorithm

    de Lucena, Rodrigo F.; Taioli, Fabio


    This paper presents a study on Rayleigh wave modeling. After model implementation using Matlab software, unpublished studies were conducted of dispersion curve sensitivity to percentage changes in parameter values, including S- and P-wave velocities, substrate density, and layer thickness. The study of the sensitivity of dispersion curves demonstrated that parameters such as S-wave velocity and layer thickness cannot be ignored as inversion parameters, while P-wave velocity and density can be considered as known parameters since their influence is minimal. However, the results showed limitations that should be considered and overcome when choosing the known and unknown parameters through determining a good initial model or/and by gathering a priori information. A methodology considering the sensitivity study of dispersion curves was developed and evaluated to generate initial values (initial model) to be included in the local search inversion algorithm, clearly establishing initial favorable conditions for data inversion.

  1. Structure of the Crust beneath Cameroon, West Africa, from the Joint Inversion of Rayleigh Wave Group Velocities and Receiver Functions

    Tokam, A K; Tabod, C T; Nyblade, A A; Julia, J; Wiens, D A; Pasyanos, M E


    Cameroon using 1-D shear wave velocity models obtained from the joint inversion of Rayleigh wave group velocities and P-receiver functions for 32 broadband seismic stations. From the 1-D shear wave velocity models, we obtain new insights into the composition and structure of the crust and upper mantle across Cameroon. After briefly reviewing the geological framework of Cameroon, we describe the data and the joint inversion method, and then interpret variations in crustal structure found beneath Cameroon in terms of the tectonic history of the region.

  2. High-Frequency Rayleigh-Wave Method

    Jianghai Xia; Richard D Millerg; Xu Yixian; Luo Yinhe; Chen Chao; Liu Jiangping; Julian Ivanov; Chong Zeng


    High-frequency (≥2 Hz) Rayleigh-wave data acquired with a multichannei recording sys-tem have been utilized to determine shear (S)-wave velocities in near-surface geophysics since the early 1980s. This overview article discusses the main research results of high-frequency surface-wave tech-niques achieved by research groups at the Kansas Geological Survey and China University of Geosciences in the last 15 years. The multichannel analysis of surface wave (MASW) method is a nou-iuvasive acoustic approach to estimate near-surface S-wave velocity. The differences between MASW results and direct borehole measurements are approximately 15% or less and random. Studies show that simultaneous inversion with higher modes and the fundamental mode can increase model resolution and an investigation depth. The other important seismic property, quality factor (Q), can also be estimated with the MASW method by inverting attenuation coefficients of Rayleigh waves. An inverted model (S-wave velocity or Q) obtained using a damped least-squares method can be assessed by an optimal damping vector in a vicinity of the inverted model determined by an objective function, which is the trace of a weighted sum of model-resolution and model-covariance matrices. Current developments include modeling high-frequency Rayleigh-waves in near-surface media, which builds a foundation for shallow seismic or Rayleigh-wave inversion in the time-offset domain; imaging dispersive energy with high resolution in the frequency-velocity domain and possibly with data in an arbitrary acquisition geometry, which opens a door for 3D surface-wave techniques; and successfully separating surface-wave modes, which provides a valuable tool to perform S-wave velocity profiling with high-horizontal resolution.

  3. Rayleigh Wave Ellipticity Modeling and Inversion for Shallow Structure at the Proposed InSight Landing Site in Elysium Planitia, Mars

    Knapmeyer-Endrun, Brigitte; Golombek, Matthew P.; Ohrnberger, Matthias


    The SEIS (Seismic Experiment for Interior Structure) instrument onboard the InSight mission will be the first seismometer directly deployed on the surface of Mars. From studies on the Earth and the Moon, it is well known that site amplification in low-velocity sediments on top of more competent rocks has a strong influence on seismic signals, but can also be used to constrain the subsurface structure. Here we simulate ambient vibration wavefields in a model of the shallow sub-surface at the InSight landing site in Elysium Planitia and demonstrate how the high-frequency Rayleigh wave ellipticity can be extracted from these data and inverted for shallow structure. We find that, depending on model parameters, higher mode ellipticity information can be extracted from single-station data, which significantly reduces uncertainties in inversion. Though the data are most sensitive to properties of the upper-most layer and show a strong trade-off between layer depth and velocity, it is possible to estimate the velocity and thickness of the sub-regolith layer by using reasonable constraints on regolith properties. Model parameters are best constrained if either higher mode data can be used or additional constraints on regolith properties from seismic analysis of the hammer strokes of InSight's heat flow probe HP3 are available. In addition, the Rayleigh wave ellipticity can distinguish between models with a constant regolith velocity and models with a velocity increase in the regolith, information which is difficult to obtain otherwise.

  4. Seismic evidence of crustal heterogeneity beneath the northwestern Deccan volcanic province of India from joint inversion of Rayleigh wave dispersion measurements and P receiver functions

    Deshpande, A. A.; Mohan, G.


    The northwestern Deccan volcanic province (NWDVP) of India, encompassing the Saurashtra peninsula and the adjoining Gulf of Cambay, is investigated through joint inversion of surface wave dispersion measurements and teleseismic P receiver functions, to estimate the crustal and shallow upper mantle shear wave velocity (Vs) structure. The Mw ∼ 7.7 Bhuj earthquake and the post Bhuj regional events, recorded during the period 2001-2010 at 7 stations along 37 source-receiver paths were used along with 35 teleseismic events. A joint curve fitting inversion technique is applied to obtain a best fit for the fundamental mode Rayleigh wave group velocity dispersion curves for time periods 5-50 s and high quality crustal P wave receiver functions obtained at each station. Significant crustal heterogeneity is observed within the study region with the average crustal Vs ranging from 3.5 km/s to 3.8 km/s with the paths cutting across the Gulf of Cambay exhibiting large reduction in shear wave velocities. Utilizing the average crustal Vs ≈ 3.66 km/s estimated for Saurashtra, together with the average crustal P wave velocity (Vp) ≈ 6.54 km/s derived independently through deep seismic sounding studies, yields a bulk Vp/Vs ratio of 1.786 or an equivalent crustal Poisson's ratio of 0.271. A major contribution to the high Poisson's ratio comes from the 12 to 16 km thick lower crustal layers with shear velocities ranging from 3.8 km/s to 4.19 km/s suggesting widespread magmatic underplating due to emplacement of mafic cumulates in the lower crust. The shallow uppermost mantle shear velocities are in the range 4.2-4.5 km/s averaging 4.36 km/s, which is less than that observed for the Indian shield, indicating the effects of residual thermal anomaly. The variation in the crustal Vs, high Poisson's ratios and low upper mantle shear velocities reflect the thermal and compositional effects of the Deccan volcanism which are manifested in terms of pervasive presence of mafic dykes

  5. Wave Equation Inversion of Skeletonized SurfaceWaves

    Zhang, Zhendong


    We present a surface-wave inversion method that inverts for the S-wave velocity from the Rayleigh dispersion curve for the fundamental-mode. We call this wave equation inversion of skeletonized surface waves because the dispersion curve for the fundamental-mode Rayleigh wave is inverted using finite-difference solutions to the wave equation. The best match between the predicted and observed dispersion curves provides the optimal S-wave velocity model. Results with synthetic and field data illustrate the benefits and limitations of this method.

  6. Modeling of Rayleigh wave dispersion in Iberia

    José Badal


    Full Text Available Phase and group velocities of 15–70 s Rayleigh waves propagating across the Iberian Peninsula have been transformed into local dispersion curves by linear inversion of travel times. The procedure permits that the waveform dispersion to be obtained as a continuous period-dependent velocity function at grid points belonging to the area probed by the waves, thus providing phase- and group-velocity contour maps for several periods within the interval of interest. The regionalization process rests on a homogeneous initial data set in which the number of observations remains almost constant for all periods of reference. Damped least-squares inversion of the local dispersion curves for shear-wave velocity structure is performed to obtain depth-dependent S-wave velocity profiles at the grid points covering the model region. The reliability of the results should improve significantly owing to the use of phase and group velocities simultaneously. On this basis, we have built horizontal depth sections that give an updated view of the seismic velocity structure of the peninsula at lithospheric and upper mantle depths (20–200 km. After averaging all the pure-path S-wave velocities previously determined at each grid point, the velocity-depth models so obtained for major tectonic units allow the comparison between the Hercynian basement and other areas of Mesozoic folding and Tertiary basins.

  7. Wave-equation dispersion inversion

    Li, Jing


    We present the theory for wave-equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. The dispersion curves are obtained from Rayleigh waves recorded by vertical-component geophones. Similar to wave-equation traveltime tomography, the complicated surface wave arrivals in traces are skeletonized as simpler data, namely the picked dispersion curves in the phase-velocity and frequency domains. Solutions to the elastic wave equation and an iterative optimization method are then used to invert these curves for 2-D or 3-D S-wave velocity models. This procedure, denoted as wave-equation dispersion inversion (WD), does not require the assumption of a layered model and is significantly less prone to the cycle-skipping problems of full waveform inversion. The synthetic and field data examples demonstrate that WD can approximately reconstruct the S-wave velocity distributions in laterally heterogeneous media if the dispersion curves can be identified and picked. The WD method is easily extended to anisotropic data and the inversion of dispersion curves associated with Love waves.

  8. A 3D algorithm based on the combined inversion of Rayleigh and Love waves for imaging and monitoring of shallow structures

    Pilz, Marco; Parolai, Stefano; Woith, Heiko


    SUMMARYIn recent years there has been increasing interest in the study of seismic noise interferometry as it can provide a complementary approach to active source or earthquake based methods for imaging and continuous monitoring the shallow structure of the Earth. This meaningful information is extracted from wavefields propagating between those receiver positions at which seismic noise was recorded. Until recently, noise-based imaging relied mostly on Rayleigh waves. However, considering similar wavelengths, a combined use of Rayleigh and Love wave tomography can succeed in retrieving velocity heterogeneities at depth due to their different sensitivity kernels. Here we present a novel one-step algorithm for simultaneously inverting Rayleigh and Love wave dispersion data aiming at identifying and describing complex 3D velocity structures. The algorithm may help to accurately and efficiently map the shear-wave velocities and the Poisson ratio of the surficial soil layers. In the high-frequency range, the scattered part of the correlation functions stabilizes sufficiently fast to provide a reliable estimate of the velocity structure not only for imaging purposes but also allows for changes in the medium properties to be monitored. Such monitoring can be achieved with a high spatial resolution in 3D and with a time resolution as small as a few hours. In this article, we describe a recent array experiment in a volcanic environment in Solfatara (Italy) and we show that this novel approach has identified strong velocity variations at the interface between liquids and gas-dominated reservoirs, allowing localizing a region which is highly dynamic due to the interaction between the deep convection and its surroundings.

  9. Bayes Estimation for Inverse Rayleigh Model under Different Loss Functions

    Guobing Fan


    Full Text Available The inverse Rayleigh distribution plays an important role in life test and reliability domain. The aim of this article is study the Bayes estimation of parameter of inverse Rayleigh distribution. Bayes estimators are obtained under squared error loss, LINEX loss and entropy loss functions on the basis of quasi-prior distribution. Comparisons in terms of risks with the estimators of parameter under three loss functions are also studied. Finally, a numerical example is used to illustrate the results.

  10. Retrieval of Rayleigh Wave Ellipticity from Ambient Vibration Recordings

    Maranò, Stefano; Hobiger, Manuel; Fäh, Donat


    The analysis of ambient vibrations is a useful tool in microzonation and geotechnical investigations. Ambient vibrations are composed to a large part of surface waves, both Love and Rayleigh waves. One reason to analyse surface waves is that they carry information about the subsurface. The dispersion curve of Rayleigh waves and Love waves can be retrieved using array processing techniques. The Rayleigh wave ellipticity, including the sense of rotation of the particle motion, can also be retrieved using array techniques. These quantities are used in an inversion procedure aimed at obtaining a structural model of the subsurface. The focus of this work is the retrieval of Rayleigh wave ellipticity. We show applications of the (ML) method presented in Maranó et al. (2012) to a number of sites in Switzerland. The sites examined are chosen to reflect a wide range of soil conditions that are of interest in microzonation studies. Using a synthetic wavefield with known structural model, we compare our results with theoretical ellipticity curves and we show the accuracy of the considered algorithm. The sense of rotation of the particle motion (prograde vs. retrograde) is also estimated. In addition, we show that by modelling the presence of both Love and Rayleigh waves it is possible to mitigate the disruptive influence of Love waves on the estimation of Rayleigh wave ellipticity. Using recordings from several real sites, we show that it is possible to retrieve the ellipticity curve over a broad range of frequencies. Fundamental modes and higher modes are retrieved. Singularities of the ellipticity, corresponding to a change of the sense of rotation from prograde to retrograde (or vice versa), are detected with great accuracy. Knowledge of Rayleigh wave ellipticity, including the sense of rotation, is useful in several ways. The ellipticity angle allows us to pinpoint accurately the frequency of singularities (i.e., peaks and zeros of the H/V representation of the

  11. Reflectometry using longitudinal, shear and Rayleigh waves.

    Chen, W; Wu, J


    A new technique of reflectometry using longitudinal, shear and Rayleigh waves is presented. Reflection coefficient as a function of angle incidence of an ultrasound beam with a finite beamwidth was measured for water-aluminum, water-brass, and water-glass interfaces. The measured values have matched very favorably with the results of numerical calculations based on the angular spectrum of waves method. It has been shown that the speeds of longitudinal, shear and Rayleigh waves of a solid can be determined very accurately by measuring a spectacularly reflected signal versus angle of incidence.

  12. Wave-equation Qs Inversion of Skeletonized Surface Waves

    Li, Jing


    We present a skeletonized inversion method that inverts surface-wave data for the Qs quality factor. Similar to the inversion of dispersion curves for the S-wave velocity model, the complicated surface-wave arrivals are skeletonized as simpler data, namely the amplitude spectra of the windowed Rayleigh-wave arrivals. The optimal Qs model is the one that minimizes the difference in the peak frequencies of the predicted and observed Rayleigh wave arrivals using a gradient-based wave-equation optimization method. Solutions to the viscoelastic wave-equation are used to compute the predicted Rayleigh-wave arrivals and the misfit gradient at every iteration. This procedure, denoted as wave-equation Qs inversion (WQs), does not require the assumption of a layered model and tends to have fast and robust convergence compared to full waveform inversion (FWI). Numerical examples with synthetic and field data demonstrate that the WQs method can accurately invert for a smoothed approximation to the subsurface Qs distribution as long as the Vs model is known with sufficient accuracy.

  13. Rayleigh wave scattering at the foot of a mountain

    P. S. Deshwal


    Full Text Available A theoretical study of scattering of seismic waves at the foot of a mountain is discussed here. A mountain of an arbitrary shape and of width a (0≤x≤a, z=0 in the surface of an elastic solid medium (z≥0 is hit by a Rayleigh wave. The method of solution is the technique of Wiener and Hopf. The reflected, transmitted and scattered waves are obtained by inversion of Fourier transforms. The scattered waves behave as decaying cylindrical waves at distant points and have a large amplitude near the foot of the mountain. The transmitted wave decreases exponentially as its distance from the other end of the mountain increases.

  14. mitants of Order Statistics from Bivariate Inverse Rayleigh Distribution

    Muhammad Aleem


    Full Text Available The probability density function (pdf of the rth, 1 r n and joint pdf of the rth and sth, 1 rInverse Rayleigh Distribution and their moments, product moments are obtained. Its percentiles are also obtained.

  15. Leaky Rayleigh wave investigation on mortar samples.

    Neuenschwander, J; Schmidt, Th; Lüthi, Th; Romer, M


    Aggressive mineralized ground water may harm the concrete cover of tunnels and other underground constructions. Within a current research project mortar samples are used to study the effects of sulfate interaction in accelerated laboratory experiments. A nondestructive test method based on ultrasonic surface waves was developed to investigate the topmost layer of mortar samples. A pitch and catch arrangement is introduced for the generation and reception of leaky Rayleigh waves in an immersion technique allowing the measurement of their propagation velocity. The technique has been successfully verified for the reference materials aluminium, copper, and stainless steel. First measurements performed on mortar specimens demonstrate the applicability of this new diagnostic tool.

  16. Imaging Rayleigh wave attenuation with USArray

    Bao, Xueyang; Dalton, Colleen A.; Jin, Ge; Gaherty, James B.; Shen, Yang


    The EarthScope USArray provides an opportunity to obtain detailed images of the continental upper mantle at an unprecedented scale. The majority of mantle models derived from USArray data to date contain spatial variations in seismic-wave speed; however, in many cases these data sets do not by themselves allow a non-unique interpretation. Joint interpretation of seismic attenuation and velocity models can improve upon the interpretations based only on velocity and provide important constraints on the temperature, composition, melt content, and volatile content of the mantle. The surface wave amplitudes that constrain upper-mantle attenuation are sensitive to factors in addition to attenuation, including the earthquake source excitation, focusing and defocusing by elastic structure, and local site amplification. Because of the difficulty of isolating attenuation from these other factors, little is known about the attenuation structure of the North American upper mantle. In this study, Rayleigh wave traveltime and amplitude in the period range 25-100 s are measured using an interstation cross-correlation technique, which takes advantage of waveform similarity at nearby stations. Several estimates of Rayleigh wave attenuation and site amplification are generated at each period, using different approaches to separate the effects of attenuation and local site amplification on amplitude. It is assumed that focusing and defocusing effects can be described by the Laplacian of the traveltime field. All approaches identify the same large-scale patterns in attenuation, including areas where the attenuation values are likely contaminated by unmodelled focusing and defocusing effects. Regionally averaged attenuation maps are constructed after removal of the contaminated attenuation values, and the variations in intrinsic shear attenuation that are suggested by these Rayleigh wave attenuation maps are explored.

  17. Demonstration of Shear Waves, Lamb Waves, and Rayleigh Waves by Mode Conversion.

    Leung, W. P.


    Introduces an experiment that can be demonstrated in the classroom to show that shear waves, Rayleigh waves, and Lamb waves can be easily generated and observed by means of mode conversion. (Author/CS)

  18. Rayleigh waves ellipticity and mode mis-identification in multi-channel analysis of surface waves

    Boaga, Jacopo; Cassiani, Giorgio; Strobbia, Claudio

    dispersion curve which is then inverted. Typically, single component vertical and multi channel receivers are used. In most cases the inversion of the dispersion properties is carried out assuming that the experimental dispersion curve corresponds to a single mode, mostly the fundamental Rayleigh mode......-identification known as ‘osculation’ (‘kissing’). In general it is called ‘osculation point’ the point where the energy peak shifts at low frequencies from the fundamental to the first higher mode. This jump occurs, with a continuous smooth transition, around a well-define frequency where the two modes get very close...... the vertical component of ground motion, as the mode osculation is linked to the Rayleigh wave ellipticity polarization, and therefore we conclude that multi-component data, using also horizontal receivers, can help discern the multi-modal nature of surface waves. Finally we introduce a-priori detectors...

  19. Application of particle swarm optimization to interpret Rayleigh wave dispersion curves

    Song, Xianhai; Tang, Li; Lv, Xiaochun; Fang, Hongping; Gu, Hanming


    Rayleigh waves have been used increasingly as an appealing tool to obtain near-surface shear (S)-wave velocity profiles. However, inversion of Rayleigh wave dispersion curves is challenging for most local-search methods due to its high nonlinearity and to its multimodality. In this study, we proposed and tested a new Rayleigh wave dispersion curve inversion scheme based on particle swarm optimization (PSO). PSO is a global optimization strategy that simulates the social behavior observed in a flock (swarm) of birds searching for food. A simple search strategy in PSO guides the algorithm toward the best solution through constant updating of the cognitive knowledge and social behavior of the particles in the swarm. To evaluate calculation efficiency and stability of PSO to inversion of surface wave data, we first inverted three noise-free and three noise-corrupted synthetic data sets. Then, we made a comparative analysis with genetic algorithms (GA) and a Monte Carlo (MC) sampler and reconstructed a histogram of model parameters sampled on a low-misfit region less than 15% relative error to further investigate the performance of the proposed inverse procedure. Finally, we inverted a real-world example from a waste disposal site in NE Italy to examine the applicability of PSO on Rayleigh wave dispersion curves. Results from both synthetic and field data demonstrate that particle swarm optimization can be used for quantitative interpretation of Rayleigh wave dispersion curves. PSO seems superior to GA and MC in terms of both reliability and computational efforts. The great advantages of PSO are fast in locating the low misfit region and easy to implement. Also there are only three parameters to tune (inertia weight or constriction factor, local and global acceleration constants). Theoretical results exist to explain how to tune these parameters.

  20. Passive retrieval of Rayleigh waves in disordered elastic media.

    Larose, Eric; Derode, Arnaud; Clorennec, Dominique; Margerin, Ludovic; Campillo, Michel


    When averaged over sources or disorder, cross correlation of diffuse fields yields the Green's function between two passive sensors. This technique is applied to elastic ultrasonic waves in an open scattering slab mimicking seismic waves in the Earth's crust. It appears that the Rayleigh wave reconstruction depends on the scattering properties of the elastic slab. Special attention is paid to the specific role of bulk to Rayleigh wave coupling, which may result in unexpected phenomena, such as a persistent time asymmetry in the diffuse regime.

  1. Crust and upper mantle shear wave structure of Northeast Algeria from Rayleigh wave dispersion analysis

    Radi, Zohir; Yelles-Chaouche, Abdelkrim; Corchete, Victor; Guettouche, Salim


    We resolve the crust and upper mantle structure beneath Northeast Algeria at depths of 0-400 km, using inversion of fundamental mode Rayleigh wave. Our data set consists of 490 earthquakes recorded between 2007 and 2014 by five permanent broadband seismic stations in the study area. Applying a combination of different filtering technics and inversion method shear wave velocities structure were determined as functions of depth. The resolved changes in Vs at 50 km depth are in perfect agreement with crustal thickness estimates, which reflect the study area's orogenic setting, partly overlying the collision zone between the African and Eurasian plates. The inferred Moho discontinuity depths are close to those estimated for other convergent areas. In addition, there is good agreement between our results and variations in orientations of regional seismic anisotropy. At depths of 80-180 km, negative Vs anomalies at station CBBR suggest the existence of a failed subduction slab.

  2. Attenuation of Rayleigh Surface Waves in a Porous Material



    Using acoustic microscopy at higher frequency,we show the velocity evolutions of surface acoustic waves,in particular Rayleigh waves that depend on porosity for a mesoporous silicon layer.The velocities are obtained from different V(z) curves,which are determined experimentally at a frequency of 600MHz.The analysis of V(z) data yields attenuation that is directly dependent on porosity.On the other hand,αN attenuation has been modeled and allows us to investigate its influence on the velocity VR of the propagation for Rayleigh waves.%Using acoustic microscopy at higher frequency, we show the velocity evolutions of surface acoustic waves, in particular Rayleigh waves that depend on porosity for a mesoporous silicon layer. The velocities are obtained from different V(z) curves, which are determined experimentally at a frequency of 600 MHz. The analysis of V(z) data yields attenuation that is directly dependent on porosity. On the other hand, αN attenuation has been modeled and allows us to investigate its influence on the velocity VR of the propagation for Rayleigh waves.

  3. Experimental study of ultrasonic beam sectors for energy conversion into Lamb waves and Rayleigh waves.

    Declercq, Nico Felicien


    When a bounded beam is incident on an immersed plate Lamb waves or Rayleigh waves can be generated. Because the amplitude of a bounded beam is not constant along its wave front, a specific beam profile is formed that influences the local efficiency of energy conversion of incident sound into Lamb waves or Rayleigh waves. Understanding this phenomenon is important for ultrasonic immersion experiments of objects because the quality of such experiments highly depends on the amount of energy transmitted into the object. This paper shows by means of experiments based on monochromatic Schlieren photography that the area within the bounded beam responsible for Lamb wave generation differs from that responsible for Rayleigh wave generation. Furthermore it provides experimental verification of an earlier numerical study concerning Rayleigh wave generation.

  4. Seismic metasurfaces: Sub-wavelength resonators and Rayleigh wave interaction

    Colquitt, D J; Craster, R V; Roux, P; Guenneau, S R L


    We consider the canonical problem of an array of rods, which act as resonators, placed on an elastic substrate; the substrate being either a thin elastic plate or an elastic half-space. In both cases the flexural plate, or Rayleigh surface, waves in the substrate interact with the resonators to create interesting effects such as effective band-gaps for surface waves or filters that transform surface waves into bulk waves; these effects have parallels in the field of optics where such sub-wavelength resonators create metamaterials, and metasurfaces, in the bulk and at the surface respectively. Here we carefully analyse this canonical problem by extracting the dispersion relations analytically thereby examining the influence of both the flexural and compressional resonances on the propagating wave. For an array of resonators atop an elastic half-space we augment the analysis with numerical simulations. Amongst other effects, we demonstrate the striking effect of a dispersion curve that transitions from Rayleigh...


    Rajneesh Kumar; Geeta Partap


    The propagation of waves in a homogeneous isotropic micropolar elastic cylindrical plate subjected to stress free conditions is investigated. The secular equations for symmetric and skew symmetric wave mode propagation are derived. At short wave limit,the secular equations for symmetric and skew symmetric waves in a stress free circular plate reduces to Rayleigh surface wave frequency equation. Thin plate results are also obtained. The amplitudes of displacements and microrotation components are obtained and depicted graphically. Some special cases are also deduced from the present investigations. The secular equations for symmetric and skew symmetric modes are also presented graphically.

  6. On Lamb and Rayleigh wave convergence in viscoelastic tissues

    Nenadic, Ivan Z; Urban, Matthew W; Aristizabal, Sara; Mitchell, Scott A; Humphrey, Tye C; Greenleaf, James F, E-mail: [Department of Biomedical Engineering, Mayo Clinic College of Medicine, Rochester, MN, 55905 (United States)


    Characterization of the viscoelastic material properties of soft tissue has become an important area of research over the last two decades. Our group has been investigating the feasibility of using a shear wave dispersion ultrasound vibrometry (SDUV) method to excite Lamb waves in organs with plate-like geometry to estimate the viscoelasticity of the medium of interest. The use of Lamb wave dispersion ultrasound vibrometry to quantify the mechanical properties of viscoelastic solids has previously been reported. Two organs, the heart wall and the spleen, can be readily modeled using plate-like geometries. The elasticity of these two organs is important because they change in pathological conditions. Diastolic dysfunction is the inability of the left ventricle (LV) of the heart to supply sufficient stroke volumes into the systemic circulation and is accompanied by the loss of compliance and stiffening of the LV myocardium. It has been shown that there is a correlation between high splenic stiffness in patients with chronic liver disease and strong correlation between spleen and liver stiffness. Here, we investigate the use of the SDUV method to quantify the viscoelasticity of the LV free-wall myocardium and spleen by exciting Rayleigh waves on the organ's surface and measuring the wave dispersion (change of wave velocity as a function of frequency) in the frequency range 40-500 Hz. An equation for Rayleigh wave dispersion due to cylindrical excitation was derived by modeling the excised myocardium and spleen with a homogenous Voigt material plate immersed in a nonviscous fluid. Boundary conditions and wave potential functions were solved for the surface wave velocity. Analytical and experimental convergence between the Lamb and Rayleigh waves is reported in a finite element model of a plate in a fluid of similar density, gelatin plate and excised porcine spleen and left-ventricular free-wall myocardium.

  7. On Lamb and Rayleigh wave convergence in viscoelastic tissues.

    Nenadic, Ivan Z; Urban, Matthew W; Aristizabal, Sara; Mitchell, Scott A; Humphrey, Tye C; Greenleaf, James F


    Characterization of the viscoelastic material properties of soft tissue has become an important area of research over the last two decades. Our group has been investigating the feasibility of using a shear wave dispersion ultrasound vibrometry (SDUV) method to excite Lamb waves in organs with plate-like geometry to estimate the viscoelasticity of the medium of interest. The use of Lamb wave dispersion ultrasound vibrometry to quantify the mechanical properties of viscoelastic solids has previously been reported. Two organs, the heart wall and the spleen, can be readily modeled using plate-like geometries. The elasticity of these two organs is important because they change in pathological conditions. Diastolic dysfunction is the inability of the left ventricle (LV) of the heart to supply sufficient stroke volumes into the systemic circulation and is accompanied by the loss of compliance and stiffening of the LV myocardium. It has been shown that there is a correlation between high splenic stiffness in patients with chronic liver disease and strong correlation between spleen and liver stiffness. Here, we investigate the use of the SDUV method to quantify the viscoelasticity of the LV free-wall myocardium and spleen by exciting Rayleigh waves on the organ's surface and measuring the wave dispersion (change of wave velocity as a function of frequency) in the frequency range 40–500 Hz. An equation for Rayleigh wave dispersion due to cylindrical excitation was derived by modeling the excised myocardium and spleen with a homogenous Voigt material plate immersed in a nonviscous fluid. Boundary conditions and wave potential functions were solved for the surface wave velocity. Analytical and experimental convergence between the Lamb and Rayleigh waves is reported in a finite element model of a plate in a fluid of similar density, gelatin plate and excised porcine spleen and left-ventricular free-wall myocardium.

  8. On Lamb and Rayleigh Wave Convergence in Viscoelastic Tissues

    Nenadic, Ivan Z.; Urban, Matthew W.; Aristizabal, Sara; Mitchell, Scott A.; Humphrey, Tye C.; Greenleaf, James F.


    Characterization of the viscoelastic material properties of soft tissue has become an important area of research over the last two decades. Our group has been investigating the feasibility of using Shearwave Dispersion Ultrasound Vibrometry (SDUV) method to excite Lamb waves in organs with plate-like geometry to estimate the viscoelasticity of the medium of interest. The use of Lamb wave Dispersion Ultrasound Vibrometry (LDUV) to quantify mechanical properties of viscoelastic solids has previously been reported. Two organs, the heart wall and the spleen, can be readily modeled using plate-like geometries. The elasticity of these two organs is important because they change in pathological conditions. Diastolic dysfunction is the inability of the left ventricle (LV) of the heart to supply sufficient stroke volumes into the systemic circulation and is accompanied by the loss of compliance and stiffening of the LV myocardium. It has been shown that there is a correlation between high splenic stiffness in patients with chronic liver disease and strong correlation between spleen and liver stiffness. Here, we investigate the use of the SDUV method to quantify viscoelasticity of the LV free-wall myocardium and spleen by exciting Rayleigh waves on the organ’s surface and measuring the wave dispersion (change of wave velocity as a function of frequency) in the frequency range 40–500 Hz. An equation for Rayleigh wave dispersion due to cylindrical excitation was derived by modeling the excised myocardium and spleen with a homogenous Voigt material plate immersed in a nonviscous fluid. Boundary conditions and wave potential functions were solved for the surface wave velocity. Analytical and experimental convergence between the Lamb and Rayleigh waves is reported in a finite element model of a plate in a fluid of similar density, gelatin plate and excised porcine spleen and left-ventricular free-wall myocardium. PMID:21970846

  9. Nonlinear mixing of laser generated narrowband Rayleigh surface waves

    Bakre, Chaitanya; Rajagopal, Prabhu; Balasubramaniam, Krishnan


    This research presents the nonlinear mixing technique of two co-directionally travelling Rayleigh surface waves generated and detected using laser ultrasonics. The optical generation of Rayleigh waves on the specimen is obtained by shadow mask method. In conventional nonlinear measurements, the inherently small higher harmonics are greatly influenced by the nonlinearities caused by coupling variabilities and surface roughness between the transducer and specimen interface. The proposed technique is completely contactless and it should be possible to eliminate this problem. Moreover, the nonlinear mixing phenomenon yields not only the second harmonics, but also the sum and difference frequency components, which can be used to measure the acoustic nonlinearity of the specimen. In this paper, we will be addressing the experimental configurations for this technique. The proposed technique is validated experimentally on Aluminum 7075 alloy specimen.

  10. Experimental and theoretical study of Rayleigh-Lamb wave propagation

    Rogers, Wayne P.; Datta, Subhendu K.; Ju, T. H.


    Many space structures, such as the Space Station Freedom, contain critical thin-walled components. The structural integrity of thin-walled plates and shells can be monitored effectively using acoustic emission and ultrasonic testing in the Rayleigh-Lamb wave frequency range. A new PVDF piezoelectric sensor has been developed that is well suited to remote, inservice nondestructive evaluation of space structures. In the present study the new sensor was used to investigate Rayleigh-Lamb wave propagation in a plate. The experimental apparatus consisted of a glass plate (2.3 m x 25.4 mm x 5.6 mm) with PVDF sensor (3 mm diam.) mounted at various positions along its length. A steel ball impact served as a simulated acoustic emission source, producing surface waves, shear waves and longitudinal waves with dominant frequencies between 1 kHz and 200 kHz. The experimental time domain wave-forms were compared with theoretical predictions of the wave propagation in the plate. The model uses an analytical solution for the Green's function and the measured response at a single position to predict response at any other position in the plate. Close agreement was found between the experimental and theoretical results.

  11. Analysis of group-velocity dispersion of high-frequency Rayleigh waves for near-surface applications

    Luo, Y.; Xia, J.; Xu, Y.; Zeng, C.


    The Multichannel Analysis of Surface Waves (MASW) method is an efficient tool to obtain the vertical shear (S)-wave velocity profile using the dispersive characteristic of Rayleigh waves. Most MASW researchers mainly apply Rayleigh-wave phase-velocity dispersion for S-wave velocity estimation with a few exceptions applying Rayleigh-wave group-velocity dispersion. Herein, we first compare sensitivities of fundamental surface-wave phase velocities with group velocities with three four-layer models including a low-velocity layer or a high-velocity layer. Then synthetic data are simulated by a finite difference method. Images of group-velocity dispersive energy of the synthetic data are generated using the Multiple Filter Analysis (MFA) method. Finally we invert a high-frequency surface-wave group-velocity dispersion curve of a real-world example. Results demonstrate that (1) the sensitivities of group velocities are higher than those of phase velocities and usable frequency ranges are wider than that of phase velocities, which is very helpful in improving inversion stability because for a stable inversion system, small changes in phase velocities do not result in a large fluctuation in inverted S-wave velocities; (2) group-velocity dispersive energy can be measured using single-trace data if Rayleigh-wave fundamental-mode energy is dominant, which suggests that the number of shots required in data acquisition can be dramatically reduced and the horizontal resolution can be greatly improved using analysis of group-velocity dispersion; and (3) the suspension logging results of the real-world example demonstrate that inversion of group velocities generated by the MFA method can successfully estimate near-surface S-wave velocities. ?? 2011 Elsevier B.V.

  12. Wave equation dispersion inversion using a difference approximation to the dispersion-curve misfit gradient

    Zhang, Zhendong


    We present a surface-wave inversion method that inverts for the S-wave velocity from the Rayleigh wave dispersion curve using a difference approximation to the gradient of the misfit function. We call this wave equation inversion of skeletonized surface waves because the skeletonized dispersion curve for the fundamental-mode Rayleigh wave is inverted using finite-difference solutions to the multi-dimensional elastic wave equation. The best match between the predicted and observed dispersion curves provides the optimal S-wave velocity model. Our method can invert for lateral velocity variations and also can mitigate the local minimum problem in full waveform inversion with a reasonable computation cost for simple models. Results with synthetic and field data illustrate the benefits and limitations of this method. © 2016 Elsevier B.V.

  13. Rayleigh scattering of a spherical sound wave.

    Godin, Oleg A


    Acoustic Green's functions for a homogeneous medium with an embedded spherical obstacle arise in analyses of scattering by objects on or near an interface, radiation by finite sources, sound attenuation in and scattering from clouds of suspended particles, etc. An exact solution of the problem of diffraction of a monochromatic spherical sound wave on a sphere is given by an infinite series involving products of Bessel functions and Legendre polynomials. In this paper, a simple, closed-form solution is obtained for scattering by a sphere with a radius that is small compared to the wavelength. Soft, hard, impedance, and fluid obstacles are considered. The solution is valid for arbitrary positions of the source and receiver relative to the scatterer. Low-frequency scattering is shown to be rather sensitive to boundary conditions on the surface of the obstacle. Low-frequency asymptotics of the scattered acoustic field are extended to transient incident waves. The asymptotic expansions admit an intuitive interpretation in terms of image sources and reduce to classical results in appropriate limiting cases.


    Lunarska, E.; Fiore, N.


    The attenuation of 2-6 MHz Rayleigh waves /RW/ was measured in sheet samples of Fe which were undergoing electrolytic charging with H. The cathodic polarization and As2O3 addition into electrolyte were found to effect the attenuation and velocity of the surface waves. The attenuation changes were retarded by the deposition of a thin /2µm/ layer of Cu on the Fe surface, with the Cu acting as a H-permeation barrier. The decrease in attenuation was caused by the entry of H into solid solution at...

  15. Selective Manipulation of Microscopic Particles with Precursor Swirling Rayleigh Waves

    Riaud, Antoine; Baudoin, Michael; Bou Matar, Olivier; Becerra, Loic; Thomas, Jean-Louis


    Contactless manipulation of microparticles is demonstrated with single-beam acoustical tweezers based on precursor swirling Rayleigh waves. These surface waves degenerate into acoustical vortices when crossing a stack made of a fluid layer and its solid support, hence creating a localized acoustical trap in a fluid cavity. They can be synthesized with a single interdigitated transducer whose spiraling shape encodes the phase of the field like a hologram. For applications, these tweezers have many attractive features: they are selective, flat, easily integrable, and compatible with disposable substrates.

  16. Rayleigh-Wave Group-Velocity Tomography of Saudi Arabia

    Tang, Zheng; Mai, P. Martin; Chang, Sung-Joon; Zahran, Hani


    We use surface-wave tomography to investigate the lithospheric structure of the Arabian plate, which is traditionally divided into the Arabian shield in the west and the Arabian platform in the east. The Arabian shield is a complicated mélange of crustal material, composed of several Proterozoic terrains separated by ophiolite-bearing suture zones and dotted by outcropping Cenozoic volcanic rocks. The Arabian platform is primarily covered by very thick Paleozoic, Mesozoic and Cenozoic sediments. We develop high-resolution tomographic images from fundamental-mode Rayleigh-wave group-velocities across Saudi Arabia, utilizing the teleseismic data recorded by the permanent Saudi National Seismic Network (SNSN). Our study extends previous efforts on surface wave work by increasing ray path density and improving spatial resolution. Good quality dispersion measurements for roughly 3000 Rayleigh-wave paths have been obtained and utilized for the group-velocity tomography. We have applied the Fast Marching Surface Tomography (FMST) scheme of Rawlinson (2005) to obtain Rayleigh-wave group-velocity images for periods from 8 s to 40 s on a 0.8° 0.8° grid and at resolutions approaching 2.5° based on the checkerboard tests. Our results indicate that short-period group-velocity maps (8-15 s) correlate well with surface geology, with slow velocities delineating the main sedimentary features including the Arabian platform, the Persian Gulf and Mesopotamia. For longer periods (20-40 s), the velocity contrast is due to the differences in crustal thickness and subduction/collision zones. The lower velocities are sensitive to the thicker continental crust beneath the eastern Arabia and the subduction/collision zones between the Arabian and Eurasian plate, while the higher velocities in the west infer mantle velocity.

  17. A trade-off between model resolution and variance with selected Rayleigh-wave data

    Xia, J.; Miller, R.D.; Xu, Y.


    Inversion of multimode surface-wave data is of increasing interest in the near-surface geophysics community. For a given near-surface geophysical problem, it is essential to understand how well the data, calculated according to a layered-earth model, might match the observed data. A data-resolution matrix is a function of the data kernel (determined by a geophysical model and a priori information applied to the problem), not the data. A data-resolution matrix of high-frequency (??? 2 Hz) Rayleigh-wave phase velocities, therefore, offers a quantitative tool for designing field surveys and predicting the match between calculated and observed data. First, we employed a data-resolution matrix to select data that would be well predicted and to explain advantages of incorporating higher modes in inversion. The resulting discussion using the data-resolution matrix provides insight into the process of inverting Rayleigh-wave phase velocities with higher mode data to estimate S-wave velocity structure. Discussion also suggested that each near-surface geophysical target can only be resolved using Rayleigh-wave phase velocities within specific frequency ranges, and higher mode data are normally more accurately predicted than fundamental mode data because of restrictions on the data kernel for the inversion system. Second, we obtained an optimal damping vector in a vicinity of an inverted model by the singular value decomposition of a trade-off function of model resolution and variance. In the end of the paper, we used a real-world example to demonstrate that selected data with the data-resolution matrix can provide better inversion results and to explain with the data-resolution matrix why incorporating higher mode data in inversion can provide better results. We also calculated model-resolution matrices of these examples to show the potential of increasing model resolution with selected surface-wave data. With the optimal damping vector, we can improve and assess an inverted

  18. Fast evaluation of the Rayleigh integral and applications to inverse acoustics

    Wind, J.W.; Wijnant, Y.H.; Boer, de A.


    In this paper we present a fast evaluation of the Rayleigh integral, which leads to fast and robust solutions in inverse acoustics. The method commonly used to reconstruct acoustic sources on a plane in space is Planar Nearfield Acoustic Holography (PNAH). Some of the most important recent improveme

  19. S-wave velocity structure in the Nankai accretionary prism derived from Rayleigh admittance

    Tonegawa, Takashi; Araki, Eiichiro; Kimura, Toshinori; Nakamura, Takeshi; Nakano, Masaru; Suzuki, Kensuke


    Two cabled seafloor networks with 22 and 29 stations (DONET 1 and 2: Dense Oceanfloor Network System for Earthquake and Tsunamis) have been constructed on the accretionary prism at the Nankai subduction zone of Japan since March 2010. The observation periods of DONET 1 and 2 exceed more than 5 years and 10 months, respectively. Each station contains broadband seismometers and absolute and differential pressure gauges. In this study, using Rayleigh waves of microseisms and earthquakes, we calculate the Rayleigh admittance (Ruan et al., 2014, JGR) at the seafloor for each station, i.e., an amplitude transfer function from pressure to displacement, particularly for the frequencies of 0.1-0.2 Hz (ambient noise) and 0.04-0.1 Hz (earthquake signal), and estimate S-wave velocity (Vs) structure beneath stations in DONET 1 and 2. We calculated the displacement seismogram by removing the instrument response from the velocity seismogram for each station. The pressure record observed at the differential pressure gauge was used in this study because of a high resolution of the pressure observation. In addition to Rayleigh waves of microseisms, we collected waveforms of Rayleigh waves for earthquakes with an epicentral distance of 15-90°, M>5.0, and focal depth shallower than 50 km. In the frequency domain, we smoothed the transfer function of displacement/pressure with the Parzen window of ±0.01 Hz. In order to determine one-dimensional Vs profiles, we performed a nonlinear inversion technique, i.e., simulated annealing. As a result, Vs profiles obtained at stations near the land show simple Vs structure, i.e., Vs increases with depth. However, some profiles located at the toe of the acceretionary prism have a low-velocity zone (LVZ) at a depth of 5-7 km within the accretinary sediment. The velocity reduction is approximately 5-20 %. Park et al. (2010) reported such a large reduction in P-wave velocity in the region of DONET 1 (eastern network and southeast of the Kii

  20. Field-Correlation Effects on Rayleigh-Enhanced Nondegenerate Four-Wave Mixing

    王延帮; 姜谦; 米辛; 俞祖和; 傅盘铭


    We study Rayleigh-enhanced nondegenerate four-wave mixing (NFWM) with time-delayed, correlated fluctuating fields. The importance of the field correlation is revealed in the Rayleigh-enhanced NFWM spectrum when the time delay is varied. The Rayleigh-enhanced NFWM is employed to study the ultrafast processes in the frequency domain. A relaxation time as short as 220 fs was deduced in the Rayleigh-enhanced NFWM experiments in carbon disulphide.

  1. Rayleigh Wave Tomography of Mid-Continent Rift (MCR) using Earthquake and Ambient Noise Data

    Aleqabi, G. I.; Wiens, D.; Wysession, M. E.; Shen, W.; van der Lee, S.; Revenaugh, J.; Frederiksen, A. W.; Darbyshire, F. A.; Stein, S. A.; Jurdy, D. M.; Wolin, E.; Bollmann, T. A.


    The structure of the North American Mid-Continent Rift Zone (MCRZ) is examined using Rayleigh waves from teleseismic earthquakes and ambient seismic noise recorded by the Superior Province Rifting EarthScope Experiment (SPREE). Eighty-four broadband seismometers were deployed during 2011-2013 in Minnesota and Wisconsin, USA, and Ontario, CA, along three lines; two across the rift axis and the third along the rift axis. These stations, together with the EarthScope Transportable Array, provided excellent coverage of the MCRZ. The 1.1 Ga Mesoproterozoic failed rift consists of two arms, buried under post-rifting sedimentary formations that meet at Lake Superior. We compare two array-based tomography methods using teleseismic fundamental mode Rayleigh waves phase and amplitude measurements: the two-plane wave method (TPWM, Forsyth, 1998) and the automated surface wave phase velocity measuring system (ASWMS, Jin and Gaherty, 2015). Both array methods and the ambient noise method give relatively similar results showing low velocity zones extending along the MCRZ arms. The teleseismic Rayleigh wave results from 18 - 180 s period are combined with short period phase velocity results (period 8-30 s) obtained from ambient noise by cross correlation. Phase velocities from the methods are very similar at periods of 18-30 where results overlap; in this period range we use the average of the noise and teleseismic results. Finally the combined phase velocity curve is inverted using a Monte-Carlo inversion method at each geographic point in the model. The results show low velocities at shallow depths (5-10 km) that are the result of very deep sedimentary fill within the MCRZ. Deeper-seated low velocity regions may correspond to mafic underplating of the rift zone.

  2. Wave fields and spectra of Rayleigh waves in poroelastic media in the exploration seismic frequency band

    Zhang, Yu; Xu, Yixian; Xia, Jianghai


    A better understanding of the influences of different surface fluid drainage conditions on the propagation and attenuation of surface waves as the stipulated frequency is varied is a key issue to apply surface wave method to detect subsurface hydrological properties. Our study develops three-dimensional dynamical Green's functions in poroelastic media for Rayleigh waves of possible free surface conditions: permeable - "open pore," impermeable - "closed pore," and partially permeable boundaries. The full transient response of wave fields and spectra due to a stress impulse wavelet on the surface are investigated in the exploration seismic frequency band for typical surface drainage conditions, viscous coupling-damping, solid frame properties and porous fluid flowing configuration. Our numerical results show that, due to the slow dilatational wave - P2 wave, two types of Rayleigh waves, designated as R1 and R2 waves, exist along the surface. R1 wave possesses high energy as classic Rayleigh waves in pure elastic media for each porous materials. A surface fluid drainage condition is a significant factor to influence dispersion and attenuation, especially attenuation of R1 waves. R2 wave for closed pore and partially permeable surfaces is only observed for a low coupling-damping coefficient. The non-physical wave for partially surface conditions causes the R1 wave radiates into the R2 wave in the negative attenuation frequency range. It makes weaker R1 wave and stronger R2 wave to closed pore surface. Moreover, it is observed that wave fields and spectra of R1 wave are sensitive to frame elastic moduli change for an open pore surface, and to pore fluid flow condition change for closed pore and partially permeable surface.

  3. The uppermost crust structure of Ischia (southern Italy) from ambient noise Rayleigh waves

    Strollo, R.; Nunziata, C.; Iannotta, A.; Iannotta, D.


    Ambient noise measurements were performed at the island of Ischia (southern Italy) along alignments of 2.4-7 km by using two three-component seismic stations. Synchronous noise recordings of 2-20 h were cross-correlated over 20-30 s windows, stacked and iteratively band-pass filtered to enhance the dispersive wave trains. Frequency time analysis was performed on the vertical and radial components of cross-correlations and the fundamental-mode Rayleigh wave group velocity was obtained. Validation of the dispersion data was possible with those obtained from an earthquake recording along a close path. The non-linear inversion of average Rayleigh wave group velocity dispersion curves along 13 paths (receiver inter-distances) allowed the definition of shear wave velocity models in the uppermost 1-2 km of the crust. The correlation of VS profiles vs. depth and drilling stratigraphy allowed to attribute VS lower than 1 km/s to tuffs and VS of 1.41 km/s to very fractured lavas. Higher VS are found in the central area of the island, in correspondence of the resurgent area. The top of the trachytic lava basement, with VS of 2.2-2.4 km/s and density of 2.3 g/cm3 is about 0.6-0.7 km deep b.s.l. in the centre of Ischia, below altered, very fractured lava or thermally altered tuff.

  4. Sensitivity comparisons of layered Rayleigh wave and Love wave acoustic devices

    Pedrick, Michael K.; Tittmann, Bernhard R.


    Due to their high sensitivity, layered Surface Acoustic Wave (SAW) devices are ideal for various film characterization and sensor applications. Two prominent wave types realized in these devices are Rayleigh waves consisting of coupled Shear Vertical and Longitudinal displacements and Love waves consisting of Shear Horizontal displacements. Theoretical calculations of sensitivity of SAW devices to pertubations in wave propagation are limited to idealized scenarios. Derivations of sensitivity to mass change in an overlayer are often based on the effect of rigid body motion of the overlayer on the propagation of one of the aforementioned wave types. These devices often utilize polymer overlayers for enhanced sensitivity. The low moduli of such overlayers are not sufficiently stiff to accommodate the rigid body motion assumption. This work presents device modeling based on the Finite Element Method. A coupled-field model allows for a complete description of device operation including displacement profiles, frequency, wave velocity, and insertion loss through the inclusion of transmitting and receiving IDTs. Geometric rotations and coordinate transformations allow for the modeling of different crystal orientations in piezoelectric substrates. The generation of Rayleigh and Love Wave propagation was realized with this model by examining propagation in ST Quartz both normal to and in the direction of the X axis known to support Love Waves and Rayleigh Waves, respectively. Sensitivities of layered SAW devices to pertubations in mass, layer thickness, and mechanical property changes of a Polymethyl methacrylate (PMMA) and SU-8 overlayers were characterized and compared. Experimental validation of these models is presented.

  5. Estimation of elastic moduli in a compressible Gibson half-space by inverting Rayleigh-wave phase velocity

    Xia, J.; Xu, Y.; Miller, R.D.; Chen, C.


    A Gibson half-space model (a non-layered Earth model) has the shear modulus varying linearly with depth in an inhomogeneous elastic half-space. In a half-space of sedimentary granular soil under a geostatic state of initial stress, the density and the Poisson's ratio do not vary considerably with depth. In such an Earth body, the dynamic shear modulus is the parameter that mainly affects the dispersion of propagating waves. We have estimated shear-wave velocities in the compressible Gibson half-space by inverting Rayleigh-wave phase velocities. An analytical dispersion law of Rayleigh-type waves in a compressible Gibson half-space is given in an algebraic form, which makes our inversion process extremely simple and fast. The convergence of the weighted damping solution is guaranteed through selection of the damping factor using the Levenberg-Marquardt method. Calculation efficiency is achieved by reconstructing a weighted damping solution using singular value decomposition techniques. The main advantage of this algorithm is that only three parameters define the compressible Gibson half-space model. Theoretically, to determine the model by the inversion, only three Rayleigh-wave phase velocities at different frequencies are required. This is useful in practice where Rayleigh-wave energy is only developed in a limited frequency range or at certain frequencies as data acquired at manmade structures such as dams and levees. Two real examples are presented and verified by borehole S-wave velocity measurements. The results of these real examples are also compared with the results of the layered-Earth model. ?? Springer 2006.

  6. Rayleigh-type waves in nonlocal micropolar solid half-space.

    Khurana, Aarti; Tomar, S K


    Propagation of Rayleigh type surface waves in nonlocal micropolar elastic solid half-space has been investigated. Two modes of Rayleigh-type waves are found to propagate under certain approximations. Frequency equations of these Rayleigh type modes and their conditions of existence have been derived. These frequency equations are found to be dispersive in character due to the presence of micropolarity and nonlocality parameters in the medium. One of the frequency equations is a counterpart of the classical Rayleigh waves and the other is new and has appeared due to micropolarity of the medium. Phase speeds of these waves are computed numerically for Magnesium crystal and their variation against wavenumber are presented graphically. Comparisons have been made between the phase speeds of Rayleigh type waves through nonlocal micropolar, local micropolar and elastic solid half-spaces. Copyright © 2016 Elsevier B.V. All rights reserved.

  7. Waveform inversion of mantle Love waves: The born seismogram approach

    Tanimoto, T.


    Normal mode theory, extended to the slightly laterally heterogeneous Earth by the first-order Born approximation, is applied to the waveform inversion of mantle Love waves (200-500 sec) for the Earth's lateral heterogeneity at l=2 and a spherically symmetric anelasticity (Q sub mu) structure. The data are from the Global Digital Seismograph Network (GDSN). The l=2 pattern is very similar to the results of other studies that used either different methods, such as phase velocity measurements and multiplet location measurements, or a different data set, such as mantle Rayleigh waves from different instruments. The results are carefully analyzed for variance reduction and are most naturally explained by heterogeneity in the upper 420 km. Because of the poor resolution of the data set for the deep interior, however, a fairly large heterogeneity in the transition zones, of the order of up to 3.5% in shear wave velocity, is allowed. It is noteworthy that Love waves of this period range can not constrain the structure below 420 km and thus any model presented by similar studies below this depth are likely to be constrained by Rayleigh waves (spheroidal modes) only.

  8. Waveform inversion of mantle Love waves - The Born seismogram approach

    Tanimoto, T.


    Normal mode theory, extended to the slightly laterally heterogeneous earth by the first-order Born approximation, is applied to the waveform inversion of mantle Love waves (200-500 sec) for the earth's lateral heterogeneity at l = 2 and a spherically symmetric anelasticity (Q sub mu) structure. The data are from the Global Digital Seismograph Network (GDSN). The l = 2 pattern is very similar to the results of other studies that used either different methods, such as phase velocity measurements and multiplet location measurements, or a different data set, such as mantle Rayleigh waves from different instruments. The results are carefully analyzed for variance reduction and are most naturally explained by heterogeneity in the upper 420 km. Because of the poor resolution of the data set for the deep interior, however, a fairly large heterogeneity in the transition zones, of the order of up to 3.5 percent in shear wave velocity, is allowed. It is noteworthy that Love waves of this period range can not constrain the structure below 420 km and thus any model presented by similar studies below this depth are likely to be constrained by Rayleigh waves (spheroidal modes) only.

  9. Coexisting Raman- and Rayleigh-Enhanced Four-Wave Mixing in Femtosecond Polarization Beats

    NIE Zhi-Qiang; ZHAO Yan; ZHANG Yan-Peng; GAN Chen-Li; ZHENG Huai-Sin; LI Chang-Biao; LU Ke-Qing


    Based on the polarization interference of Raman- and Rayleigh-enhanced four-wave mixing processes,heterodyne detection of the Raman,Rayleigh and coexisting Raman and Rayleigh femtosecond difference-frequency polarization beats is investigated in the cw and the three Markovian stochastic models,respectively.These two processes exhibit asymmetric and symmetric spectra,respectively,and the thermal effect in them can be suppressed by a field-correlation method.Such studies of coexisting Raman- and Rayleigh-enhanced four-wave mixing processes can have important applications in coherence quantum control,and quantum information processing.

  10. Pushing the upper limit of Rayleigh-scatter Temperatures Retrievals into the Lower Thermosphere Using an Inversion Approach

    Bandoro, J.; Sica, R. J.; Argall, S.


    An important aspect of solar terrestrial relations is the coupling between the lower and upper atmosphere-ionosphere system. The coupling is evident in the general circulation of the atmosphere, where waves generate in the lower atmosphere play an important role in the dynamics of the upper atmosphere, which feeds back on the lower atmosphere's circulation. To address coupling problems requires measurements over the broadest range of heights possible. A recently developed retrieval method for temperature profiles from Rayleigh-scatter lidar measurements using an inversion approach allows the upward extension of the altitude range of temperature by 10 to 15 km over the conventional method, thus producing the equivalent of increasing the systems power-aperture product by 4 times [1]. The method requires no changes to the lidar's hardware and thus, can be applied to the body of existing measurements. In addition, since the uncertainties of the retrieved temperature profile are found by a Monte Carlo error analysis, it is possible to isolate systematic and random uncertainties to model the effect of each one on the final uncertainty product for the temperature profile. This unambiguous separation of uncertainties was not previously possible as only the propagation of the statistical uncertainties are typically reported. For the Purple Crow Lidar, corrections for saturation (e.g. non-linearity) in the photocount returns, ozone extinction and background removal all contribute to the overall systematic uncertainty. Results of individually varying each systematic correction and the effect on the final temperature uncertainty through Monte Carlo realizations are presented to determine the importance for each one. For example, it was found that treatment of the background correction as a systematic versus statistical uncertainty gave results in agreement with each other. This new method is then applied to measurements obtained by the Purple Crow lidar' Rayleigh

  11. Spectral Ratios for Crack Detection Using P and Rayleigh Waves

    Enrique Olivera-Villaseñor


    Full Text Available We obtain numerical results to help the detection and characterization of subsurface cracks in solids by the application of P and Rayleigh elastic waves. The response is obtained from boundary integral equations, which belongs to the field of elastodynamics. Once the implementation of the boundary conditions has been done, a system of Fredholm integral equations of the second kind and order zero is found. This system is solved using the method of Gaussian elimination. Resonance peaks in the frequency domain allow us to infer the presence of cracks using spectral ratios. Several models of cracked media were analyzed, where effects due to different crack orientations and locations were observed. The results obtained are in good agreement with those published in the references.

  12. Wave-equation dispersion inversion of surface waves recorded on irregular topography

    Li, Jing


    Significant topographic variations will strongly influence the amplitudes and phases of propagating surface waves. Such effects should be taken into account, otherwise the S-velocity model inverted from the Rayleigh dispersion curves will contain significant inaccuracies. We now show that the recently developed wave-equation dispersion inversion (WD) method naturally takes into account the effects of topography to give accurate S-velocity tomograms. Application of topographic WD to demonstrates that WD can accurately invert dispersion curves from seismic data recorded over variable topography. We also apply this method to field data recorded on the crest of mountainous terrain and find with higher resolution than the standard WD tomogram.

  13. Quasi-Rayleigh waves in butt-welded thick steel plate

    Kamas, Tuncay; Giurgiutiu, Victor; Lin, Bin


    This paper discusses theoretical and experimental analyses of weld guided surface acoustic waves (SAW) through the guided wave propagation (GWP) analyses. The GWP analyses have been carried out by utilizing piezoelectric wafer active sensors (PWAS) for in situ structural inspection of a thick steel plate with butt weld as the weld bead is ground flush. Ultrasonic techniques are commonly used for validation of welded structures in many in-situ monitoring applications, e.g. in off-shore structures, in nuclear and pressure vessel industries and in a range of naval applications. PWAS is recently employed in such ultrasonic applications as a resonator as well as a transducer. Quasi-Rayleigh waves a.k.a. SAW can be generated in relatively thick isotropic elastic plate having the same phase velocity as Rayleigh waves whereas Rayleigh waves are a high frequency approximation of the first symmetric (S0) and anti-symmetric (A0) Lamb wave modes. As the frequency becomes very high the S0 and the A0 wave speeds coalesce, and both have the same value. This value is exactly the Rayleigh wave speed and becomes constant along the frequency i.e. Rayleigh waves are non-dispersive guided surface acoustic waves. The study is followed with weld-GWP tests through the pitch-catch method along the butt weld line. The tuning curves of quasi-Rayleigh wave are determined to show the tuning and trapping effect of the weld bead that has higher thickness than the adjacent plates on producing a dominant quasi-Rayleigh wave mode. The significant usage of the weld tuned and guided quasi-Rayleigh wave mode is essentially discussed for the applications in the in-situ inspection of relatively thick structures with butt weld such as naval offshore structures. The paper ends with summary, conclusions and suggestions for future work.

  14. Quasi-Rayleigh waves in butt-welded thick steel plate

    Kamas, Tuncay, E-mail:, E-mail:, E-mail:; Giurgiutiu, Victor, E-mail:, E-mail:, E-mail:; Lin, Bin, E-mail:, E-mail:, E-mail: [Mechanical Engineering University of South Carolina, 300 Main Str., Columbia, SC 29208 (United States)


    This paper discusses theoretical and experimental analyses of weld guided surface acoustic waves (SAW) through the guided wave propagation (GWP) analyses. The GWP analyses have been carried out by utilizing piezoelectric wafer active sensors (PWAS) for in situ structural inspection of a thick steel plate with butt weld as the weld bead is ground flush. Ultrasonic techniques are commonly used for validation of welded structures in many in-situ monitoring applications, e.g. in off-shore structures, in nuclear and pressure vessel industries and in a range of naval applications. PWAS is recently employed in such ultrasonic applications as a resonator as well as a transducer. Quasi-Rayleigh waves a.k.a. SAW can be generated in relatively thick isotropic elastic plate having the same phase velocity as Rayleigh waves whereas Rayleigh waves are a high frequency approximation of the first symmetric (S0) and anti-symmetric (A0) Lamb wave modes. As the frequency becomes very high the S0 and the A0 wave speeds coalesce, and both have the same value. This value is exactly the Rayleigh wave speed and becomes constant along the frequency i.e. Rayleigh waves are non-dispersive guided surface acoustic waves. The study is followed with weld-GWP tests through the pitch-catch method along the butt weld line. The tuning curves of quasi-Rayleigh wave are determined to show the tuning and trapping effect of the weld bead that has higher thickness than the adjacent plates on producing a dominant quasi-Rayleigh wave mode. The significant usage of the weld tuned and guided quasi-Rayleigh wave mode is essentially discussed for the applications in the in-situ inspection of relatively thick structures with butt weld such as naval offshore structures. The paper ends with summary, conclusions and suggestions for future work.

  15. Ellipticity of Rayleigh waves in basin and hard-rock sites in Northern Italy

    Berbellini, Andrea; Morelli, Andrea; Ferreira, Ana M. G.


    We measure ellipticity of teleseismic Rayleigh waves at 95 seismic stations in Northern Italy, for wave period between 10 and 110 s, using an automatic technique and a large volume of high-quality seismic recordings from over 500 global earthquakes that occurred in 2008-2014. Northern Italy includes a wide range of crustal structures, from the wide and deep Po Plain sedimentary basin to outcropping sedimentary and crystalline rocks in the Northern Apennines and Alps. It thus provides an excellent case for studying the influence of shallow earth structure on polarization of surface waves. The ellipticity measurements show excellent spatial correlation with geological features in the region, such as high ellipticity associated with regions of low seismic velocity in the Po Plain and low ellipticity values in faster, hard rock regions in the Alps and Apennine mountains. Moreover, the observed ellipticity values also relate to the thickness of the basement, as highlighted by observed differences beneath the Alps and the Apennines. Comparison between observations and predicted ellipticity from a reference crustal model of the region show substantial fit, particularly for T ˜ 38 s data. Discrepancy for shorter wave period suggests that slight modifications of the model are needed, and that the ellipticity measurements could help to better constrain the shallow crustal structure of the region. Predictions for the Po Plain are larger than the observations by a factor of four or more and transition from retrograde to prograde Rayleigh wave motion at the surface for periods of T ˜ 10-13 s is predicted for seismic stations in the plain. Analysis of corresponding real data indicates a possible detection of teleseismic prograde particle motion, but the weak teleseismic earthquake signals are mixed with ambient noise signals at the predicted, short, transition periods. Detection of the period of polarity inversion from the joint analysis of earthquake and ambient noise

  16. Full Dynamic Compound Inverse Method: Extension to General and Rayleigh damping

    Pioldi, Fabio; Rizzi, Egidio


    The present paper takes from the original output-only identification approach named Full Dynamic Compound Inverse Method (FDCIM), recently published on this journal by the authors, and proposes an innovative, much enhanced version, in the description of more general forms of structural damping, including for classically adopted Rayleigh damping. This has led to an extended FDCIM formulation, which offers superior performance, on all the targeted identification parameters, namely: modal properties, Rayleigh damping coefficients, structural features at the element-level and input seismic excitation time history. Synthetic earthquake-induced structural response signals are adopted as input channels for the FDCIM approach, towards comparison and validation. The identification algorithm is run first on a benchmark 3-storey shear-type frame, and then on a realistic 10-storey frame, also by considering noise added to the response signals. Consistency of the identification results is demonstrated, with definite superiority of this latter FDCIM proposal.

  17. Full Dynamic Compound Inverse Method: Extension to General and Rayleigh damping

    Pioldi, Fabio; Rizzi, Egidio


    The present paper takes from the original output-only identification approach named Full Dynamic Compound Inverse Method (FDCIM), recently published on this journal by the authors, and proposes an innovative, much enhanced version, in the description of more general forms of structural damping, including for classically adopted Rayleigh damping. This has led to an extended FDCIM formulation, which offers superior performance, on all the targeted identification parameters, namely: modal properties, Rayleigh damping coefficients, structural features at the element-level and input seismic excitation time history. Synthetic earthquake-induced structural response signals are adopted as input channels for the FDCIM approach, towards comparison and validation. The identification algorithm is run first on a benchmark 3-storey shear-type frame, and then on a realistic 10-storey frame, also by considering noise added to the response signals. Consistency of the identification results is demonstrated, with definite superiority of this latter FDCIM proposal.

  18. A new algorithm for three-dimensional joint inversion of body wave and surface wave data and its application to the Southern California plate boundary region

    Fang, Hongjian; Zhang, Haijiang; Yao, Huajian; Allam, Amir; Zigone, Dimitri; Ben-Zion, Yehuda; Thurber, Clifford; van der Hilst, Robert D.


    We introduce a new algorithm for joint inversion of body wave and surface wave data to get better 3-D P wave (Vp) and S wave (Vs) velocity models by taking advantage of the complementary strengths of each data set. Our joint inversion algorithm uses a one-step inversion of surface wave traveltime measurements at different periods for 3-D Vs and Vp models without constructing the intermediate phase or group velocity maps. This allows a more straightforward modeling of surface wave traveltime data with the body wave arrival times. We take into consideration the sensitivity of surface wave data with respect to Vp in addition to its large sensitivity to Vs, which means both models are constrained by two different data types. The method is applied to determine 3-D crustal Vp and Vs models using body wave and Rayleigh wave data in the Southern California plate boundary region, which has previously been studied with both double-difference tomography method using body wave arrival times and ambient noise tomography method with Rayleigh and Love wave group velocity dispersion measurements. Our approach creates self-consistent and unique models with no prominent gaps, with Rayleigh wave data resolving shallow and large-scale features and body wave data constraining relatively deeper structures where their ray coverage is good. The velocity model from the joint inversion is consistent with local geological structures and produces better fits to observed seismic waveforms than the current Southern California Earthquake Center (SCEC) model.

  19. Rayleigh Waves in a Rotating Orthotropic Micropolar Elastic Solid Half-Space

    Baljeet Singh


    Full Text Available A problem on Rayleigh wave in a rotating half-space of an orthotropic micropolar material is considered. The governing equations are solved for surface wave solutions in the half space of the material. These solutions satisfy the boundary conditions at free surface of the half-space to obtain the frequency equation of the Rayleigh wave. For numerical purpose, the frequency equation is approximated. The nondimensional speed of Rayleigh wave is computed and shown graphically versus nondimensional frequency and rotation-frequency ratio for both orthotropic micropolar elastic and isotropic micropolar elastic cases. The numerical results show the effects of rotation, orthotropy, and nondimensional frequency on the nondimensional speed of the Rayleigh wave.

  20. Inversion of multimode Rayleigh-wave dispersion curves of soft interlayer based on Bayesian theory%基于贝叶斯理论的软夹层多模式瑞雷波频散曲线反演研究

    付代光; 刘江平; 周黎明; 徐浩; 廖锦芳; 陈松; 郭道龙


    获得较高精度的软夹层横波速度和厚度是瑞雷波频散曲线反演的难点之一,尤其对一些低敏感性的软夹层而言,单纯依靠传统的算法改进以及多模式反演,反演效果往往不是非常显著。首次尝试采用算法改进、多模式及非线性贝叶斯定理相结合反演低敏感性软夹层。算法改进体现在,将阻尼惯性权和混沌思想融入到粒子群算法中,但改进算法并未解决软夹层模型低敏感性的困扰;为从反演解的角度分析评价影响反演精度因素,采用无偏Metropolis-Hastings sampling(MHS)方法对后验概率进行数值积分,并通过参数旋转提高采用效率,积分得到的1D和混合边缘概率分布以及参数相关系数矩阵等参数反应了反演解的不确定性和参数间相关性等信息。为解决低敏感性反演精度低问题,尝试采用贝叶斯信息准则(BIC),判断出最佳参数化模型,而此准则得到的最佳模型与理论模型更为吻合。应用非线性贝叶斯方法和BIC准则反演实测防渗墙数据,得到的反演剖面也与已知防渗墙结构较好吻合。%Obtaining shear-wave velocity and thickness of soft interlayer with higher precision is always one of the difficulties in inversion of Rayleigh-wave dispersion curve, and it is not obviously improved when only depending on the improved algorithm and multimode inversion for low-sensitivity soft interlayer. The improved algorithm and combination of multimode and nonlinear Bayes' theorem are adopted to invert low-sensitivity soft interlayer. The damping inertia weight and chaos are added into the particle swarm optimization as improved algorithm. However, the improved algorithm does not solve the problem with low-sensitivity soft interlayer models. To analyze and evaluate the factors affecting the accuracy of inversion from the perspective of the inversion solution, the unbiased Metropolis-Hastings sampling (MHS) method

  1. Rayleigh wave group velocity tomography of Gujarat region, Western India and its implications to mantle dynamics

    de Lorenzo, Salvatore; Michele, Maddalena; Emolo, Antonio; Tallarico, Andrea


    In the present study, fundamental Rayleigh waves with varying period from 10 to 80 s are used to obtain group velocity maps in the northwest Deccan Volcanic Province of India. About 350 paths are obtained using 53 earthquakes (4.8 ≤ M ≥ 7.9) recorded by the SeisNetG (Seismic Network of Gujarat). Individual dispersion curves of group velocity of Rayleigh wave for each source-station path are estimated using multiple filter technique. These curves are used to determine lateral distribution of Rayleigh wave group velocity by tomographic inversion method. Our estimated Rayleigh group velocity at varying depths showed conspicuous corroboration with three tectonic blocks [Kachchh Rift Basin (KRB), Saurashtra Horst (SH), and Mainland Gujarat (MG)] in the region. The seismically active KRB with a thicker crust is characterized as a low velocity zone at a period varying from 10 to 30 s as indicative of mantle downwarping or sagging of the mantle beneath the KRB, while the SH and MG are found to be associated with higher group velocities, indicating the existence of the reduced crustal thickness. The trend of higher group velocity was found prevailed adjacent to the Narmada and Cambay rift basins that also correspond to the reduced crust, suggesting the processes of mantle upwarping or uplifting due to mantle upwelling. The low velocities at periods longer than 40 s beneath the KRB indicate thicker lithosphere. The known Moho depth correlates well with the observed velocities at a period of about 30 s in the Gujarat region. Our estimates of relatively lower group velocities at periods varying from 70 to 80 s may correspond to the asthenospheric flow beneath the region. It is interesting to image higher group velocity for the thinner crust beneath the Arabian Sea adjacent to the west coast of Gujarat at the period of 40 s that may correspond to the upwarped or upwelled mantle beneath the Arabian Sea. Our results have better resolution estimated by a radius of equivalent

  2. Crustal structure below Popocat\\'epetl Volcano (Mexico) from analysis of Rayleigh waves

    De Barros, Louis; Métaxian, J -P; Valdés-Gonzales, C; Lesage, Philippe


    An array of ten broadband stations was installed on the Popocat\\'epetl volcano (Mexico) for five months between October 2002 and February 2003. 26 regional and teleseismic earthquakes were selected and filtered in the frequency time domain to extract the fundamental mode of the Rayleigh wave. The average dispersion curve was obtained in two steps. Firstly, phase velocities were measured in the period range [2-50] s from the phase difference between pairs of stations, using Wiener filtering. Secondly, the average dispersion curve was calculated by combining observations from all events in order to reduce diffraction effects. The inversion of the mean phase velocity yielded a crustal model for the volcano which is consistent with previous models of the Mexican Volcanic Belt. The overall crustal structure beneath Popocat\\'epetl is therefore not different from the surrounding area, and the velocities in the lower crust are confirmed to be relatively low. Lateral variations of the structure were also investigated ...

  3. Effects on PP waves and Rayleigh waves of water column approximation

    Zhou, Y.; Ni, S.


    Spectral-element method (SEM) combines the flexibility of the finite-element method and the accuracy of the pseudo-spectral method. It can handle the complexity of the 3-D earth model, such as heterogeneity of velocity and density, anisotropy, anelasticity, sharp velocity and density contrasts, topography. And with water column approximation, it can also deal with oceans. Because of its powerful ability, there are a wide range of application of SEM in studies of PP waves and Rayleigh waves. PP wave and its precursors have been used in measuring topography of 410 km or 660 km. Rayleigh waves are the most recognizable part of the seismograms and have been broadly applied in crustal and uppermost mantle tomography. In global SEM simulation, oceans are usually assumed to be incompressible, which means that the entire water column moves as a whole as a result of the normal displacement of the seafloor. It is necessary to investigate the accuracy of water column approximation when thickness of ocean approaches wavelength of the wave in the ocean water. In this paper, based on plane wave assumption, we study both the accurate form and water column approximate form of effective boundary condition. The reflection coefficient equation of PP waves with effective boundary of water was derived. Accurate and approximate PP reflection coefficient with oceans in different depth is demonstrated. The formula of Rayleigh wave phase velocity dispersion with effective water boundary is also investigated. It is shown that water column approximation in global SEM simulation is not sufficient for some parts of the ocean.

  4. Empirical evidence of Rayleigh waves in Norcia (central Italy) and their quantitative contribution to ground motion

    Caffagni, Enrico; Cattaneo, Marco; Bordoni, Paola


    Spectral ratio techniques, such as the Horizontal-to-Vertical (HV) and Standard (SSR) may exhibit different trends in specific frequency bands when conducted in alluvial basins. A possible explanation of this discrepancy can be provided by the presence of Rayleigh oscillations, that are considered responsible of an amplification of the vertical component with respect to the horizontal. We propose a new methodology for the identification of Rayleigh waves arrivals, to test on small-size basins. With this procedure, candidate Rayleigh waves are localized in time-frequency domain on an instantaneous polarization plane which is constructed by defining the instantaneous maximum vertical and horizontal spectral amplitudes. Validation of the candidate Rayleigh arrivals is performed by evaluating the instantaneous ellipticity. This step yields to a quantitative measure of the polarization, providing an indicator of the Rayleigh contribution to ground motion. We tested this methodology in the Norcia basin (central Italy) using a 18 selected earthquakes (2.0 L'Aquila sequence (2009). We demonstrate the robustness of our methodology by localizing evidences of Rayleigh wave arrivals immediately from (1 s) up to 30 s after the first S-wave group, even for low-magnitude events (Ml < 3.0). The generation of the detected Rayleigh waves analyzed in time-frequency range, appears to be magnitude-dependent and in function of the location in the basin. Our quantitative estimate of the Rayleigh polarization resulted to be comparable to the HV response value in specific frequency bands, for example in deamplification, demonstrating a plausible connection with Rayleigh oscillations. The authors encourage the usage or implementation of similar procedures conducted in basin studies, in order to determine quantitatively the Rayleigh contribution to ground motion, for a better characterization of the local seismic response.

  5. Interval Estimation of Stress-Strength Reliability Based on Lower Record Values from Inverse Rayleigh Distribution

    Bahman Tarvirdizade


    Full Text Available We consider the estimation of stress-strength reliability based on lower record values when X and Y are independently but not identically inverse Rayleigh distributed random variables. The maximum likelihood, Bayes, and empirical Bayes estimators of R are obtained and their properties are studied. Confidence intervals, exact and approximate, as well as the Bayesian credible sets for R are obtained. A real example is presented in order to illustrate the inferences discussed in the previous sections. A simulation study is conducted to investigate and compare the performance of the intervals presented in this paper and some bootstrap intervals.

  6. Pseudo Rayleigh wave in a partially saturated non-dissipative porous solid

    Sharma, M. D.


    Propagation of surface waves is studied at the pervious boundary of a porous solid saturated with a mixture of two immiscible fluids. An approach, based on continuum mixture theory, is used to derive a secular equation for the propagation of harmonic waves at the stress-free plane surface of this non-dissipative medium. Numerical analysis shows that this secular equation may not represent the propagation of true surface wave in the porous aggregate. Then, this equation is solved numerically for the propagation of pseudo Rayleigh wave or the leaky surface waves. To ensure the existence of pseudo Rayleigh wave, capillary effect between two (wetting and non-wetting) pore-fluids is related to the partial saturation. Effects of porosity and partial saturation coupled with capillary effect are observed on the phase velocity of pseudo Rayleigh waves in sandstone saturated with water-CO2 mixture.

  7. Inversion of Love wave phase velocity using smoothness-constrained least-squares technique; Heikatsuka seiyakutsuki saisho jijoho ni yoru love ha iso sokudo no inversion

    Kawamura, S. [Nippon Geophysical Prospecting Co. Ltd., Tokyo (Japan)


    Smoothness-constrained least-squares technique with ABIC minimization was applied to the inversion of phase velocity of surface waves during geophysical exploration, to confirm its usefulness. Since this study aimed mainly at the applicability of the technique, Love wave was used which is easier to treat theoretically than Rayleigh wave. Stable successive approximation solutions could be obtained by the repeated improvement of velocity model of S-wave, and an objective model with high reliability could be determined. While, for the inversion with simple minimization of the residuals squares sum, stable solutions could be obtained by the repeated improvement, but the judgment of convergence was very hard due to the smoothness-constraint, which might make the obtained model in a state of over-fitting. In this study, Love wave was used to examine the applicability of the smoothness-constrained least-squares technique with ABIC minimization. Applicability of this to Rayleigh wave will be investigated. 8 refs.

  8. Skeletonized wave equation of surface wave dispersion inversion

    Li, Jing


    We present the theory for wave equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. Similar to wave-equation travel-time inversion, the complicated surface-wave arrivals in traces are skeletonized as simpler data, namely the picked dispersion curves in the (kx,ω) domain. Solutions to the elastic wave equation and an iterative optimization method are then used to invert these curves for 2D or 3D velocity models. This procedure, denoted as wave equation dispersion inversion (WD), does not require the assumption of a layered model and is less prone to the cycle skipping problems of full waveform inversion (FWI). The synthetic and field data examples demonstrate that WD can accurately reconstruct the S-wave velocity distribution in laterally heterogeneous media.

  9. Characterization of surface damage of a solid plate under tensile loading using nonlinear Rayleigh waves


    This letter reports experimental observation of a direct correlation between the acoustic nonlinearity parameter (NP) measured with nonlinear Rayleigh waves and the accumulation of plasticity damage in an AZ31 magnesium alloy plate specimen.Rayleigh waves are generated and detected with wedge transducers,and the NPs are measured at different stress levels.The results show that there is a significant increase in the NPs with monotonic tensile loads surpassing the material's yielding stress.The research sugge...

  10. Identification of the Rayleigh surface waves for estimation of viscoelasticity using the surface wave elastography technique.

    Zhang, Xiaoming


    The purpose of this Letter to the Editor is to demonstrate an effective method for estimating viscoelasticity based on measurements of the Rayleigh surface wave speed. It is important to identify the surface wave mode for measuring surface wave speed. A concept of start frequency of surface waves is proposed. The surface wave speeds above the start frequency should be used to estimate the viscoelasticity of tissue. The motivation was to develop a noninvasive surface wave elastography (SWE) technique for assessing skin disease by measuring skin viscoelastic properties. Using an optical based SWE system, the author generated a local harmonic vibration on the surface of phantom using an electromechanical shaker and measured the resulting surface waves on the phantom using an optical vibrometer system. The surface wave speed was measured using a phase gradient method. It was shown that different standing wave modes were generated below the start frequency because of wave reflection. However, the pure symmetric surface waves were generated from the excitation above the start frequency. Using the wave speed dispersion above the start frequency, the viscoelasticity of the phantom can be correctly estimated.

  11. Enhanced sensing and conversion of ultrasonic Rayleigh waves by elastic metasurfaces.

    Colombi, Andrea; Ageeva, Victoria; Smith, Richard J; Clare, Adam; Patel, Rikesh; Clark, Matt; Colquitt, Daniel; Roux, Philippe; Guenneau, Sebastien; Craster, Richard V


    Recent years have heralded the introduction of metasurfaces that advantageously combine the vision of sub-wavelength wave manipulation, with the design, fabrication and size advantages associated with surface excitation. An important topic within metasurfaces is the tailored rainbow trapping and selective spatial frequency separation of electromagnetic and acoustic waves using graded metasurfaces. This frequency dependent trapping and spatial frequency segregation has implications for energy concentrators and associated energy harvesting, sensing and wave filtering techniques. Different demonstrations of acoustic and electromagnetic rainbow devices have been performed, however not for deep elastic substrates that support both shear and compressional waves, together with surface Rayleigh waves; these allow not only for Rayleigh wave rainbow effects to exist but also for mode conversion from surface into shear waves. Here we demonstrate experimentally not only elastic Rayleigh wave rainbow trapping, by taking advantage of a stop-band for surface waves, but also selective mode conversion of surface Rayleigh waves to shear waves. These experiments performed at ultrasonic frequencies, in the range of 400-600 kHz, are complemented by time domain numerical simulations. The metasurfaces we design are not limited to guided ultrasonic waves and are a general phenomenon in elastic waves that can be translated across scales.

  12. Orienting ocean-bottom seismometers from P-wave and Rayleigh wave polarizations

    Scholz, John-Robert; Barruol, Guilhem; Fontaine, Fabrice R.; Sigloch, Karin; Crawford, Wayne C.; Deen, Martha


    We present two independent, automated methods for estimating the absolute horizontal misorientation of seismic sensors. We apply both methods to 44 free-fall ocean-bottom seismometers (OBSs) of the RHUM-RUM experiment ( The techniques measure the 3-D directions of particle motion of (1) P-waves and (2) Rayleigh waves of earthquake recordings. For P-waves, we used a principal component analysis to determine the directions of particle motions (polarizations) in multiple frequency passbands. We correct for polarization deviations due to seismic anisotropy and dipping discontinuities using a simple fit equation, which yields significantly more accurate OBS orientations. For Rayleigh waves, we evaluated the degree of elliptical polarization in the vertical plane in the time and frequency domain. The results obtained for the RHUM-RUM OBS stations differed, on average, by 3.1° and 3.7° between the methods, using circular mean and median statistics, which is within the methods' estimate uncertainties. Using P-waves, we obtained orientation estimates for 31 ocean-bottom seismometers with an average uncertainty (95 per cent confidence interval) of 11° per station. For 7 of these OBS, data coverage was sufficient to correct polarization measurements for underlying seismic anisotropy and dipping discontinuities, improving their average orientation uncertainty from 11° to 6° per station. Using Rayleigh waves, we obtained misorientation estimates for 40 OBS, with an average uncertainty of 16° per station. The good agreement of results obtained using the two methods indicates that they should also be useful for detecting misorientations of terrestrial seismic stations.

  13. Crustal thickness variation beneath the Romanian seismic network from Rayleigh wave dispersion and receiver function analysis

    Tataru, Dragos; Grecu, Bogdan; Zaharia, Bogdan


    Variations in crustal thickness in Romania where determined by joint inversion of P wave receiver functions (RFs) and Rayleigh wave group velocity dispersion. We present new models of shear wave velocity structure of the crust beneath Romanian broad band stations. The data set consist in more than 500 teleseismic earthquake with epicentral distance between 30° and 95°, magnitude greater than 6 and a signal-to-noise ratio greater than 3 for the P-wave pulse. Most epicenters are situated along the northern Pacific Rim and arrive with backazimuths (BAZs) between 0° and 135° at the Romanian seismic network. We combine receiver functions with fundamental-mode of the Rayleigh wave group velocities to further constrain the shear-wave velocity structure.To extract the group velocities we applied the Multiple Filter Technique analysis to the vertical components of the earthquakes recordings. This technique allowed us to identify the Rayleigh wave fundamental mode and to compute the dispersion curves of the group velocities at periods between 10 and 150 s allowing us to resolve shear wave velocities to a depth of 100 km. The time-domain iterative deconvolution procedure of Ligorrıa and Ammon (1999) was employed to deconvolve the vertical component of the teleseismic P waveforms from the corresponding horizontal components and obtain radial and transverse receiver functions at each broadband station. The data are inverted using a joint, linearized inversion scheme (Hermann, 2002) which accounts for the relative influence of each set of observations, and allows a trade-off between fitting the observations, constructing a smooth model, and matching a priori constraints. The results show a thin crust for stations located inside the Pannonian basin (28-30 km) and a thicker crust for those in the East European Platform (36-40 km). The stations within the Southern and Central Carpathian Orogen are characterized by crustal depths of ~35 km. For stations located in the Northern

  14. Rayleigh surface waves, phonon mode conversion, and thermal transport in nanostructures

    Maurer, Leon; Knezevic, Irena

    We study the effects of phonon mode conversion and Rayleigh (surface) waves on thermal transport in nanostructures. We present a technique to calculate thermal conductivity in the elastic-solid approximation: a finite-difference time-domain (FDTD) solution of the elastic or scalar wave equations combined with the Green-Kubo formula. The technique is similar to an equilibrium molecular dynamics simulation, captures phonon wave behavior, and scales well to nanostructures that are too large to simulate with many other techniques. By imposing fixed or free boundary conditions, we can selectively turn off mode conversion and Rayleigh waves to study their effects. In the example case of graphenelike nanoribbons with rough edges, we find that mode conversion among bulk modes has little effect on thermal transport, but that conversion between bulk and Rayleigh waves can significantly reduce thermal conductivity. With increasing surface disorder, Rayleigh waves readily become trapped by the disorder and draw energy away from the propagating bulk modes, which lowers thermal conductivity. We discuss the implications on the accuracy of popular phonon-surface scattering models that stem from scalar wave equations and cannot capture mode conversion to Rayleigh waves.

  15. Assessing the viscoelasticity of chicken liver by OCE and a Rayleigh wave model

    Han, Zhaolong; Liu, Chih-hao; Singh, Manmohan; Aglyamov, Salavat R.; Raghunathan, Raksha; Wu, Chen; Larin, Kirill V.


    This study investigates the feasibility of quantifying the viscoelasticity of soft tissues with a dynamic noncontact optical coherence elastography (OCE) technique coupled with a Rayleigh wave model. Spectral analysis of an air-pulse induced elastic wave as measured by OCE provided the elastic wave dispersion curve. The dispersion curve was fitted to an analytical solution of the Rayleigh wave model to determine the Young's modulus and shear viscosity of samples. In order to validate the method, 10% gelatin phantoms with and without different concentrations of oil were prepared and tested by OCE and mechanical testing. Results demonstrated that the elasticities as assessed by the Rayleigh wave model generally agreed well with mechanical testing, and that the viscosity in the phantom with oil samples was higher than the phantoms without oil, which is in agreement with the literature. Further, this method was applied to quantify the viscoelasticity of chicken liver. The Young's modulus was E=2.04+/-0.88 kPa and the shear viscosity was η=1.20+/-0.13 Pa·s with R2=0.96+/-0.04 between the OCE-measured dispersion curve and Rayleigh wave model analytical solution. Combining OCE and the Rayleigh wave model shows promise as an effective tool for noninvasively quantifying the viscoelasticity of soft tissues.

  16. Analysis of Rayleigh waves with circular wavefront: a maximum likelihood approach

    Maranò, Stefano; Hobiger, Manuel; Bergamo, Paolo; Fäh, Donat


    Analysis of Rayleigh waves is an important task in seismology and geotechnical investigations. In fact, properties of Rayleigh waves such as velocity and polarization are important observables that carry information about the structure of the subsoil. Applications analysing Rayleigh waves include active and passive seismic surveys. In active surveys, there is a controlled source of seismic energy and the sensors are typically placed near the source. In passive surveys, there is not a controlled source, rather, seismic waves from ambient vibrations are analysed and the sources are assumed to be far outside the array, simplifying the analysis by the assumption of plane waves. Whenever the source is in the proximity of the array of sensors or even within the array it is necessary to model the wave propagation accounting for the circular wavefront. In addition, it is also necessary to model the amplitude decay due to geometrical spreading. This is the case of active seismic surveys in which sensors are located near the seismic source. In this work, we propose a maximum likelihood (ML) approach for the analysis of Rayleigh waves generated at a near source. Our statistical model accounts for the curvature of the wavefront and amplitude decay due to geometrical spreading. Using our method, we show applications on real data of the retrieval of Rayleigh wave dispersion and ellipticity. We employ arrays with arbitrary geometry. Furthermore, we show how it is possible to combine active and passive surveys. This enables us to enlarge the analysable frequency range and therefore the depths investigated. We retrieve properties of Rayleigh waves from both active and passive surveys and show the excellent agreement of the results from the two surveys. In our approach we use the same array of sensors for both the passive and the active survey. This greatly simplifies the logistics necessary to perform a survey.

  17. Parallel Algorithm in Surface Wave Waveform Inversion


    In Surface wave waveform inversion, we want to reconstruct 3Dshear wav e velocity structure, which calculation beyond the capability of the powerful pr esent day personal computer or even workstation. So we designed a high parallele d algorithm and carried out the inversion on Parallel computer based on the part itioned waveform inversion (PWI). It partitions the large scale optimization pro blem into a number of independent small scale problems and reduces the computati onal effort by several orders of magnitude. We adopted surface waveform inversio n with a equal block(2°×2°) discretization.

  18. Forward problem for Love and quasi-Rayleigh waves: Exact dispersion relations and their sensitivities

    Dalton, David R.; Slawinski, Michael A.; Stachura, Piotr; Stanoev, Theodore


    We examine two types of guided waves: the Love and the quasi-Rayleigh waves. Both waves propagate in the same model of an elastic isotropic layer above an elastic isotropic halfspace. From their dispersion relations, we calculate their speeds as functions of the elasticity parameters, mass densities, frequency and layer thickness. We examine the sensitivity of these relations to the model and wave properties.

  19. Harmonic excitation of mantle Rayleigh waves by the 1991 eruption of Mount Pinatubo, Philippines

    Kanamori, Hiroo; MORI, Jim


    An unusually long (at least two hours) seismic wave train having periods of about 230 sec was recorded at many worldwide seismic stations during the major eruption of Mount Pinatubo in the Philippines on June 15, 1991. This wave train exhibits two sharp spectral peaks at 228 and 270 sec. The group velocity, phase velocity, and the particle motion of this wave train indicate that it is a Rayleigh wave. The most probable excitation mechanism is acoustic coupling of atmospheric oscillations that...

  20. Rayleigh-wave mode separation by high-resolution linear radon transform

    Luo, Y.; Xia, J.; Miller, R.D.; Xu, Y.; Liu, J.; Liu, Q.


    Multichannel analysis of surface waves (MASW) method is an effective tool for obtaining vertical shear wave profiles from a single non-invasive measurement. One key step of the MASW method is generation of a dispersion image and extraction of a reliable dispersion curve from raw multichannel shot records. Because different Rayleigh-wave modes normally interfere with each other in the time and space domain, it is necessary to perform mode separation and reconstruction to increase the accuracy of phase velocities determined from a dispersion image. In this paper, we demonstrate the effectiveness of high-resolution linear Radon transform (LRT) as a means of separating and reconstructing multimode, dispersive Rayleigh-wave energy. We first introduce high-resolution LRT methods and Rayleigh-wave mode separation using high-resolution LRT. Next, we use synthetic data and a real-world example to demonstrate the effectiveness of Rayleigh-wave mode separation using high-resolution LRT. Our synthetic and real-world results demonstrate that (1) high-resolution LRT successfully separates and reconstructs multimode dispersive Rayleigh-wave energy with high resolution allowing the multimode energy to be more accurately determined. The horizontal resolution of the Rayleigh-wave method can be increased by extraction of dispersion curves from a pair of traces in the mode-separated shot gather and (2) multimode separation and reconstruction expand the usable frequency range of higher mode dispersive energy, which increases the depth of investigation and provides a means for accurately determining cut-off frequencies. ?? 2009 The Authors Journal compilation ?? 2009 RAS.

  1. Propagation of Rayleigh surface waves with small wavelengths in nonlocal visco-elastic solids

    D P Acharya; Asit Mondal


    This paper investigates Rayleigh waves, propagating on the surface of a visco-elastic solid under the linear theory of nonlocal elasticity. Dispersion relations are obtained. It is observed that the waves are dispersive in nature for small wavelengths. Numerical calculations and discussions presented in this paper lead us to some important conclusions.

  2. Inverse obstacle scattering for elastic waves

    Li, Peijun; Wang, Yuliang; Wang, Zewen; Zhao, Yue


    Consider the scattering of a time-harmonic plane wave by a rigid obstacle which is embedded in an open space filled with a homogeneous and isotropic elastic medium. An exact transparent boundary condition is introduced to reduce the scattering problem into a boundary value problem in a bounded domain. Given the incident field, the direct problem is to determine the displacement of the wave field from the known obstacle; the inverse problem is to determine the obstacle’s surface from the measurement of the displacement on an artificial boundary enclosing the obstacle. In this paper, we consider both the direct and inverse problems. The direct problem is shown to have a unique weak solution by examining its variational formulation. The domain derivative is derived for the displacement with respect to the variation of the surface. A continuation method with respect to the frequency is developed for the inverse problem. Numerical experiments are presented to demonstrate the effectiveness of the proposed method.

  3. An implementation of differential search algorithm (DSA) for inversion of surface wave data

    Song, Xianhai; Li, Lei; Zhang, Xueqiang; Shi, Xinchun; Huang, Jianquan; Cai, Jianchao; Jin, Si; Ding, Jianping


    Surface wave dispersion analysis is widely used in geophysics to infer near-surface shear (S)-wave velocity profiles for a wide variety of applications. However, inversion of surface wave data is challenging for most local-search methods due to its high nonlinearity and to its multimodality. In this work, we proposed and implemented a new Rayleigh wave dispersion curve inversion scheme based on differential search algorithm (DSA), one of recently developed swarm intelligence-based algorithms. DSA is inspired from seasonal migration behavior of species of the living beings throughout the year for solving highly nonlinear, multivariable, and multimodal optimization problems. The proposed inverse procedure is applied to nonlinear inversion of fundamental-mode Rayleigh wave dispersion curves for near-surface S-wave velocity profiles. To evaluate calculation efficiency and stability of DSA, four noise-free and four noisy synthetic data sets are firstly inverted. Then, the performance of DSA is compared with that of genetic algorithms (GA) by two noise-free synthetic data sets. Finally, a real-world example from a waste disposal site in NE Italy is inverted to examine the applicability and robustness of the proposed approach on surface wave data. Furthermore, the performance of DSA is compared against that of GA by real data to further evaluate scores of the inverse procedure described here. Simulation results from both synthetic and actual field data demonstrate that differential search algorithm (DSA) applied to nonlinear inversion of surface wave data should be considered good not only in terms of the accuracy but also in terms of the convergence speed. The great advantages of DSA are that the algorithm is simple, robust and easy to implement. Also there are fewer control parameters to tune.

  4. On the reliability of direct Rayleigh-wave estimation from multicomponent cross-correlations

    Xu, Zongbo; Mikesell, T. Dylan


    Seismic interferometry is routinely used to image and characterize underground geology. The vertical component cross-correlations (CZZ) are often analysed in this process; although one can also use radial component and multicomponent cross-correlations (CRR and CZR, respectively), which have been shown to provide a more accurate Rayleigh-wave Green's function than CZZ when sources are unevenly distributed. In this letter, we identify the relationship between the multicomponent cross-correlations (CZR and CRR) and the Rayleigh-wave Green's functions to show why CZR and CRR are less sensitive than CZZ to non-stationary phase source energy. We demonstrate the robustness of CRR with a synthetic seismic noise data example. These results provide a compelling reason as to why CRR should be used to estimate the dispersive characteristics of the direct Rayleigh wave with seismic interferometry when the signal-to-noise ratio is high.

  5. Pseudospectral modeling and dispersion analysis of Rayleigh waves in viscoelastic media

    Zhang, K.; Luo, Y.; Xia, J.; Chen, C.


    Multichannel Analysis of Surface Waves (MASW) is one of the most widely used techniques in environmental and engineering geophysics to determine shear-wave velocities and dynamic properties, which is based on the elastic layered system theory. Wave propagation in the Earth, however, has been recognized as viscoelastic and the propagation of Rayleigh waves presents substantial differences in viscoelastic media as compared with elastic media. Therefore, it is necessary to carry out numerical simulation and dispersion analysis of Rayleigh waves in viscoelastic media to better understand Rayleigh-wave behaviors in the real world. We apply a pseudospectral method to the calculation of the spatial derivatives using a Chebyshev difference operator in the vertical direction and a Fourier difference operator in the horizontal direction based on the velocity-stress elastodynamic equations and relations of linear viscoelastic solids. This approach stretches the spatial discrete grid to have a minimum grid size near the free surface so that high accuracy and resolution are achieved at the free surface, which allows an effective incorporation of the free surface boundary conditions since the Chebyshev method is nonperiodic. We first use an elastic homogeneous half-space model to demonstrate the accuracy of the pseudospectral method comparing with the analytical solution, and verify the correctness of the numerical modeling results for a viscoelastic half-space comparing the phase velocities of Rayleigh wave between the theoretical values and the dispersive image generated by high-resolution linear Radon transform. We then simulate three types of two-layer models to analyze dispersive-energy characteristics for near-surface applications. Results demonstrate that the phase velocity of Rayleigh waves in viscoelastic media is relatively higher than in elastic media and the fundamental mode increases by 10-16% when the frequency is above 10. Hz due to the velocity dispersion of P

  6. Nonlinear dynamic acousto-elasticity measurement by Rayleigh wave in concrete cover evaluation

    Vu, Quang Anh; Garnier, Vincent; Payan, Cédric; Chaix, Jean-François; Lott, Martin; Eiras, Jesús N.


    This paper presents local non-destructive evaluation of concrete cover by using surface Rayleigh wave in nonlinear Dynamic Acousto-Elasticity (DAE) measurement. Dynamic non classical nonlinear elastic behavior like modulus decrease under applied stress and slow dynamic process has been observed in many varieties of solid, also in concrete. The measurements conducted in laboratory, consist in qualitative evaluation of concrete thermal damage. Nonlinear elastic parameters especially conditioning offset are analyzed for the cover concrete by Rayleigh wave. The results of DAE method show enhanced sensitivity when compared to velocity measurement. Afterward, this technique broadens measurements to the field.

  7. Methods to increase the depth and precision of transient Rayleigh wave exploration

    ZHANG Jian-jun(张建军); WEI Xiu-cheng(魏修成); LIU Yang(刘洋)


    In order to increase the exploration depth of Rayleigh wave, new idea that different from the former principles in data acquisition was applied. Suitable data acquisition parameter was given out on the basis of large amount of experiments. By reducing the group interval, the low frequency signal are enhanced instead of been attenuated. Furthermore, to solve the problem that the precision of Rayleigh wave exploration method count much to the signal-to-noise ratio, some preprocessing methods were put forward. By using zero shift rectifying, digital F-K filtering and cutting, noises can be effectively eliminated.

  8. Estimate of Rayleigh-to-Love wave ratio in the secondary microseism by colocated ring laser and seismograph

    Tanimoto, T; Hadziioannou, C; H. Igel; Wasserman, J.; U. Schreiber; Gebauer, A.


    ©2015. American Geophysical Union. All Rights Reserved. Using a colocated ring laser and an STS-2 seismograph, we estimate the ratio of Rayleigh-to-Love waves in the secondary microseism at Wettzell, Germany, for frequencies between 0.13 and 0.30 Hz. Rayleigh wave surface acceleration was derived from the vertical component of STS-2, and Love wave surface acceleration was derived from the ring laser. Surface wave amplitudes are comparable; near the spectral peak about 0.22 Hz, Rayleigh wave a...

  9. Azimuthal anisotropy of Rayleigh waves beneath the Tibetan Plateau and adjacent areas


    The crustal and upper mantle azimuthal anisotropy of the Tibetan Plateau and adjacent areas was studied by Rayleigh wave tomography. We collected sufficient broadband digital seismograms trav-ersing the Tibetan Plateau and adjacent areas from available stations, including especially some data from the temporary stations newly deployed in Yunnan, eastern Tibet, and western Sichuan. They made an adequate path coverage in most regions to achieve a reasonable resolution for the inversion. The model resolution tests show that the anisotropic features of scope greater than 400 km and strength greater than 2% are reliable. The azimuthal anisotropy pattern inside the Tibetan Plateau was similar to the characteristic of tectonic partition. The crustal anisotropy strength is greater than 2% in most re-gions of East Tibet, and the anisotropy shows clockwise rotation surrounding the eastern Himalayan syntaxis. Vertically, the anisotropy direction indicates a coherent pattern within the upper crust, lower crust, and lithosphere mantle of the Tibetan Plateau, which also is consistent with GPS velocity field and SKS fast polarization directions. The result supports that the crust-mantle deformation beneath the Tibetan Plateau is vertically coherent. The anisotropy strength of crust and lithospheric upper mantle in Yunnan outside the Tibetan Plateau is lower than 2%, so SKS splitting from core-mantle boundary to station should largely be attributed to the anisotropy of asthenosphere.

  10. Azimuthal anisotropy of Rayleigh waves beneath the Tibetan Plateau and adjacent areas

    SU Wei; WANG ChunYong; HUANG ZhongXian


    The crustal and upper mantle azimuthal anisotropy of the Tibetan Plateau and adjacent areas was studied by Rayleigh wave tomography. We collected sufficient broadband digital seismograms traversing the Tibetan Plateau and adjacent areas from available stations, including especially some data from the temporary stations newly deployed in Yunnan, eastern Tibet, and western Sichuan. They made an adequate path coverage in most regions to achieve a reasonable resolution for the inversion. The model resolution tests show that the anisotropic features of scope greater than 400 km and strength greater than 2% are reliable. The azimuthal anisotropy pattern inside the Tibetan Plateau was similar to the characteristic of tectonic partition. The crustal anisotropy strength is greater than 2% in most regions of East Tibet, and the anisotropy shows clockwise rotation surrounding the eastern Himalayan syntaxis. Vertically, the anisotropy direction indicates a coherent pattern within the upper crust, lower crust, and lithosphere mantle of the Tibetan Plateau, which also is consistent with GPS velocity field and SKS fast polarization directions. The result supports that the crust-mantle deformation beneath the Tibetan Plateau is vertically coherent. The anisotropy strength of crust and lithospheric upper mantle in Yunnan outside the Tibetan Plateau is lower than 2%, so SKS splitting from core-mantle boundary to station should largely be attributed to the anisotropy of asthenosphere.

  11. The acoustoelastic effect on Rayleigh waves in elastic-plastic deformed layered rocks

    Liu Jin-Xia; Cui Zhi-Wen; Wang Ke-Xie


    On the basis of the acoustoelastic theory for elastic-plastic materials, the influence of statically deformed states including both the elastic and plastic deformations induced by applied uniaxial stresses on the Rayleigh wave in layered rocks is investigated by using a transfer matrix method. The acoustoelastic effects of elastic-plastic strains in rocks caused by static deformations, are discussed in detail. The Rayleigh-type and Sezawa modes exhibit similar trends in acoustoelastic effect: the acoustoelastic effect increasing rapidly with the frequency-thickness product and the phase velocity change approaching a constant value for thick layer and high frequency limit. Elastic-plastic deformations in the Castlegate layered rock obviously modify the phase velocity of the Rayleigh wave and the cutoff points for the Sezawa modes. The investigation may be useful for seismic exploration, geotechnical engineering and ultrasonic detection.

  12. Shear-wave velocity structure of the south-eastern part of the Iberian Peninsula from Rayleigh wave analysis

    Corchete, V.; Chourak, M.


    In this study, we present the lithospheric structure of the south-eastern part of the Iberian Peninsula by means of a set of 2D images of shear velocity, for depths ranging from 0 to 50 km. This goal will be attained by means of the inversion of the Rayleigh wave dispersion. For it, the traces of 25 earthquakes occurred on the neighbouring of the study area, from 2001 to 2003, will be considered. These earthquakes have been registered by 11 broadband stations located on Iberia. All seismic events have been grouped in source zones to get an average dispersion curve for each source-station path. The dispersion curves have been measured for periods between 2 and 45 s, by combination of two digital filtering techniques: Multiple Filter Technique and Time Variable Filtering. The resulting set of source-station averaged dispersion curves has been inverted according to the generalized inversion theory, to get S-wave velocity models for each source-station path. Later, these models have been interpolated using the method of kriging, to obtain a 2D mapping of the S-wave velocity structure for the south-eastern part of Iberia. The results presented in this paper show that the techniques used here are a powerful tool to investigate the crust and upper mantle structure, through the dispersion analysis and its inversion to obtain shear velocity distributions with depth. By means of this analysis, principal structural features of the south-eastern part of Iberia, such as the existence of lateral and vertical heterogeneity in the whole study area, or the location of the Moho discontinuity at 30 km of depth (with an average S-velocity of uppermost mantle of 4.7 km/s), have been revealed. Other important structural features revealed by this analysis have been that the uppermost of Iberian massif shows higher velocity values than the uppermost of the Alpine domain, indicating that the massif is old and tectonically stable. The average velocity of the crust in Betic cordillera is of

  13. Wave-equation reflection traveltime inversion

    Zhang, Sanzong


    The main difficulty with iterative waveform inversion using a gradient optimization method is that it tends to get stuck in local minima associated within the waveform misfit function. This is because the waveform misfit function is highly nonlinear with respect to changes in the velocity model. To reduce this nonlinearity, we present a reflection traveltime tomography method based on the wave equation which enjoys a more quasi-linear relationship between the model and the data. A local crosscorrelation of the windowed downgoing direct wave and the upgoing reflection wave at the image point yields the lag time that maximizes the correlation. This lag time represents the reflection traveltime residual that is back-projected into the earth model to update the velocity in the same way as wave-equation transmission traveltime inversion. No travel-time picking is needed and no high-frequency approximation is assumed. The mathematical derivation and the numerical examples are presented to partly demonstrate its efficiency and robustness. © 2011 Society of Exploration Geophysicists.

  14. Direction dependent Love and Rayleigh wave noise characteristics using multiple arrays across Europe

    Juretzek, Carina; Perleth, Magdalena; Hadziioannou, Celine


    Seismic noise has become an important signal source for tomography and monitoring purposes. Better understanding of the noise field characteristics is crucial to further improve noise applications. Our knowledge about common and different origins of Love and Rayleigh waves in the microseism band is still limited. This applies in particular for constraints on source locations and source mechanisms of Love waves. Here, 3-component beamforming is used to distinguish between the different polarized wave types in the primary and secondary microseism noise field recorded at several arrays across Europe. We compare characteristics of Love and Rayleigh wave noise, such as source directions and frequency content. Further, Love to Rayleigh wave ratios are measured and a dependence on direction is found, especially in the primary microseism band. Estimates of the kinetic energy density ratios propose a dominance of coherent Love waves in the primary, but not in the secondary microseism band. The seasonality of the noise field characteristics is examined by using a full year of data in 2013 and is found to be stable.

  15. The preliminary results: Seismic ambient noise Rayleigh wave tomography around Merapi volcano, central Java, Indonesia

    Trichandi, Rahmantara, E-mail: [Geophysical Engineering, Faculty of Mining and Petroleum Engineering, Institut Teknologi Bandung, 40132, Bandung (Indonesia); Yudistira, Tedi; Nugraha, Andri Dian [Global Geophysics Research Group, Faculty of Mining and Petroleum Engineering, Institut Teknologi Bandung, Bandung, 40132 (Indonesia); Zulhan, Zulfakriza [Earth Science Graduate Program, Faculty of Earth Science and Technology, Institut Teknologi Bandung, Bandung, 40132 (Indonesia); Saygin, Erdinc [Research School of Earth Sciences, The Australian National University, Canberra ACT 0200 (Australia)


    Ambient noise tomography is relatively a new method for imaging the shallow structure of the Earth subsurface. We presents the application of this method to produce a Rayleigh wave group velocity maps around the Merapi Volcano, Central Java. Rayleigh waves group velocity maps were reconstructed from the cross-correlation of ambient noise recorded by the DOMERAPI array which consists 43 broadband seismometers. In the processing stage, we first filtered the observation data to separatethe noise from the signal that dominated by the strong volcanic activities. Next, we cross-correlate the filtered data and stack to obtain the Green’s function for all possible station pairs. Then we carefully picked the peak of each Green’s function to estimate the dispersion trend and appliedMultiple Filter Technique to obtain the dispersion curve. Inter-station group velocity curvesare inverted to produceRayleigh wave group velocity maps for periods 1 to 10 s. The resulted Rayleigh group velocity maps show the interesting features around the Merapi Volcano which generally agree with the previous studies. Merapi-Lawu Anomaly (MLA) is emerged as a relatively low anomaly in our group velocity maps.

  16. The preliminary results: Seismic ambient noise Rayleigh wave tomography around Merapi volcano, central Java, Indonesia

    Trichandi, Rahmantara; Yudistira, Tedi; Nugraha, Andri Dian; Zulhan, Zulfakriza; Saygin, Erdinc


    Ambient noise tomography is relatively a new method for imaging the shallow structure of the Earth subsurface. We presents the application of this method to produce a Rayleigh wave group velocity maps around the Merapi Volcano, Central Java. Rayleigh waves group velocity maps were reconstructed from the cross-correlation of ambient noise recorded by the DOMERAPI array which consists 43 broadband seismometers. In the processing stage, we first filtered the observation data to separatethe noise from the signal that dominated by the strong volcanic activities. Next, we cross-correlate the filtered data and stack to obtain the Green's function for all possible station pairs. Then we carefully picked the peak of each Green's function to estimate the dispersion trend and appliedMultiple Filter Technique to obtain the dispersion curve. Inter-station group velocity curvesare inverted to produceRayleigh wave group velocity maps for periods 1 to 10 s. The resulted Rayleigh group velocity maps show the interesting features around the Merapi Volcano which generally agree with the previous studies. Merapi-Lawu Anomaly (MLA) is emerged as a relatively low anomaly in our group velocity maps.

  17. Modeling of atmospheric-coupled Rayleigh waves on planets with atmosphere: From Earth observation to Mars and Venus perspectives.

    Lognonné, Philippe; Karakostas, Foivos; Rolland, Lucie; Nishikawa, Yasuhiro


    Acoustic coupling between solid Earth and atmosphere has been observed since the 1960s, first from ground-based seismic, pressure, and ionospheric sensors and since 20 years with various satellite measurements, including with global positioning system (GPS) satellites. This coupling leads to the excitation of the Rayleigh surface waves by local atmospheric sources such as large natural explosions from volcanoes, meteor atmospheric air-bursts, or artificial explosions. It contributes also in the continuous excitation of Rayleigh waves and associated normal modes by atmospheric winds and pressure fluctuations. The same coupling allows the observation of Rayleigh waves in the thermosphere most of the time through ionospheric monitoring with Doppler sounders or GPS. The authors review briefly in this paper observations made on Earth and describe the general frame of the theory enabling the computation of Rayleigh waves for models of telluric planets with atmosphere. The authors then focus on Mars and Venus and give in both cases the atmospheric properties of the Rayleigh normal modes and associated surface waves compared to Earth. The authors then conclude on the observation perspectives especially for Rayleigh waves excited by atmospheric sources on Mars and for remote ionospheric observations of Rayleigh waves excited by quakes on Venus.

  18. Estimating Rayleigh wave particle motion from three-component array analysis of ambient vibrations

    Poggi, Valerio; Fäh, Donat


    Several methods have been proposed in the past years to extract the Rayleigh wave ellipticity from horizontal-to-vertical spectral ratios of single station ambient noise recordings. The disadvantage of this set of techniques is the difficulty in clearly identifying and separating the contribution of higher modes. In most cases, only the fundamental mode of ellipticity can be identified. Moreover, it is generally difficult to correct for the energy of SH and Love waves present in the horizontal components of the ambient vibration wavefield. We introduce a new methodology to retrieve Rayleigh wave ellipticity using high-resolution frequency-wavenumber array analysis. The technique is applied to the three components of motion and is based on the assumption that an amplitude maximum in the f-k cross-spectrum must represent the true power amplitude of the corresponding signal. In the case of Rayleigh waves, therefore, the ratio between maxima obtained from the horizontal (radial-polarized) and vertical components of motion will also represent the frequency-dependent ellipticity function. Consequently, if we can identify the Rayleigh dispersion curves of several modes on the f-k plane, then the corresponding modal ellipticity patterns can also be separated and extracted. To test the approach, synthetic and real data sets were processed. In all tested cases, a reliable estimation of segments of the fundamental mode ellipticity was obtained. The identification of higher modes is possible in most cases. The quality of results depends on the selected array geometry and the signal-to-noise ratio, with a major improvement achieved by increasing the number of receivers employed during the survey. An experiment conducted in the town of Visp (Switzerland) allowed the retrieval of portions of ellipticity curves up to the second Rayleigh higher mode, using two concentric circular array configurations of 14 and 11 receivers each.

  19. Anisotropic wave-equation traveltime and waveform inversion

    Feng, Shihang


    The wave-equation traveltime and waveform inversion (WTW) methodology is developed to invert for anisotropic parameters in a vertical transverse isotropic (VTI) meidum. The simultaneous inversion of anisotropic parameters v0, ε and δ is initially performed using the wave-equation traveltime inversion (WT) method. The WT tomograms are then used as starting background models for VTI full waveform inversion. Preliminary numerical tests on synthetic data demonstrate the feasibility of this method for multi-parameter inversion.

  20. Source Estimation by Full Wave Form Inversion

    Sjögreen, Björn [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing; Petersson, N. Anders [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing


    Given time-dependent ground motion recordings at a number of receiver stations, we solve the inverse problem for estimating the parameters of the seismic source. The source is modeled as a point moment tensor source, characterized by its location, moment tensor components, the start time, and frequency parameter (rise time) of its source time function. In total, there are 11 unknown parameters. We use a non-linear conjugate gradient algorithm to minimize the full waveform misfit between observed and computed ground motions at the receiver stations. An important underlying assumption of the minimization problem is that the wave propagation is accurately described by the elastic wave equation in a heterogeneous isotropic material. We use a fourth order accurate finite difference method, developed in [12], to evolve the waves forwards in time. The adjoint wave equation corresponding to the discretized elastic wave equation is used to compute the gradient of the misfit, which is needed by the non-linear conjugated minimization algorithm. A new source point moment source discretization is derived that guarantees that the Hessian of the misfit is a continuous function of the source location. An efficient approach for calculating the Hessian is also presented. We show how the Hessian can be used to scale the problem to improve the convergence of the non-linear conjugated gradient algorithm. Numerical experiments are presented for estimating the source parameters from synthetic data in a layer over half-space problem (LOH.1), illustrating rapid convergence of the proposed approach.

  1. Propagation Characteristics of Laser-Generated Rayleigh Waves in Coating-Substrate Structures with Anisotropic and Viscoelastic Properties

    Sun, Hong-xiang; Zhang, Shu-yi; Xia, Jian-ping


    The propagation characteristics of laser-generated Rayleigh waves in coating-substrate structures with anisotropic and viscoelastic properties have been investigated quantitatively. Based on the plane strain theory, finite element models for simulating laser-generated Rayleigh waves in coating-substrate structures are established, in which the carbon fiber-reinforced epoxy matrix composite and aluminum are used as the coating and/or the substrate alternately. The numerical results exhibit that the characteristics of the laser-generated Rayleigh waves, including attenuation, velocity, and dispersion, are mainly and closely related to the anisotropic and viscoelastic properties of the composite in the coating-substrate structures.

  2. Influence of Initial Stress and Gravity Field on Propagation of Rayleigh and Stoneley Waves in a Thermoelastic Orthotropic Granular Medium

    S. M. Ahmed


    Full Text Available The propagation of Rayleigh and Stoneley waves in a thermoelastic orthotropic granular half-space supporting a different layer under the influence of initial stress and gravity field is studied. The frequency equation of Rayleigh waves in the form of twelfth-order determinantal expression and the frequency equation of Stoneley waves in the form of eighth-order determinantal expression are obtained. The standard equation of dispersion is discussed to obtain Rayleigh and Stoneley waves that have complex roots; the real part gives the velocity of Rayleigh or Stoneley waves but the imaginary part gives the attenuation coefficient. Finally, the numerical results have been given and illustrated graphically, and their physical meaning has been explained.

  3. Focusing of Rayleigh waves generated by high-speed trains under the condition of ground vibration boom

    Krylov, Victor V


    In the present paper, the effects of focusing of Rayleigh waves generated by high speed trains in the supporting ground under the condition of ground vibration boom are considered theoretically. These effects are similar to the effects of focusing of sound waves radiated by aircraft under the condition of sonic boom. In particular, if a railway track has a bend to provide the possibility of changing direction of train movement, the Rayleigh surface waves generated by high-speed trains under the condition of ground vibration boom may become focused. This results in concentration of their energy along a simple caustic line at one side of the track and in the corresponding increase in ground vibration amplitudes. The effect of focusing of Rayleigh waves may occur also if a train moves along a straight line with acceleration and its current speed is higher than Rayleigh wave velocity in the ground. The obtained results are illustrated by numerical calculations.

  4. Seasonal variations in the Rayleigh-to-Love wave ratio in the secondary microseism from colocated ring laser and seismograph

    Tanimoto, Toshiro; Hadziioannou, Céline; Igel, Heiner; Wassermann, Joachim; Schreiber, Ulrich; Gebauer, André; Chow, Bryant


    Monthly variations in the ratio of Rayleigh-to-Love waves in the secondary microseism are obtained from a colocated ring laser and an STS-2 seismograph at Wettzell, Germany. Two main conclusions are derived for the Rayleigh-to-Love wave kinetic energy ratios in the secondary microseism; first, the energy ratio is in the range 0.8-0.9 (Love wave energy is larger than Rayleigh wave energy most of the year by about 10-20%. Second, this ratio suddenly increases to 1.0-1.2 in June and July, indicating a larger fraction of Rayleigh wave energy. This change suggests that the locations and behaviors of excitation sources are different in these months.

  5. Rayleigh-wave Tomography and Seismic Anisotropic Structures in the Region of the Philippine Sea

    Lee, Hsin-Yu; Legendre, Cédric P.; Chang, Emmy T. Y.


    The Philippine Sea Plate (PSP) is surrounded by convergent boundaries, the Pacific plate is subducting beneath the PSP along the Izu-Bonin and Mariana trenches at the east, whereas the PSP is subducting beneath the Eurasian plate along the Nankai trough, Ryukyu trench and Philippine trench at the west. The PSP can be divided by three oceanic basins: the oldest West Philippine basin developing in 35-45 Ma in the west, and the Shikoku and Parece Vela basins in 15-30 Ma in the east. Previous studies show a large variety of the seismic anisotropy structures in the region of the PSP, which correspond different scenarios of tectonic evolution for this area. In this study, we analyze both isotropic and anisotropic Rayleigh-wave velocity structures of the PSP by means of two-station method. The earthquakes of magnitude (Mw) greater than 5.0 in-between the years 1998-2014 were acquired. Totally, 7914 teleseismic events are adopted to form the measurements of Rayleigh-wave dispersion curves along 467 station-pairs over the PSP. The measured dispersion curves are then inverted into the isotropic and azimuthally anisotropic (2ψ) velocity maps at different periods with the damped, lateral smoothing LSQR inversion. The inversion is framed by the triangular grids which knots are of 200 km spacing. The consequent velocity anomalies are referenced to the average of the phase velocity at the periods between 50 and 100 seconds. The resulting velocity anomalies show a consistent pattern with the locations of the sub-basins in the PSP at the periods of 50 and 60 sec, which can be considered to be the association of lithospheric velocity structure with basin ages. The positive velocity anomalies are seen in the West Philippine basin associating the relatively old lithosphere; whereas the negative anomalies are found in the Shikoku and Parece Vela basins which the lithospheric structures are relatively young. On the other hand, the resultant azimuthal anisotropy reveals an apparent

  6. Numerical simulation for recognition of coalfield fire areas by Rayleigh waves

    Hu Mingshun; Pan Dongming; Chen Shenen; Dong Shouhua; Li Juanjuan


    Effective recognition of a coalfield fire area improves fire-fighting efficiency and helps avoid potential geological hazards.Coalfield fire areas are hard to detect accurately using general geophysical methods.This paper describes simulations of shallow,buried coalfield fires based on real geological conditions.Recognizing the coalfield fire by Rayleigh wave is proposed.Four representative geological models are constructed,namely; the non-burning model,the pseudo-burning model,the real-burning model,and the hidden-burning model.Numerical simulation using these models shows many markedly different characteristics between them in terms of Rayleigh wave dispersion and Eigen displacement.These characteristics,as well as the shear wave velocity obtained by inverting the fundamental dispersion,make it possible to distinguish the type of the coalfield fire area and indentify the real and serious coalfield fire area.The results are very helpful for future application of Rayleigh waves for the detection of coalfield fire area.

  7. Local Effects on Strain Seismograms at Matsushiro Seismological Observatory - 2. Rayleigh Waves

    Taishi Okamoto


    Full Text Available We evaluate local effects on strain seismograms for a Rayleigh wave observed at Matsushiro Seismological Observatory, Japan Meteorological Agency, central Japan, by applying a method proposed in a previous report (Okamoto et al. 2007. The method involves examination of polarization angles, local phase velocity, and accuracy of velocity seismograms. The results are as follows: 1 Polarization angles of observed strain seismograms agree with expected ones from those of velocity seismograms also observed at Matsushiro; 2 Local phase velocity estimated by comparison between strain and velocity seismograms is 54% larger than the theoretical value calculated from the PREM velocity model; 3 Velocity spectra observed at Matsushiro have almost the same amplitude as an average of those at F-net observation stations near Matsushiro. These results indicate that both EW and NS component strain seismograms observed at Matsushiro have been reduced by 35% in amplitude for a Rayleigh wave due to local heterogeneity. The local effects on a Rayleigh wave are quite different from that on a Love wave obtained in the previous report.

  8. Lateral Variations of Rayleigh-Wave Dispersions in the Philippine Sea Region

    Wen-Yen Chang


    Full Text Available Fresh two-dimensional group and phase-velocity distribution maps of the Philippine Sea and surrounding areas are constructed using the tomographic inversion of more than 2500 Rayleigh-wave dispersion curves in the 20- to 120-sec period range. The results show that, for the periods used, both the group and phase-velocity variation patterns are very close to the geological and topographic features and are also consistent with previous studies of magnetic anomalies and evolutionary history of the Philippine Basin. On average, the periods of the peak group-velocity for the West Philippine Basin and the Oki-Daito ridge are about 40 and 32 sec for the Parece Vela and Shikoku basins. This implies that the lithosphere of the western Philippine Sea Basin is thicker, which is related to plate cooling and seafloor age. For most of the examined periods, the high velocity symmetry of the two sides of the Central Basin Ridge in the West Philippine Basin coincides well with the evolutionary history of the Philippine Sea Basin, and may be taken as additional evidence confirming the existence of the ridge. The group and phase-velocity distributions for periods longer than 80 sec are smooth throughout the whole Philippine Sea Basin, which implies that the upper mantle beneath the Philippine Sea Basin is nearly homogeneous at depths of 100 - 200 km. Moreover, the group and phase velocities in the region of the East Volcano Belt and Active Marginal Basin remain almost constant in the 36- to 80-sec period range, which indicates that the boundary between the lithosphere and asthenosphere is probably not obvious in this area.

  9. Rayleigh Wave Phase Velocity in the Upper Mantle Beneath the Indian Ocean

    Godfrey, K. E.; Dalton, C. A.; Ritsema, J.


    Most of what is currently understood about the seismic properties of oceanic upper mantle is based on either global studies or regional studies of the upper mantle beneath the Pacific Ocean. However, global seismic models and geochemical studies of mid-ocean ridge basalts indicate differences in the properties of the upper mantle beneath the Pacific, Atlantic, and Indian oceans. Though the Indian Ocean is not as well studied seismically, it is host to a number of geologically interesting features including 16,000 km of mid-ocean ridge with a range of spreading rates from 14 mm/yr along the Southwest Indian Ridge to 55-75 mm/yr along the Southeast Indian Ridge. The Indian Ocean also contains multiple volcanic hotspots, the Australian-Antarctic Discordance, and a low geoid anomaly south of India, and it overlies a portion of a large low-shear-velocity province. We are using Rayleigh waves to construct a high-resolution seismic velocity model of the Indian Ocean upper mantle. We utilize a global dataset of phase delays measured at 20 periods, between 37 and 375 seconds; the dataset includes between 700 and 20,000 that traverse our study region exclusively, with a larger number of paths at shorter periods. We explore variations in phase velocity using two separate approaches. One, we allow phase velocity to vary only as a function of seafloor age. Two, we perform a damped least-squares inversion to solve for 2-D phase velocity maps at each period. Preliminary results indicate low velocities along the Southeast Indian Ridge and Central Indian Ridge, but the expected low velocities are less apparent along the slow-spreading Southwest Indian Ridge. We observe a region of fast velocities extending from Antarctica northward between the Kerguelen and Crozet hotspots, and lower than expected velocities beneath the Reunion hotspot. Additionally, we find low velocities associated with a region of extinct seafloor spreading in the Wharton basin.

  10. Rayleigh-Taylor Gravity Waves and Quasiperiodic Oscillation Phenomenon in X-ray Binaries

    Titarchuk, Lev


    Accretion onto compact objects in X-ray binaries (black hole, neutron star (NS), white dwarf) is characterized by non-uniform flow density profiles. Such an effect of heterogeneity in presence of gravitational forces and pressure gradients exhibits Rayleigh-Taylor gravity waves (RTGW). They should be seen as quasiperiodic wave oscillations (QPO) of the accretion flow in the transition (boundary) layer between the Keplerian disk and the central object. In this paper the author shows that the main QPO frequency, which is very close to the Keplerian frequency, is split into separate frequencies (hybrid and low branch) under the influence of the gravitational forces in the rotational frame of reference. The RTGWs must be present and the related QPOs should be detected in any system where the gravity, buoyancy and Coriolis force effects cannot be excluded (even in the Earth and solar environments). The observed low and high QPO frequencies are an intrinsic signature of the RTGW. The author elaborates the conditions for the density profile when the RTGW oscillations are stable. A comparison of the inferred QPO frequencies with QPO observations is presented. The author finds that hectohertz frequencies detected from NS binaries can be identified as the RTGW low branch frequencies. The author also predicts that an observer can see the double NS spin frequency during the NS long (super) burst events when the pressure gradients and buoyant forces are suppressed. The Coriolis force is the only force which acts in the rotational frame of reference and its presence causes perfect coherent pulsations with a frequency twice of the NS spin. The QPO observations of neutron binaries have established that the high QPO frequencies do not go beyond of the certain upper limit. The author explains this observational effect as a result of the density profile inversions. Also the author demonstrates that a particular problem of the gravity waves in the rotational frame of reference in the

  11. Measurement and fitting techniques for the assessment of material nonlinearity using nonlinear Rayleigh waves

    Torello, David [GW Woodruff School of Mechanical Engineering, Georgia Tech (United States); Kim, Jin-Yeon [School of Civil and Environmental Engineering, Georgia Tech (United States); Qu, Jianmin [Department of Civil and Environmental Engineering, Northwestern University (United States); Jacobs, Laurence J. [School of Civil and Environmental Engineering, Georgia Tech and GW Woodruff School of Mechanical Engineering, Georgia Tech (United States)


    This research considers the effects of diffraction, attenuation, and the nonlinearity of generating sources on measurements of nonlinear ultrasonic Rayleigh wave propagation. A new theoretical framework for correcting measurements made with air-coupled and contact piezoelectric receivers for the aforementioned effects is provided based on analytical models and experimental considerations. A method for extracting the nonlinearity parameter β{sub 11} is proposed based on a nonlinear least squares curve-fitting algorithm that is tailored for Rayleigh wave measurements. Quantitative experiments are conducted to confirm the predictions for the nonlinearity of the piezoelectric source and to demonstrate the effectiveness of the curve-fitting procedure. These experiments are conducted on aluminum 2024 and 7075 specimens and a β{sub 11}{sup 7075}/β{sub 11}{sup 2024} measure of 1.363 agrees well with previous literature and earlier work.

  12. Elastic characterization of Au thin films utilizing laser induced acoustic Rayleigh waves

    Haim, A.; Bar-Ad, S.; Azoulay, A.


    Wide frequency-band Rayleigh waves (~100 MHz) were utilized to characterize the elastic constants of thin Au/Cr films deposited on glass substrates. The Rayleigh waves were excited utilizing laser induced thermoelastic mechanism and detected using a knife-edge technique apparatus. The dispersion of the signals in glass substrates coated with Au/Cr was measured and fitted to theory using a non-linear regression algorithm. From the fitting, the Au films Young modulus and the film thickness were extracted. The results were analyzed with regards to AFM scans performed on the samples and independent thickness measurement done by a dektak3 profiler. Results show a good agreement between the two measurements.

  13. Elastic characterization of Au thin films utilizing laser induced acoustic Rayleigh waves

    Haim, A; Azoulay, A [Ultrasonic Section, NDT Department, Soreq - Nuclear Research Center, Yavne 81800 (Israel); Bar-Ad, S, E-mail: [School of Physics and Astronomy, Faculty of Exact Sciences, Tel-Aviv University, Tel-Aviv 69978 (Israel)


    Wide frequency-band Rayleigh waves ({approx}100 MHz) were utilized to characterize the elastic constants of thin Au/Cr films deposited on glass substrates. The Rayleigh waves were excited utilizing laser induced thermoelastic mechanism and detected using a knife-edge technique apparatus. The dispersion of the signals in glass substrates coated with Au/Cr was measured and fitted to theory using a non-linear regression algorithm. From the fitting, the Au films Young modulus and the film thickness were extracted. The results were analyzed with regards to AFM scans performed on the samples and independent thickness measurement done by a dektak{sup 3} profiler. Results show a good agreement between the two measurements.

  14. The inverse problem based on a full dispersive wave equation

    Gegentana Bao; Naranmandula Bao


    The inverse problem for harmonic waves and wave packets was studied based on a full dispersive wave equation. First, a full dispersive wave equation which describes wave propagation in nondissipative microstructured linear solids is established based on the Mindlin theory, and the dispersion characteristics are discussed. Second, based on the full dispersive wave equation, an inverse problem for determining the four unknown coefficients of wave equa- tion is posed in terms of the frequencies and corresponding wave numbers of four different harmonic waves, and the inverse problem is demonstrated with rigorous mathematical theory. Research proves that the coefficients of wave equation related to material properties can be uniquely determined in cases of normal and anomalous dispersions by measuring the frequen- cies and corresponding wave numbers of four different harmonic waves which propagate in a nondissipative microstructured linear solids.

  15. Source parameters of the 1989 Loma Prieta Earthquake determined from long-period Rayleigh waves

    Zhang, Jiajun; Lay, Thorne


    The source parameters of the Loma Prieta earthquake are determined using long-period Rayleigh waves recorded by USGS/ERIS, IDA/IRIS, and GEOSCOPE stations. The source mechanism is well-constrained by the Rayleigh wave radiation pattern, with a dip = 70 (±5)°, strike = 130 (±5)°, rake = 135 (±5)°, and moment = 3.4 (±0.5) × 1019 Nm (Mw = 7.0). This mechanism is generally consistent with independent body wave determinations. The most stable long-period waves, with periods from 200 to 275 s, indicate that the source process has a centroid time of about 10 s, somewhat longer than that indicated by body waves (about 5-6 s). This discrepancy cannot be uniquely attributed to source effects because of uncertainties in the propagation corrections. The importance of using surface waves with short propagation paths for analysis of moderate size earthquakes such as the Loma Prieta event is demonstrated by the unreasonably long source durations inferred from R3 arrivals.

  16. Accuracy of the water column approximation in numerically simulating propagation of teleseismic PP waves and Rayleigh waves

    Zhou, Yong; Ni, Sidao; Chu, Risheng; Yao, Huajian


    Numerical solvers of wave equations have been widely used to simulate global seismic waves including PP waves for modelling 410/660 km discontinuity and Rayleigh waves for imaging crustal structure. In order to avoid extra computation cost due to ocean water effects, these numerical solvers usually adopt water column approximation, whose accuracy depends on frequency and needs to be investigated quantitatively. In this paper, we describe a unified representation of accurate and approximate forms of the equivalent water column boundary condition as well as the free boundary condition. Then we derive an analytical form of the PP-wave reflection coefficient with the unified boundary condition, and quantify the effects of water column approximation on amplitude and phase shift of the PP waves. We also study the effects of water column approximation on phase velocity dispersion of the fundamental mode Rayleigh wave with a propagation matrix method. We find that with the water column approximation: (1) The error of PP amplitude and phase shift is less than 5 per cent and 9° at periods greater than 25 s for most oceanic regions. But at periods of 15 s or less, PP is inaccurate up to 10 per cent in amplitude and a few seconds in time shift for deep oceans. (2) The error in Rayleigh wave phase velocity is less than 1 per cent at periods greater than 30 s in most oceanic regions, but the error is up to 2 per cent for deep oceans at periods of 20 s or less. This study confirms that the water column approximation is only accurate at long periods and it needs to be improved at shorter periods.

  17. Control of Rayleigh-like waves in thick plate Willis metamaterials

    Diatta, André; Achaoui, Younes; Brûlé, Stéphane; Enoch, Stefan; Guenneau, Sébastien


    Recent advances in control of anthropic seismic sources in structured soil led us to explore interactions of elastic waves propagating in plates (with soil parameters) structured with concrete pillars buried in the soil. Pillars are 2 m in diameter, 30 m in depth and the plate is 50 m in thickness. We study the frequency range 5 to 10 Hz, for which Rayleigh wave wavelengths are smaller than the plate thickness. This frequency range is compatible with frequency ranges of particular interest in earthquake engineering. It is demonstrated in this paper that two seismic cloaks' configurations allow for an unprecedented flow of elastodynamic energy associated with Rayleigh surface waves. The first cloak design is inspired by some approximation of ideal cloaks' parameters within the framework of thin plate theory. The second, more accomplished but more involved, cloak design is deduced from a geometric transform in the full Navier equations that preserves the symmetry of the elasticity tensor but leads to Willis' equations, well approximated by a homogenization procedure, as corroborated by numerical simulations. The two cloaks's designs are strickingly different, and the superior efficiency of the second type of cloak emphasizes the necessity for rigour in transposition of existing cloaks's designs in thin plates to the geophysics setting. Importantly, we focus our attention on geometric transforms applied to thick plates, which is an intermediate case between thin plates and semi-infinite media, not studied previously. Cloaking efficiency (reduction of the disturbance of the wave wavefront and its amplitude behind an obstacle) and protection (reduction of the wave amplitude within the center of the cloak) are studied for ideal and approximated cloaks' parameters. These results represent a preliminary step towards designs of seismic cloaks for surface Rayleigh waves propagating in sedimentary soils structured with concrete pillars.

  18. Assessment of Reinforced Concrete Surface Breaking Crack Using Rayleigh Wave Measurement.

    Lee, Foo Wei; Chai, Hwa Kian; Lim, Kok Sing


    An improved single sided Rayleigh wave (R-wave) measurement was suggested to characterize surface breaking crack in steel reinforced concrete structures. Numerical simulations were performed to clarify the behavior of R-waves interacting with surface breaking crack with different depths and degrees of inclinations. Through analysis of simulation results, correlations between R-wave parameters of interest and crack characteristics (depth and degree of inclination) were obtained, which were then validated by experimental measurement of concrete specimens instigated with vertical and inclined artificial cracks of different depths. Wave parameters including velocity and amplitude attenuation for each case were studied. The correlations allowed us to estimate the depth and inclination of cracks measured experimentally with acceptable discrepancies, particularly for cracks which are relatively shallow and when the crack depth is smaller than the wavelength.

  19. Propagation of Rayleigh waves in anisotropic layer overlying a semi-infinite sandy medium

    P.C. Pal


    Full Text Available The present investigation deals with the propagation of Rayleigh waves in anisotropic layer overlying a sandy medium. Anisotropic material is in the nature of most general case i.e. of triclinic crystal and sandy medium is of alluvial soil type. The solutions for layer and half-space are obtained analytically. The displacement components in x and z directions are obtained for both the media. The dispersion relation is obtained subjected to certain boundary conditions. The special cases are considered. The numerical results are presented in the form of wave number and phase velocity (k − c analytical curves.

  20. Elastic properties of amorphous thin films studied by Rayleigh waves

    Schwarz, R.B.; Rubin, J.B.


    Physical vapor deposition in ultra-high vacuum was used to co-deposit nickel and zirconium onto quartz single crystals and grow amorphous Ni{sub 1-x}Zr{sub x} (0.1 < x < 0.87) thin film. A high-resolution surface acoustic wave technique was developed for in situ measurement of film shear moduli. The modulus has narrow maxima at x = 0. 17, 0.22, 0.43, 0.5, 0.63, and 0.72, reflecting short-range ordering and formation of aggregates in amorphous phase. It is proposed that the aggregates correspond to polytetrahedral atom arrangements limited in size by geometrical frustration.

  1. Gravity waves observation of wind field in stratosphere based on a Rayleigh Doppler lidar.

    Zhao, Ruocan; Dou, Xiankang; Sun, Dongsong; Xue, Xianghui; Zheng, Jun; Han, Yuli; Chen, Tingdi; Wang, Guocheng; Zhou, Yingjie


    Simultaneous wind and temperature measurements in stratosphere with high time-spatial resolution for gravity waves study are scarce. In this paper we perform wind field gravity waves cases in the stratosphere observed by a mobile Rayleigh Doppler lidar. This lidar system with both wind and temperature measurements were implemented for atmosphere gravity waves research in the altitude region 15-60 km. Observations were carried out for two periods of time: 3 months started from November 4, 2014 in Xinzhou, China (38.425°N,112.729°E) and 2 months started from October 7, 2015 in Jiuquan, China (39.741°N, 98.495°E) . The mesoscale fluctuations of the horizontal wind velocity and the two dimensional spectra analysis of these fluctuations show the presence of dominant oscillatory modes with wavelength of 4-14 km and period of around 10 hours in several cases. The simultaneous temperature observations make it possible to identify gravity wave cases from the relationships between different variables: temperature and horizontal wind. The observed cases demonstrate the Rayleigh Doppler Lidar's capacity to study gravity waves.

  2. Automatic Rayleigh scattering mapping system for optical quality evaluation of test masses for gravity wave detectors

    Yan, Zewu; Zhao, Chunnong; Ju, Li; Gras, Slawomir; Baringa, Pablo; Blair, David G.


    This article describes an automatic Rayleigh scattering mapping system (ARSMS), which enables quantitative high-resolution three-dimensional mapping of inhomogeneities in optical materials. The ARSMS allows large high-grade test mass samples for gravitational wave detectors to be evaluated to ensure that an adequate low level of scattering is achieved. The ARSMS combines proprietary camera software with data analysis software and control software to achieve fully automatic operation with graphical user interfaces. This article presents the instrument concept and examples of the output. Device mapping in all degrees of freedom is shown to be better than 0.5mm, with scattering sensitivity better than 0.5ppm/cm. This system is able to scan and map the Rayleigh scattering of large samples in both of cylindrical and rectangular samples using cylindrical and Cartesian coordinates.

  3. Parametric frequency fusion by inverse four-wave mixing

    Sylvestre, Thibaut


    This work reports the experimental observation of a new type of four-wave mixing in which frequency-degenerate weak signal and idler waves are generated by mixing two pump waves of different frequencies in a normally dispersive birefringent optical fiber. This parametric frequency fusion is what we believed the first experimental evidence of inverse four-wave mixing.

  4. Degenerate RS perturbation theory. [Rayleigh-Schroedinger energies and wave functions

    Hirschfelder, J. O.; Certain, P. R.


    A concise, systematic procedure is given for determining the Rayleigh-Schroedinger energies and wave functions of degenerate states to arbitrarily high orders even when the degeneracies of the various states are resolved in arbitrary orders. The procedure is expressed in terms of an iterative cycle in which the energy through the (2n + 1)-th order is expressed in terms of the partially determined wave function through the n-th order. Both a direct and an operator derivation are given. The two approaches are equivalent and can be transcribed into each other. The direct approach deals with the wave functions (without the use of formal operators) and has the advantage that it resembles the usual treatment of nondegenerate perturbations and maintains close contact with the basic physics. In the operator approach, the wave functions are expressed in terms of infinite-order operators which are determined by the successive resolution of the space of the zeroth-order functions.

  5. Rayleigh surface acoustic wave as an efficient heating system for biological reactions: investigation of microdroplet temperature uniformity.

    Roux-Marchand, Thibaut; Beyssen, Denis; Sarry, Frederic; Elmazria, Omar


    When a microdroplet is put on the Rayleigh surface acoustic wave path, longitudinal waves are radiated into the liquid and induce several phenomena such as the wellknown surface acoustic wave streaming. At the same time, the temperature of the microdroplet increases as it has been shown. In this paper, we study the temperature uniformity of a microdroplet heated by Rayleigh surface acoustic wave for discrete microfluidic applications such as biological reactions. To precisely ascertain the temperature uniformity and not interfere with the biological reaction, we used an infrared camera. We then tested the temperature uniformity as a function of three parameters: the microdroplet volume, the Rayleigh surface acoustic wave frequency, and the continuous applied radio frequency power. Based on these results, we propose a new device structure to develop a future lab on a chip based on reaction temperatures.

  6. Rayleigh Waves in Generalized Magneto-Thermo-Viscoelastic Granular Medium under the Influence of Rotation, Gravity Field, and Initial Stress

    A. M. Abd-Alla


    Full Text Available The surface waves propagation in generalized magneto-thermo-viscoelastic granular medium subjected to continuous boundary conditions has been investigated. In addition, it is also subjected to thermal boundary conditions. The solution of the more general equations are obtained for thermoelastic coupling. The frequency equation of Rayleigh waves is obtained in the form of a determinant containing a term involving the coefficient of friction of a granular media which determines Rayleigh waves velocity as a real part and the attenuation coefficient as an imaginary part, and the effects of rotation, magnetic field, initial stress, viscosity, and gravity field on Rayleigh waves velocity and attenuation coefficient of surface waves have been studied in detail. Dispersion curves are computed numerically for a specific model and presented graphically. Some special cases have also been deduced. The results indicate that the effect of rotation, magnetic field, initial stress, and gravity field is very pronounced.

  7. Dispersion of Rayleigh waves produced by nuclear explosions. Crustal structure of western Europe

    G. PAYO


    Full Text Available Most of the nuclear explosion fired near Novaya-Zemlya
    island from September 1961 to J a n u a r y 1963 (21 in total have been recorded
    on the seismographs of Toledo Observatory. The study of these records,
    mainly concerning the dispersion of Rayleigh waves, has been the purpose
    of this paper.
    A crust-mantle s t r u c t u r e for t h e Zemlya-Toledo p a t h has been determined
    by means of group velocity curves and especially by the phase velocity
    ones obtained from Rayleigh waves of explosions. This structure supposes
    a crust of about 40 kms thick with an upper sedimentary layer with a
    thickness of about 5,5 kms and a shear velocity of 2,3 km/sec.
    The average shear velocity in the granitic and basaltic layers jointly,
    is about 3,65 km/sec, permitting a small ambiguity at the position of the
    Conrad discontinuity between them.
    A velocity of 4,5 km/sec has been assigned for the underlying crust
    material, but a better agreement with the data recorded is obtained by
    taking 0.28 for the Poisson ratio value.
    Dispersion of Rayleigh waves of these explosions has been compared
    to the Rayleigh dispersion of some earthquakes of Eurasia, three of them
    with epicentral distances similar to those of the explosions and other four
    with the same azimuth in respect to that of Toledo-Zemlya, but more
    The results do not show any notable difference either in dispersion
    between explosion and earthquakes or in structure of the path considered.
    The phase velocity between Toledo and Malaga Observatories supports
    t h e same above structure for this short path.
    The velocity of Lg waves, which clearly appears on the record of the
    explosions, confirms this admitted structure, which serves to deduce t h e more
    probable transmission mechanism for these channel waves.
    Also atmospheric pressure waves have been recorded on the three

  8. Sensitivities of surface wave velocities to the medium parameters in a radially anisotropic spherical Earth and inversion strategies

    Sankar N. Bhattacharya


    Full Text Available Sensitivity kernels or partial derivatives of phase velocity (c and group velocity (U with respect to medium parameters are useful to interpret a given set of observed surface wave velocity data. In addition to phase velocities, group velocities are also being observed to find the radial anisotropy of the crust and mantle. However, sensitivities of group velocity for a radially anisotropic Earth have rarely been studied. Here we show sensitivities of group velocity along with those of phase velocity to the medium parameters VSV, VSH , VPV, VPH , h and density in a radially anisotropic spherical Earth. The peak sensitivities for U are generally twice of those for c; thus U is more efficient than c to explore anisotropic nature of the medium. Love waves mainly depends on VSH while Rayleigh waves is nearly independent of VSH . The sensitivities show that there are trade-offs among these parameters during inversion and there is a need to reduce the number of parameters to be evaluated independently. It is suggested to use a nonlinear inversion jointly for Rayleigh and Love waves; in such a nonlinear inversion best solutions are obtained among the model parameters within prescribed limits for each parameter. We first choose VSH, VSV and VPH within their corresponding limits; VPV and h can be evaluated from empirical relations among the parameters. The density has small effect on surface wave velocities and it can be considered from other studies or from empirical relation of density to average P-wave velocity.

  9. The thermal structure of cratonic lithosphere from global Rayleigh wave attenuation

    Dalton, Colleen A.; Bao, Xueyang; Ma, Zhitu


    The resolution of and level of agreement between different attenuation models have historically been limited by complexities associated with extracting attenuation from seismic-wave amplitudes, which are also affected by the source, the receiver, and propagation through velocity heterogeneities. For intermediate- and long-period Rayleigh waves, removing the amplitude signal due to focusing and defocusing effects is the greatest challenge. In this paper, three independent data sets of fundamental-mode Rayleigh wave amplitude are analyzed to investigate how three factors contribute to discrepancies between the attenuation models: uncertainties in the amplitude measurements themselves, variable path coverage, and the treatment of focusing effects. Regionalized pure-path and fully two-dimensional attenuation models are derived and compared. The approach for determining attenuation models from real data is guided by an analysis of amplitudes measured from synthetic spectral-element waveforms, for which the input Earth model is perfectly known. The results show that differences in the amplitude measurements introduce only very minor differences between the attenuation models; path coverage and the removal of focusing effects are more important. The pure-path attenuation values exhibit a clear dependence on tectonic region at shorter periods that disappears at long periods, in agreement with pure-path phase-velocity results obtained by inverting Rayleigh wave phase delays. The 2-D attenuation maps are highly correlated with each other to spherical-harmonic degree 16 and can resolve smaller features than the previous generation of global attenuation models. Anomalously low attenuation is nearly perfectly associated with continental cratons. Variations in lithospheric thickness are determined by forward modeling the global attenuation variations as a thermal boundary layer of variable thickness. Temperature profiles that satisfy the attenuation values systematically

  10. Shear wave velocity structure in North America from large-scale waveform inversions of surface waves

    Alsina, D.; Woodward, R. L.; Snieder, R. K.


    correcting for the crustal thickness the phase velocity perturbations obtained from the subsequent linear waveform inversion for the different period bands are converted to a three-layer model of S velocity perturbations (layer 1, 25-100 km; layer 2, 100-200 km; layer 3, 200-300 km). We have applied this method on 275 high-quality Rayleigh waves recorded by a variety of instruments in North America (IRIS/USGS, IRIS/IDA, TERRAscope, RSTN). Sensitivity tests indicate that the lateral resolution is especially good in the densely sampled western continental United States, Mexico, and the Gulf of Mexico.

  11. Shear wave velocity structure in North America from large-scale waveform inversions of surface waves

    Alsina, D.; Woodward, R.L.; Snieder, R.K.


    correcting for the crustal thickness the phase velocity perturbations obtained from the subsequent linear waveform inversion for the different period bands are converted to a three-layer model of S velocity perturbations (layer 1, 25-100 km; layer 2, 100-200 km) layer 3, 200-300 km). We have applied this method on 275 high-quality Rayleigh waves recorded by a variety of instruments in North America (IRIS/USGS, IRIS/IDA, TERRAscope, RSTN). Sensitivity tests indicate that the lateral resolution is especially good in the densely sampled western continental United States, Mexico, and the Gulf of Mexico.

  12. Full wavefield decomposition of high-frequency secondary microseisms reveals distinct arrival azimuths for Rayleigh and Love waves

    Gal, M.; Reading, A. M.; Ellingsen, S. P.; Koper, K. D.; Burlacu, R.


    In the secondary microseism band (0.1-1.0 Hz) the theoretical excitation of Rayleigh waves (Rg/LR), through oceanic wave-wave interaction, is well understood. For Love waves (LQ), the excitation mechanism in the secondary microseism band is less clear. We explore high-frequency secondary microseism excitation between 0.35 and 1 Hz by analyzing a full year (2013) of records from a three-component seismic array in Pilbara (PSAR), Australia. Our recently developed three-component waveform decomposition algorithm (CLEAN-3C) fully decomposes the beam power in slowness space into multiple point sources. This method allows for a directionally dependent power estimation for all separable wave phases. In this contribution, we compare quantitatively microseismic energy recorded on vertical and transverse components. We find the mean power representation of Rayleigh and Love waves to have differing azimuthal distributions, which are likely a result of their respective generation mechanisms. Rayleigh waves show correlation with convex coastlines, while Love waves correlate with seafloor sedimentary basins. The observations are compared to the WAVEWATCH III ocean model, implemented at the Institut Français de Recherche pour l'Exploitation de la Mer (IFREMER), which describes the spatial and temporal characteristics of microseismic source excitation. We find Love wave energy to originate from raypaths coinciding with seafloor sedimentary basins where strong Rayleigh wave excitation is predicted by the ocean model. The total power of Rg waves is found to dominate at 0.35-0.6 Hz, and the Rayleigh/Love wave power ratio strongly varies with direction and frequency.

  13. High quality broadband spatial reflections of slow Rayleigh surface acoustic waves modulated by a graded grooved surface

    Xu, Yanlong


    We report high quality broadband spatial reflections of Rayleigh surface acoustic waves (SAWs) through a graded grooved surface. High quality means that no wave is allowed to transmit and the incident wave is nearly all reflected to the input side. The graded grooved surface is structured by drilling one dimensional array of graded grooves with increased depths on a flat surface. We investigate SAW dispersion relations, wave field distribution at several typical SAW wavelengths, and time evolution of a Gaussian pulse through the graded grooved surface. Results show that the input broadband Rayleigh SAWs can be slowed, spatially enhanced and stopped, and finally reflected to the input side. The study suggests that engraving the flat surface can be used as an efficient and economical way to manipulate Rayleigh SAWs, which has potential application in novel SAW devices such as filters, reflectors, sensors, energy harvesters, and diodes.

  14. Resonant excitation of coupled Rayleigh waves in a short and narrow fluid channel clad between two identical metal plates

    Victor M. García-Chocano


    Full Text Available Transmission of ultrasonic waves through a slit between two water immersed brass plates is studied for sub-wavelength plate thicknesses and slit apertures. Extraordinary high absorption is observed at discrete frequencies corresponding to resonant excitation of Rayleigh waves on the both sides of the channel. The coupling of the Rayleigh waves occurs through the fluid and the corresponding contribution to the dispersion has been theoretically derived and also experimentally confirmed. Symmetric and anti-symmetric modes are predicted but only the symmetric mode resonances have been observed. It follows from the dispersion equation that the coupled Rayleigh waves cannot be excited in a channel with apertures less than the critical one. The calculated critical aperture is in a good agreement with the measured acoustic spectra. These findings could be applied to design a broadband absorptive metamaterial.

  15. Broad-band Rayleigh wave phase velocity maps (10-150 s) across the United States from ambient noise data

    Zhao, Kaifeng; Luo, Yinhe; Xie, Jun


    In this study, we demonstrate the feasibility of imaging broad-band (10-150 s) Rayleigh wave phase velocity maps on a continental scale using ambient noise tomography (ANT). We obtain broad-band Rayleigh waves from cross-correlations of ambient noise data between all station pairs of USArray and measure the dispersion curves from these cross-correlations at a period band of 10-150 s. The large-scale dense USArray enables us to obtain over 500 000 surface wave paths which cover the contiguous United States densely. Using these paths, we generate Rayleigh wave phase velocity maps at 10-150 s periods. Our phase velocity maps are similar to other reported phase velocity maps based on ambient noise data at short periods (phase velocity maps from ANT can be used to construct 3-D lithospheric and asthenospheric velocity structures.

  16. Rayleigh and acoustic gravity waves detection on magnetograms during the Japanese Tsunami, 2011

    Klausner, Virginia; Muella, Marcio T A H; Mendes, Odim; Domingues, Margarete O; Papa, Andres R R


    The continuous geomagnetic field survey holds an important potential in future prevention of tsunami damages, and also, it could be used in tsunami forecast. In this work, we were able to detected for the first time Rayleigh and ionospheric acoustic gravity wave propagation in the Z-component of the geomagnetic field due to the Japanese tsunami, 2011 prior to the tsunami arrival. The geomagnetic measurements were obtained in the epicentral near and far-field. Also, these waves were detected within minutes to few hours of the tsunami arrival. For these reasons, these results are very encouraging, and confirmed that the geomagnetic field monitoring could play an important role in the tsunami warning systems, and also, it could provide additional information in the induced ionospheric wave propagation models due to tsunamis.

  17. Modelling of Rayleigh-type seam waves in disturbed coal seams and around a coal mine roadway

    Essen, Katja; Bohlen, Thomas; Friederich, Wolfgang; Meier, Thomas


    Wave propagation in coal seams is numerically modelled in order to identify approaches towards the reconnaissance beyond the heading face of an advancing coal mine roadway. Complete synthetic wavefields including P-SV body waves and Rayleigh-type seam waves are calculated using a Green's function approach for simple, laterally homogeneous models and a parallel elastic 2-D/3-D finite difference modelling code for more realistic geometries. For a simple three-layer model the wavefield within the seam is dominated by a fundamental Rayleigh seam mode symmetrical with respect to the centre of the seam on the vertical component and antisymmetrical on the horizontal component. If the seam contains an interleaved dirt band with higher velocities and density, higher modes dominate the wave propagation, depending on the thickness of the dirt band. Wave propagation in laterally inhomogeneous coal seam models with disturbances like seam ends, faults, thinning, washouts and seam splitting is strongly influenced by the type of disturbance. Amplitudes of seam waves reflected from these disturbances strongly depend on the fault throw and the degree of thinning or washout. In some cases, conversion to higher modes can occur. In all investigated models, those Rayleigh seam wave phases are preferably reflected, which have frequencies above the fundamental mode Airy phase. Lower frequency phases are preferably transmitted. However, seam waves are not reflected from a seam splitting disturbance. Thus a detection of seam splitting with reflected seam waves appears to be impossible. FD computations for 3-D models containing an ending tunnel parallel to the seam and a source beyond the heading face of the tunnel show that seam waves are converted into Rayleigh waves at the tunnel face. They propagate along the surface of the tunnel and interfere with the seam waves propagating beside the tunnel. This effect has to be taken into account for subsequent treatment of experimental data, where

  18. Crustal structure of northern Italy from the ellipticity of Rayleigh waves

    Berbellini, Andrea; Morelli, Andrea; Ferreira, Ana M. G.


    Northern Italy is a diverse geological region, including the wide and thick Po Plain sedimentary basin, which is bounded by the Alps and the Apennines. The seismically slow shallow structure of the Po Plain is difficult to retrieve with classical seismic measurements such as surface wave dispersion, yet the detailed structure of the region greatly affects seismic wave propagation and hence seismic ground shaking. Here we invert Rayleigh wave ellipticity measurements in the period range 10-60 s for 95 stations in northern Italy using a fully non linear approach to constrain vertical vS,vP and density profiles of the crust beneath each station. The ellipticity of Rayleigh wave ground motion is primarily sensitive to shear-wave velocity beneath the recording station, which reduces along-path contamination effects. We use the 3D layering structure in MAMBo, a previous model based on a compilation of geological and geophysical information for the Po Plain and surrounding regions of northern Italy, and employ ellipticity data to constrain vS,vP and density within its layers. We show that ellipticity data from ballistic teleseismic wave trains alone constrain the crustal structure well. This leads to MAMBo-E, an updated seismic model of the region's crust that inherits information available from previous seismic prospection and geological studies, while fitting new seismic data well. MAMBo-E brings new insights into lateral heterogeneity in the region's subsurface. Compared to MAMBo, it shows overall faster seismic anomalies in the region's Quaternary, Pliocene and Oligo-Miocene layers and better delineates the seismic structures of the Po Plain at depth. Two low velocity regions are mapped in the Mesozoic layer in the western and eastern parts of the Plain, which seem to correspond to the Monferrato sedimentary basin and to the Ferrara-Romagna thrust system, respectively.

  19. Constraints on the variable subglacial structure of Whillans Ice Stream from ambient noise Rayleigh wave H/V ratios

    Pratt, M. J.; Shen, W.; Wiens, D.; Winberry, J. P.; Anandakrishnan, S.


    Horizontal-to-vertical (H/V) ellipticity ratios of Rayleigh waves have been used to determine shallow (reflection imaging showing a deeper sedimentary package that extends to an unknown depth. It is also known that the frictional properties of the WIS ice-bed interface at 700 m depth are highly heterogeneous, including stick-spots of high friction, possibly as a result of compacted sediment or bedrock, and active subglacial lakes where frictional coefficients are effectively zero. Ambient noise cross-correlations are calculated between all station pairs, restricting the minimum interstation distance to 20 km, as well as constraining valid H/V ratios of radial and vertical sources between the same station pair to wave energy with good signal-to-noise between 6 s and 20 s that are sensitive to the shear velocity of the shallowest sedimentary layers beneath the ice stream and is combined with average phase and group velocity of the area to help constrain the inversion. H/V ratio modeling results suggest that ratios are highly susceptible to sedimentary layer thickness. Ratios also increase over the observed frequency band with the presence of a shallow, saturated sedimentary layer with high Vp/Vs. In preliminary results, we observe an increase in H/V ratio towards the grounding line as well as at stations where hydro-potential surface is high. These higher ratios can be attributed to higher water content within sediments, or an increase in the sedimentary layer thickness.

  20. Lateral heterogeneity and azimuthal anistropy of the upper mantle: Love and Rayleigh waves 100-250 sec

    Tanimoto, T.; Anderson, D. L.


    The lateral heterogeneity and apparent anisotropy of the upper mantle are studied by measuring Rayleigh and Love wave phase velocities in the period range 100-250 sec. Spherical harmonic descriptions of the lateral heterogeneity are obtained for order and degree up to 1=m=10. Slow regions are evident at the East Pacific rise, northeast Africa, Tibet, Tasman sea, southwestern North America and triple junctions in the Northern Atlantic and Indian oceans. Fast regions occur in Australia, western Pacific and the eastern Atlantic. Details which are not evident in previous studies include two fast regions in the central Pacific and the subduction zone in the Scotia Arc region. Inversion for azimuthal dependence showed (1) little correlation between the fast phase velocity directions and the plate motion vector in plate interiors, but (2) correlation of the fast direction with the perpendicular direction to trenches and ridges. Phase velocity is high when waves propagate perpendicular to these structures. Severe tradeoffs exist between heterogeneity and azimuthal dependence because of the yet unsatisfactory path coverage.

  1. Lateral heterogeneity and azimuthal anisotropy of the upper mantle - Love and Rayleigh waves 100-250 sec

    Tanimoto, T.; Anderson, D. L.


    The lateral heterogeneity and apparent anisotropy of the upper mantle are studied by measuring Rayleigh and Love wave phase velocities in the period range 100-250 sec. Spherical harmonic descriptions of the lateral heterogeneity are obtained for order and degree up to 1=m=10. Slow regions are evident at the East Pacific rise, northeast Africa, Tibet, Tasman sea, southwestern North America and triple junctions in the Northern Atlantic and Indian oceans. Fast regions occur in Australia, western Pacific and the eastern Atlantic. Details which are not evident in previous studies include two fast regions in the central Pacific and the subduction zone in the Scotia Arc region. Inversion for azimuthal dependence showed (1) little correlation between the fast phase velocity directions and the plate motion vector in plate interiors, but (2) correlation of the fast direction with the perpendicular direction to trenches and ridges. Phase velocity is high when waves propagate perpendicular to these structures. Severe tradeoffs exist between heterogeneity and azimuthal dependence because of the yet unsatisfactory path coverage.

  2. Crust and upper mantle velocity structure of the northwestern Indian Peninsular Shield from inter-station phase velocities of Rayleigh and Love waves

    Gaddale Suresh


    Full Text Available We measure the inter-station Rayleigh and Love wave phase velocities across the northwestern Indian Peninsular shield (NW-IP through cross-correlation and invert these velocities to evaluate the underneath crust and upper mantle velocity structure down to 400 km. We consider a cluster of three stations in the northern tip of the Peninsula and another cluster of eight stations in the south. We measure phase velocities along 28 paths for Rayleigh waves and 17 paths for Love waves joining two stations with one from each cluster and using broadband records of earthquakes which lie nearly on the great circle joining the pair of stations. The phase velocities are in the period range of 10 to 275 s for Rayleigh waves and of 10 to 120 s for Love waves. The isotropic model obtained through inversion of the phase velocities indicates 199.1 km thick lithosphere with 3-layered crust of thickness 36.3 km; the top two layers have nearly same velocities and both constitute the upper crust with thickness of 12.6 km. The upper crust is mafic, whereas the lower crust is felsic. In the mantle lid, velocities increase with depth. The velocities of mantle lid beneath NW-IP is lower than those beneath south Indian Peninsula showing the former is hotter than the later perhaps due to large Phanerozoic impact on NW-IP. The significant upper mantle low velocity zone beneath NW-IP indicates high temperature which could be attributed to the past existence of a broad plume head at the west-central part of the Peninsula.

  3. Constraints on Shear Velocity in the Cratonic Upper Mantle From Rayleigh Wave Phase Velocity

    Hirsch, A. C.; Dalton, C. A.


    In recent years, the prevailing notion of Precambrian continental lithosphere as a thick boundary layer (200-300 km), defined by a depleted composition and a steady-state conductively cooled temperature structure, has been challenged by several lines of seismological evidence. One, profiles of shear velocity with depth beneath cratons exhibit lower wave speed at shallow depths and higher wave speed at greater depths than can be explained by temperature alone. These profiles are also characterized by positive or flat velocity gradients with depth and anomalously high attenuation in the uppermost mantle, both of which are difficult to reconcile with the low temperatures and large thermal gradient expected with a thermal boundary layer. Two, body-wave receiver-function studies have detected a mid-lithospheric discontinuity that requires a large and abrupt velocity decrease with depth in cratonic regions that cannot be achieved by thermal gradients alone. Here, we used forward-modeling to identify the suite of shear-velocity profiles that are consistent with phase-velocity observations made for Rayleigh waves that primarily traversed cratons in North America, South America, Africa, and Australia. We considered two approaches; with the first, depth profiles of shear velocity were predicted from thermal models of the cratonic upper mantle that correspond to a range of assumed values of mantle potential temperature, surface heat flow, and radiogenic heat production in the crust and upper mantle. With the second approach, depth profiles of shear velocity were randomly generated. In both cases, Rayleigh wave phase velocity was calculated from the Earth models and compared to the observed values. We show that it is very difficult to match the observations with an Earth model containing a low-velocity zone in the upper mantle; instead, the best-fit models contain a flat or positive velocity gradient with depth. We explore the implications of this result for the thermal and

  4. A theoretical study of the propagation of Rayleigh waves in a functionally graded piezoelectric material (FGPM).

    Ben Salah, Issam; Njeh, Anouar; Ben Ghozlen, Mohamed Hédi


    An exact approach is used to investigate Rayleigh waves in a functionally graded piezoelectric material (FGPM) layer bonded to a semi infinite homogenous solid. The piezoelectric material is polarized when the six fold symmetry axis is put along the propagation direction x(1). The FGPM character imposes that the material properties change gradually with the thickness of the layer. Contrary to the analytical approach, the adopted numerical methods, including the ordinary differential equation (ODE) and the stiffness matrix method (SMM), treat separately the electrical and mechanical gradients. The influences of graded variations applied to FGPM film coefficients on the dispersion curves of Rayleigh waves are discussed. The effects of gradient coefficients on electromechanical coupling factor, displacement fields, stress distributions and electrical potential, are reported. The obtained deviations in comparison with the ungraded homogenous film are plotted with respect to the dimensionless wavenumber. Opposite effects are observed on the coupling factor when graded variations are applied separately. A particular attention has been devoted to the maximum of the coupling factor and it dependence on the stratification rate and the gradient coefficient. This work provides with a theoretical foundation for the design and practical applications of SAW devices with high performance.

  5. Control of Rayleigh-like waves in thick plate Willis metamaterials

    Diatta, Andre; Brûlé, Stéphane; Enoch, Stefan; Guenneau, Sébastien


    Recent advances in control of anthropic seismic sources in structured soil led us to explore interactions of elastic waves propagating in plates (with soil parameters) structured with concrete pillars buried in the soil. Pillars are $40$ m in depth and the plate is $100$ m in thickness, so that typical frequencies under study are in the frequency range 4 to 8 Hz, which is compatible with frequency ranges of particular interest in earthquake engineering. It is demonstrated in this paper that two seismic cloaks' configurations allow for an unprecedented flow of elastodynamic energy associated with Rayleigh surface waves. These designs are inspired by some ideal cloaks' parameters deduced from a geometric transform in the Navier equations that preserves the symmetry of the elasticity tensor but leads to Willis' equations as corroborated by numerical simulations. Importantly, we focus our attention on geometric transforms applied to thick plates, which is an intermediate case between thin plates and semi-infinite...

  6. Assessment of precipitation in alloy steel using nonlinear Rayleigh surface waves

    Thiele, Sebastian; Matlack, Kathryn H.; Kim, Jin-Yeon; Qu, Jianmin; Wall, James J.; Jacobs, Laurence J.


    Nonlinear ultrasonic waves have shown to be sensitive to various microstructural changes in metals including coherent precipitates; these precipitates introduce a strain field in the lattice structure. The thermal aging of certain alloy steels leads to the formation of coherent precipitates, which pin dislocations and contribute to the generation of a second harmonic component. A precipitate hardenable material namely 17-4 PH stainless steel is thermally treated in this research to obtain different precipitation stages, and then the influence of precipitates on the acoustic nonlinearity parameter is assessed. Conclusions about the microstrucutural changes in the material are drawn based on the results from a nonlinear Rayleigh surface wave measurement and complementary thermo-electric power, hardness and ultrasonic velocity measurements. The results show that the nonlinear parameter is sensitive to coherent precipitates in the material and moreover that precipitation characteristics can be characterized based on the obtained experimental data.

  7. Inverse problems and inverse scattering of plane waves

    Ghosh Roy, Dilip N


    The purpose of this text is to present the theory and mathematics of inverse scattering, in a simple way, to the many researchers and professionals who use it in their everyday research. While applications range across a broad spectrum of disciplines, examples in this text will focus primarly, but not exclusively, on acoustics. The text will be especially valuable for those applied workers who would like to delve more deeply into the fundamentally mathematical character of the subject matter.Practitioners in this field comprise applied physicists, engineers, and technologists, whereas the theory is almost entirely in the domain of abstract mathematics. This gulf between the two, if bridged, can only lead to improvement in the level of scholarship in this highly important discipline. This is the book''s primary focus.

  8. Detection of near-surface cavities by generalized S-transform of Rayleigh waves

    Shao, Guang-zhou; Tsoflias, George P.; Li, Chang-jiang


    The near-surface cavities can cause a huge hidden trouble for urban infrastructure construction, such as, foundation settlement and roadbed subsidence, and so on. So, it is an important task to detect the underground cavities effectively for many engineering projects. At the same time, because of the complexity of near-surface materials and the limited resolution of geophysical methods, detecting the location of the hidden cavities quantitatively is still a technical challenge which needs to be studied further. Base on the study of Xia et al. (Xia et al., 2007), we performed a little modification to the travel time equation for the Rayleigh-wave diffraction. We put forward another way to detect the shallow subsurface voids. The generalized S-transform was adopted to extract the arrival times of the diffracted Rayleigh waves from the near and far-offset boundaries of the void at a certain receiver. Then the arrival times were used to calculate the boundary locations of the void. Three half-space void models and a two-layered void model were used to demonstrate the feasibility and effect of detecting a void with the generalized S-transform. A rotated staggered-grid finite-difference method was adopted in wave field modeling to obtain the synthetic seismic record. Finally, a real world field data was used to verify the detecting effect. The theoretical models and the real world example showed that it is feasible and effective to use the generalized S-transform to detect the near-surface cavities.

  9. Optical coherence elastography assessment of corneal viscoelasticity with a modified Rayleigh-Lamb wave model.

    Han, Zhaolong; Li, Jiasong; Singh, Manmohan; Wu, Chen; Liu, Chih-Hao; Raghunathan, Raksha; Aglyamov, Salavat R; Vantipalli, Srilatha; Twa, Michael D; Larin, Kirill V


    The biomechanical properties of the cornea play a critical role in forming vision. Diseases such as keratoconus can structurally degenerate the cornea causing a pathological loss in visual acuity. UV-A/riboflavin corneal collagen crosslinking (CXL) is a clinically available treatment to stiffen the cornea and restore its healthy shape and function. However, current CXL techniques do not account for pre-existing biomechanical properties of the cornea nor the effects of the CXL treatment itself. In addition to the inherent corneal structure, the intraocular pressure (IOP) can also dramatically affect the measured biomechanical properties of the cornea. In this work, we present the details and development of a modified Rayleigh-Lamb frequency equation model for quantifying corneal biomechanical properties. After comparison with finite element modeling, the model was utilized to quantify the viscoelasticity of in situ porcine corneas in the whole eye-globe configuration before and after CXL based on noncontact optical coherence elastography measurements. Moreover, the viscoelasticity of the untreated and CXL-treated eyes was quantified at various IOPs. The results showed that the stiffness of the cornea increased after CXL and that corneal stiffness is close to linear as a function of IOP. These results show that the modified Rayleigh-Lamb wave model can provide an accurate assessment of corneal viscoelasticity, which could be used for customized CXL therapies.

  10. Application of negative velocity dispersion curves to the distinction between layer and substrate Rayleigh waves

    Hadjoub, Zahia; Touati, Ibtissem; Doghmane, Malika; Doghmane, Abdellaziz


    This work concerns the investigation of loading layers/substrate structures in order to determine the critical thickness at which Rayleigh wave characteristics of layers can be completely distinguished from those of the substrates. To do so, we first calculate Rayleigh velocity dispersion curves of several thin film materials (about thirty) deposited on different slow and fast substrates (Be, Al 2O 3, AlN, Si, SiO 2, Mg, SiC, TiN, WC and Pyrex). Then, from the beginning of curve saturation (corresponding to the onset of intrinsic layer characteristics) we deduced normalized thickness transition for all layers/substrates combinations. Thus, we were able to deduce an analytical linear expression relating the critical thickness to combined effects of densities and velocities of both layers and substrates. Such a simple relation can be used, as an alternative method, to predict the transition critical thickness for any layer/substrate combination without the usual lengthy calculation of dispersion curves. To cite this article: Z. Hadjoub et al., C. R. Physique 9 (2008).


    Je-Woong Park; Do-Jung Kim; Kwang-Hee Im; Sang-Kyu Park; David K.Hsu; Adam H.Kite; Sun-Kyu Kim; Kil-Sung Lee; In-Young Yang


    It was found that a pitch-catch signal was more sensitive than normal incidence backwall echo of longitudinal wave to subtle flaw conditions in the composites (damages,fiber orientation,low level porosity,ply waviness,and cracks).Both the strength and stiffness depend on the fiber orientation and porosity volume in the composites.The porosity content of a composite structure is critical to the strength and performance of the structure in general.The depth of the sampling volume where the pitch-catch signal came from was relatively shallow with the head to-head miniature Rayleigh probes,but the depth can be increased by increasing the separation distance of the transmitting and receiving probes.Also,a method was utilized to determine the porosity content of a composite lay-up by processing micrograph images of the laminate.A free software package was utilized to process micrograph images of the test sample.The results from the image processing method were compared with existing data.Beam profile was characterized in unidirectional CFRP(carbon fiber reinforced plastics) using pitch-catch Rayleigh probes and the one-sided pitch-catch technique was utilized to produce C-scan images with the aid of the automatic scanner.

  12. Rayleigh's, Stoneley's, and Scholte's Interface Waves in Elastic Models Using a Boundary Element Method

    Esteban Flores-Mendez


    Full Text Available This work is focused on studying interface waves for three canonical models, that is, interfaces formed by vacuum-solid, solid-solid, and liquid-solid. These interfaces excited by dynamic loads cause the emergence of Rayleigh's, Stoneley's, and Scholte's waves, respectively. To perform the study, the indirect boundary element method is used, which has proved to be a powerful tool for numerical modeling of problems in elastodynamics. In essence, the method expresses the diffracted wave field of stresses, pressures, and displacements by a boundary integral, also known as single-layer representation, whose shape can be regarded as a Fredholm's integral representation of second kind and zero order. This representation can be considered as an exemplification of Huygens' principle, which is equivalent to Somigliana's representation theorem. Results in frequency domain for the three types of interfaces are presented; then, using the fourier discrete transform, we derive the results in time domain, where the emergence of interface waves is highlighted.

  13. Rayleigh surface wave interaction with the 2D exciton Bose-Einstein condensate

    Boev, M. V.; Kovalev, V. M., E-mail: [Russian Academy of Sciences, Institute of Semiconductor Physics, Siberian Branch (Russian Federation)


    We describe the interaction of a Rayleigh surface acoustic wave (SAW) traveling on the semiconductor substrate with the excitonic gas in a double quantum well located on the substrate surface. We study the SAW attenuation and its velocity renormalization due to the coupling to excitons. Both the deformation potential and piezoelectric mechanisms of the SAW-exciton interaction are considered. We focus on the frequency and excitonic density dependences of the SAW absorption coefficient and velocity renormalization at temperatures both above and well below the critical temperature of Bose-Einstein condensation of the excitonic gas. We demonstrate that the SAW attenuation and velocity renormalization are strongly different below and above the critical temperature.

  14. Crustal thinning between the Ethiopian and East African Plateaus from modeling Rayleigh wave dispersion

    Benoit, M H; Nyblade, A A; Pasyanos, M E


    The East African and Ethiopian Plateaus have long been recognized to be part of a much larger topographic anomaly on the African Plate called the African Superswell. One of the few places within the African Superswell that exhibit elevations of less than 1 km is southeastern Sudan and northern Kenya, an area containing both Mesozoic and Cenozoic rift basins. Crustal structure and uppermost mantle velocities are investigated in this area by modeling Rayleigh wave dispersion. Modeling results indicate an average crustal thickness of 25 {+-} 5 km, some 10-15 km thinner than the crust beneath the adjacent East African and Ethiopian Plateaus. The low elevations can therefore be readily attributed to an isostatic response from crustal thinning. Low Sn velocities of 4.1-4.3 km/s also characterize this region.

  15. Single-scattering parabolic equation solutions for elastic media propagation, including Rayleigh waves.

    Metzler, Adam M; Siegmann, William L; Collins, Michael D


    The parabolic equation method with a single-scattering correction allows for accurate modeling of range-dependent environments in elastic layered media. For problems with large contrasts, accuracy and efficiency are gained by subdividing vertical interfaces into a series of two or more single-scattering problems. This approach generates several computational parameters, such as the number of interface slices, an iteration convergence parameter τ, and the number of iterations n for convergence. Using a narrow-angle approximation, the choices of n=1 and τ=2 give accurate solutions. Analogous results from the narrow-angle approximation extend to environments with larger variations when slices are used as needed at vertical interfaces. The approach is applied to a generic ocean waveguide that includes the generation of a Rayleigh interface wave. Results are presented in both frequency and time domains.

  16. Development of nondestructive system for detecting the cracks in KTX brake disk using Rayleigh wave

    Kim, Min Soo; Lee, Ho Yong [Korea Railroad Research Institute, Uiwang (Korea, Republic of); Yeom, Yun Taek; Park, Jin Hyun; Song, Sung Jing; Kim, Hak Joon [Dept. of Mechanical Engineering, Sungkyunkwan University, Suwon (Korea, Republic of); Kwon, Sung Duck [Dept. of Physics, Andong National University, Andong (Korea, Republic of)


    Recently, KTX (Korean Train Express) train stoppage accidents were mainly caused by malfunctioning equipment, aging and cracking of railway vehicles, crack breakages of brake disks, and breakages of brake disks. Breakage of brake disk can cause large-scale casualties such as high-speed collision and concern about derailment by hitting lower axle and wheel. Therefore, in this study, a brake disk with solid and ventilation type, which is the brake disk of a KTX train was modeled, and a dynamometer system was constructed to operate the disk. A Rayleigh wave was used to inspect the surface of the brake disk. An ultrasonic inspection module was developed for the brake disk by using a local immersion method due to the difficulty involved in ultrasonic inspection using an existing immersion method. In addition, the surface defects of the brake disk were evaluated using a dynamometer mock-up system and an ultrasonic inspection module of the brake disk.

  17. Rayleigh scattering in sapphire test mass for laser interferometric gravitational-wave detectors:. II: Rayleigh scattering induced noise in a laser interferometric-wave detector

    Benabid, F.; Notcutt, M.; Ju, L.; Blair, D. G.


    We present the level of noise induced by Rayleigh-scattered light from sapphire test mass, the limit of scattering loss on build-up power inside the interferometer and finally the tolerable absorption loss in order to meet the specification of the interferometer sensitivity. The results show that the Rayleigh scattering induced noise remains below h˜10 -25 Hz -1/2 and a higher tolerance on the absorption level in sapphire substrate compared with silica substrate.

  18. Temperature Frequency Characteristics of Hexamethyldisiloxane (HMDSO) Polymer Coated Rayleigh Surface Acoustic Wave (SAW) Resonators for Gas-Phase Sensor Applications

    Ekaterina I. Radeva; Esmeryan, Karekin D.; Avramov, Ivan D.


    Temperature induced frequency shifts may compromise the sensor response of polymer coated acoustic wave gas-phase sensors operating in environments of variable temperature. To correct the sensor data with the temperature response of the sensor the latter must be known. This study presents and discusses temperature frequency characteristics (TFCs) of solid hexamethyldisiloxane (HMDSO) polymer coated sensor resonators using the Rayleigh surface acoustic wave (RSAW) mode on ST-cut quartz. Using ...

  19. Mapping buried parts of a megalithic tomb with multichannel analysis of Rayleigh-waves and GPR

    Wilken, D.; Erkul, E.; Glomb, V.; Rabbel, W.


    The objective of the presented study was to image buried parts of a megalithic tomb in northern Germany with GPR and multichannel analysis of surface-waves (MASW). The latter method was applied with the aim of testing its feasibility when used on intermediate scale archaeological targets. As we do not expect MASW of being able to resolve archaeological objects in terms of inverted velocity structure, we look for spectral effects due to subsurface heterogeneity. Identifying and mapping these effects would give a distribution of possibly archaeological objects. The presented seismic dataset shows an amplitude shift between normal and a guided Rayleigh-wave mode. When mapped along parallel profiles the spatial distribution of this effect matches the geometry of the grave. The observed anomalies show good correlation to GPR results that included strong reflectors inside the grave border. Elastic finite difference modelling of the surface-wave propagation showed that the spectral effect can be reproduced by a compacted or bulked column above the GPR anomaly depth indicating that the observed anomalies may be caused by construction activities or load effects during multiple construction phases of the tomb. Observed GPR reflectors thus indicate the bottom of the disturbed zones and MASW effects map the distribution of disturbed subsoil columns.

  20. Imaging Rayleigh Wave Attenuation and Phase Velocity beneath North America with USArray

    Bao, X.; Dalton, C. A.; Jin, G.; Gaherty, J. B.


    The EarthScope USArray provides an opportunity to obtain detailed images of the continental upper mantle of United States at a novel scale. The majority of mantle models derived from USArray data contain spatial variations in velocity; however, little is known about the attenuation structure of the North American upper mantle. Joint interpretation of seismic attenuation and velocity models can improve upon the interpretations based only on velocity, and provide important constraints on the temperature, composition, melt content, and volatile content of the mantle. In this study, Rayleigh wave travel time and amplitude are measured using an interstation cross-correlation version of the Generalized Seismological Data Functional algorithm, which takes advantage of waveform similarity at nearby stations. Our data are from 670 large teleseismic earthquakes that occurred from 2006 to 2014 and were recorded by 1,764 Transportable Array stations. More than 4.8 million measurements at periods between 20 and 100 s are collected into our database. Isolating the signal of attenuation in the amplitude observations is challenging because amplitudes are sensitive to a number of factors in addition to attenuation, such as focusing/defocusing and local site amplification. We generate several Rayleigh wave attenuation maps at each period, using several different approaches to account for source and receiver effects on amplitude. This suite of attenuation maps allows us to distinguish between the robust features in the maps and the features that are sensitive to the treatment of source and receiver effects. We apply Helmholtz surface-wave tomography (Lin et al., 2012) to determine velocity and attenuation maps. A significant contrast in velocity and attenuation is observed in the transition between the western and central United States along the Rocky Mountain front. We find low Q values in the western US, along the eastern coast, and the Gulf plain. These areas are also

  1. Electromagnetic fields induced at the seafloor by Rayleigh-Stoneley waves

    Webb, S.; Cobb, C.


    We model oceanic acoustic and seismic disturbances as Rayeigh-Stoneley waves in the layered medium consisting of ocean, sediment and rock. The waves induce electromagnetic fields because of motion of conducting materials through the geomagnetic field. Low-frequency disturbances in deep water are efficient electromagnetic generators because the motions are coherent over large volumes of highly conducting seawater. For wave frequencies below 0.1 Hz in deep water, the geomagnetic field is nearly frozen to the moving water. Consequently, the electric field measured by a voltmeter attached to the seabed is approximately x F, where is the difference between the velocity of the water and of the voltmeter itself as it is moved by the motion of the seafloor, and F is the geomagnetic field. This result applied to Love waves suggests that the electric field will result largely from the movement of the detector but detailed calculations have not been made. Although the fields are weak they should be detectable because the main interference is from ionospheric sources and the fields from, these sources are greatly attenuated at the seabed by the overlying oceanic shield. The effectiveness of the shield diminishes sharply at frequencies below 0.03 Hz. At high frequencies the principal limitation to detectability is in the inherent noise level of detectors whether electric or magnetic. At present, electric detectors are more effective than magnetic. They appear to be competitive with accelerometers for seismic detection in the deep ocean in a restricted frequency band near 0.05 Hz. A layer of unconsolidated sediment underlying the ocean profoundly affects the dispersion relation of Rayleigh-Stonely waves and thereby affects the electromagnetic induction process.

  2. Identification of Upper Crustal Structures Beneath Central Java, Indonesia from of Surface Wave Dispersion Inversion

    Zulhan, Zulfakriza; Saygin, Erdinc; Cummins, Phil; Widiyantoro, Sri; Nugraha, Andri Dian; Luehr, Birger-G.; Bodin, Thomas


    Our previous study on MERAMEX data (Zulfakriza et al., 2014) obtained features of the tomographic images which correlate well with the surface geology of central Java in periods between 1 to 12 sec. Kendeng Basin and active volcanoes in the central part of this region are clearly imaged with low group velocities with values around 0.8 km/sec, while the carbonate structures in the southern part of the region correspond to higher group velocities in the range of 1.8 to 2.0 km/sec. In this current study, we invert dispersion curves obtained from seismic noise tomography to estimate shear wave-depth profiles of the region. The results are used to discuss the spatial variation of shear wave velocities for a depth range down from the surface to upper crust. Most of the shear wave velocity anomalies, including the upper crustal areas of the Kendeng basin and active volcanoes, are consistent with our previous study of Rayleigh wave group velocities and fit to the regional geology. Keywords: Dispersion Inversion; shear wave velocity; Central Java, Indonesia. Reference: Zulfakriza, Z., Saygin, E., Cummins, P., Widiyantoro, S., Nugraha, A., Luehr, B.-G., Bodin, T., 2014. Upper crustal structure of central Java, Indonesia, from transdimensional seismic ambient noise tomography. Geophys. J. Int. 197.

  3. Inversion of an Atomic Wave Packet in a Circularly Polarized Electromagnetic Wave

    ZENG Gao-Jian


    We study behavior of an atomic wave packet in a circularly polarized electromagnetic wave, and particularly calculate the atomic inversion of the wave packet. A general method of calculation is presented. The results are interesting. For example, if the wave packet is very narrow or/and the interaction is very strong, no matter the atom is initially in its ground state or excited state, the atomic inversion approaches zero as time approaches infinity. If the atom is initially in its ground state and excited state with the probability 1/2 respectively, and if the momentum density is an even function, then the atomic inversion equals zero at any time.``

  4. Shear-wave velocity structure of the Tongariro Volcanic Centre, New Zealand: Fast Rayleigh and slow Love waves indicate strong shallow anisotropy

    Godfrey, Holly J.; Fry, Bill; Savage, Martha K.


    Models of the velocity structure of volcanoes can help define possible magma pathways and contribute to calculating more accurate earthquake locations, which can help with monitoring volcanic activity. However, shear-wave velocity of volcanoes is difficult to determine from traditional seismic techniques, such as local earthquake tomography (LET) or refraction/reflection surveys. Here we use the recently developed technique of noise cross correlation of continuous seismic data to investigate the subsurface shear-wave velocity structure of the Tongariro Volcanic Centre (TgVC) of New Zealand, focusing on the active Ruapehu and Tongariro Volcanoes. We observe both the fundamental and first higher-order modes of Rayleigh and Love waves within our noise dataset, made from stacks of 15 min cross-correlation functions. We manually pick group velocity dispersion curves from over 1900 correlation functions, of which we consider 1373 to be high quality. We subsequently invert a subset of the fundamental mode Rayleigh- and Love-wave dispersion curves both independently and jointly for one dimensional shear-wave velocity (Vs) profiles at Ruapehu and Tongariro Volcanoes. Vs increases very slowly at a rate of approximately 0.2 km/s per km depth beneath Ruapehu, suggesting that progressive hydrothermal alteration mitigates the effects of compaction driven velocity increases. At Tongariro, we observe larger Vs increases with depth, which we interpret as different layers within Tongariro's volcanic system above altered basement greywacke. Slow Vs, on the order of 1-2 km/s, are compatible with P-wave velocities (using a Vp/Vs ratio of 1.7) from existing velocity profiles of areas within the TgVC, and the observations of worldwide studies of shallow volcanic systems that used ambient noise cross-correlation methods. Most of the measured group velocities of fundamental mode Love-waves across the TgVC are 0.1-0.4 km/s slower than those of fundamental mode Rayleigh-waves in the

  5. A gradient-based model parametrization using Bernstein polynomials in Bayesian inversion of surface wave dispersion

    Gosselin, Jeremy M.; Dosso, Stan E.; Cassidy, John F.; Quijano, Jorge E.; Molnar, Sheri; Dettmer, Jan


    This paper develops and applies a Bernstein-polynomial parametrization to efficiently represent general, gradient-based profiles in nonlinear geophysical inversion, with application to ambient-noise Rayleigh-wave dispersion data. Bernstein polynomials provide a stable parametrization in that small perturbations to the model parameters (basis-function coefficients) result in only small perturbations to the geophysical parameter profile. A fully nonlinear Bayesian inversion methodology is applied to estimate shear wave velocity (VS) profiles and uncertainties from surface wave dispersion data extracted from ambient seismic noise. The Bayesian information criterion is used to determine the appropriate polynomial order consistent with the resolving power of the data. Data error correlations are accounted for in the inversion using a parametric autoregressive model. The inversion solution is defined in terms of marginal posterior probability profiles for VS as a function of depth, estimated using Metropolis-Hastings sampling with parallel tempering. This methodology is applied to synthetic dispersion data as well as data processed from passive array recordings collected on the Fraser River Delta in British Columbia, Canada. Results from this work are in good agreement with previous studies, as well as with co-located invasive measurements. The approach considered here is better suited than `layered' modelling approaches in applications where smooth gradients in geophysical parameters are expected, such as soil/sediment profiles. Further, the Bernstein polynomial representation is more general than smooth models based on a fixed choice of gradient type (e.g. power-law gradient) because the form of the gradient is determined objectively by the data, rather than by a subjective parametrization choice.

  6. Joint Inversion of Earthquake Source Parameters with local and teleseismic body waves

    Chen, W.; Ni, S.; Wang, Z.


    In the classical source parameter inversion algorithm of CAP (Cut and Paste method, by Zhao and Helmberger), waveform data at near distances (typically less than 500km) are partitioned into Pnl and surface waves to account for uncertainties in the crustal models and different amplitude weight of body and surface waves. The classical CAP algorithms have proven effective for resolving source parameters (focal mechanisms, depth and moment) for earthquakes well recorded on relatively dense seismic network. However for regions covered with sparse stations, it is challenging to achieve precise source parameters . In this case, a moderate earthquake of ~M6 is usually recorded on only one or two local stations with epicentral distances less than 500 km. Fortunately, an earthquake of ~M6 can be well recorded on global seismic networks. Since the ray paths for teleseismic and local body waves sample different portions of the focal sphere, combination of teleseismic and local body wave data helps constrain source parameters better. Here we present a new CAP mothod (CAPjoint), which emploits both teleseismic body waveforms (P and SH waves) and local waveforms (Pnl, Rayleigh and Love waves) to determine source parameters. For an earthquake in Nevada that is well recorded with dense local network (USArray stations), we compare the results from CAPjoint with those from the traditional CAP method involving only of local waveforms , and explore the efficiency with bootstraping statistics to prove the results derived by CAPjoint are stable and reliable. Even with one local station included in joint inversion, accuracy of source parameters such as moment and strike can be much better improved.

  7. Highly Sensitive Rayleigh Wave Hydrogen Sensors with WO3 Sensing Layers at Room Temperature

    WANG Cheng; FAN Li; ZHANG Shu-Yi; YANG Yue-Tao; ZHOU Ding-Mao; SHUI Xiu-Ji


    Rayleigh wave hydrogen sensors based on 128° YX-LiNbO3 substrates with WO3 sensing layers operating at room temperature are studied.The experimental results indicate that the WO3 layers obtained by a sol-gel method have much higher sensitivities because the sensing layers produced by the sol-gel method have small grains and high roughness and porosity.It is also confirmed that in the sol-gel method,keeping WO3 solutions at low temperature and/or decreasing the viscosity of the solutions can decrease the grain sizes and increase the hydrogen-absorbability of the sensing layer.Under the optimized preparation conditions,the high sensitivity of the hydrogen sensors at room temperature is obtained,in which 1% hydrogen in natural air induces the frequency shift of 72 kHz at the operating frequency of 124.2 MHz.Surface acoustic wave (SAW) hydrogen sensors have attracted a great deal of attention so far,in which the sensors have achieved high sensitivity as the sensors were often operated at high temperature,such as higher than 100℃.[1-4] However,in these experiments,a heater and a thermostat were required,which induced the sensors to be more complicated and unfavorable for miniaturization,and limited their application at room temperature.Furthermore,the heater can induce extra power loss and risks of fire and explosion.%Rayleigh wave hydrogen sensors based on 128° YX-LiNbO3 substrates with WO3 sensing layers operating at room temperature are studied. The experimental results indicate that the WO3 layers obtained by a sol-gel method have much higher sensitivities because the sensing layers produced by the sol-gel method have small grains and high roughness and porosity. It is also confirmed that in the sol-gel method, keeping WO3 solutions at low temperature and/or decreasing the viscosity of the solutions can decrease the grain sizes and increase the hydrogen-absorbability of the sensing layer. Under the optimized preparation conditions, the high sensitivity of the

  8. Glottal Waves via Inverse Filtering of Vowel Sounds.

    Deng, Huiqun; Ward, Rabab; Beddoes, Michael


    This paper shows how to obtain accurate glottal waves via inverse filtering of vowel sounds and how to determine if these glottal waves contain any significant resonance of vocal tracts. We obtain vocal-tract filter (VTF) estimates for the inverse filtering from sustained vowel sounds over closed glottal phases using a new method, which minimizes the effects of glottal waves on the VTF estimates. It is common that VTF estimates contain the effects of incomplete glottal closures, and the glottal waves obtained via inverse filtering contain residual vocal-tract resonance. Our simulations show that the residual resonance appears as stationary ripples superimposed on the derivatives of the original glottal waves over the duration of a glottal cycle. The VTF estimates and the glottal waves obtained from sustained vowel sounds /a/ produced by male and female subjects are presented. The derivatives of the obtained glottal waves exhibit transient positive peaks during vocal-fold collision and negative levels in the earlier stage of vocal-fold parting.

  9. Skeletonized wave-equation inversion for Q

    Dutta, Gaurav


    A wave-equation gradient optimization method is presented that inverts for the subsurface Q distribution by minimizing a skeletonized misfit function ε. Here, ε is the sum of the squared differences between the observed and the predicted peak/centroid frequency shifts of the early-arrivals. The gradient is computed by migrating the observed traces weighted by the frequency-shift residuals. The background Q model is perturbed until the predicted and the observed traces have the same peak frequencies or the same centroid frequencies. Numerical tests show that an improved accuracy of the inverted Q model by wave-equation Q tomography (WQ) leads to a noticeable improvement in the migration image quality.

  10. Surface wave inversion for a p-wave velocity profile: Estimation of the squared slowness gradient

    Ponomarenko, A.V.; Kashtan, B.M.; Troyan, V.N.; Mulder, W.A.


    Surface waves can be used to obtain a near-surface shear wave profile. The inverse problem is usually solved for the locally 1-D problem of a set of homogeneous horizontal elastic layers. The output is a set of shear velocity values for each layer in the profile. P-wave velocity profile can be estim

  11. Incorporating Love- and Rayleigh-wave magnitudes, unequal earthquake and explosion variance assumptions and interstation complexity for improved event screening

    Anderson, Dale N [Los Alamos National Laboratory; Bonner, Jessie L [WESTON GEOPHYSICAL; Stroujkova, Anastasia [WESTON GEOPHYSICAL; Shumway, Robert [UC/DAVIS; Russell, David R [AFTAC


    Our objective is to improve seismic event screening using the properties of surface waves, We are accomplishing this through (1) the development of a Love-wave magnitude formula that is complementary to the Russell (2006) formula for Rayleigh waves and (2) quantifying differences in complexities and magnitude variances for earthquake and explosion-generated surface waves. We have applied the M{sub s} (VMAX) analysis (Bonner et al., 2006) using both Love and Rayleigh waves to events in the Middle East and Korean Peninsula, For the Middle East dataset consisting of approximately 100 events, the Love M{sub s} (VMAX) is greater than the Rayleigh M{sub s} (VMAX) estimated for individual stations for the majority of the events and azimuths, with the exception of the measurements for the smaller events from European stations to the northeast. It is unclear whether these smaller events suffer from magnitude bias for the Love waves or whether the paths, which include the Caspian and Mediterranean, have variable attenuation for Love and Rayleigh waves. For the Korean Peninsula, we have estimated Rayleigh- and Love-wave magnitudes for 31 earthquakes and two nuclear explosions, including the 25 May 2009 event. For 25 of the earthquakes, the network-averaged Love-wave magnitude is larger than the Rayleigh-wave estimate. For the 2009 nuclear explosion, the Love-wave M{sub s} (VMAX) was 3.1 while the Rayleigh-wave magnitude was 3.6. We are also utilizing the potential of observed variances in M{sub s} estimates that differ significantly in earthquake and explosion populations. We have considered two possible methods for incorporating unequal variances into the discrimination problem and compared the performance of various approaches on a population of 73 western United States earthquakes and 131 Nevada Test Site explosions. The approach proposes replacing the M{sub s} component by M{sub s} + a* {sigma}, where {sigma} denotes the interstation standard deviation obtained from the

  12. The story of a craton from heart to margins: illuminating cratonic lithosphere with Rayleigh wave phase velocities in Eastern Canada

    Petrescu, L.; Darbyshire, F. A.; Gilligan, A.; Bastow, I. D.; Totten, E. J.


    Cratons are Precambrian continental nuclei that are geologically distinct from modern continental regions and are typically underlain by seismically fast lithospheric roots (keels) to at least 200 km depth. Both plate and non-plate tectonic origin theories such as stacking of subducted slabs or multiple mantle plume underplating have been proposed to explain keel growth.Eastern Canada is an ideal continental region to investigate cratonization processes and the onset of plate tectonics. It comprises part of the largest Archean craton in the world, the Superior Province, flanked by a ~1.1 Ga Himalayan-scale orogenic belt, the Grenville Province, and the 500-300 Ma old Appalachian orogenic province, following the same general SW-NE axial trend. The region is also cross-cut by the Great Meteor Hotspot track, providing an excellent opportunity to study the interaction of hotspot tectonism with progressively younger lithospheric domains.We investigate the lithospheric structure of Precambrian Eastern Canada using teleseismic earthquake data recorded at permanent and temporary networks. We measure interstation dispersion curves of Rayleigh wave phase velocities between ~15 and 220 s, and compare the results to standard continental and cratonic reference models. We combine the dispersion curves via a tomographic inversion which solves for isotropic phase velocity heterogeneity and azimuthal anisotropy across the region at a range of periods. The phase velocity maps indicate variations in lithospheric properties from the heart of the Superior craton to the SE Canadian coast.The new regional-scale models will help to understand the processes that generated, stabilized and reworked the cratonic roots through their billion-year tectonic history. We investigate how surface tectonic boundaries relate to deeper lithospheric structural changes, and consider the effects of the multiple Wilson cycles that affected Laurentia.

  13. Determining Ocean-Bottom Seismometer Orientations from the RHUM-RUM experiment from P-wave and Rayleigh wave polarizations

    Scholz, John-Robert; Barruol, Guilhem; Fontaine, Fabrice R.; Sigloch, Karin


    To image the upper mantle structure beneath La Réunion hotspot, a large-scale seismic network has been deployed on land and at sea in the frame of the RHUM-RUM project (Réunion Hotspot and Upper Mantle - Réunions Unterer Mantel). This French-German passive seismic experiment was designed to investigate and image the deep structure beneath La Réunion, from crust to core, to precise the shape and depth origin of a mantle plume, if any, and to precise the horizontal and vertical mantle flow associated to a possible plume upwelling, to its interaction with the overlying plate and with the neighboring Indian ridges. For this purpose, 57 Ocean-Bottom Seismometers (OBS) were installed around La Réunion and along the Central and Southwest Indian ridges. Broad-band instruments were deployed with the French R/V Marion Dufresne in late 2012 (cruise MD192), and recovered 13 months later by the German R/V Meteor (cruise M101). The pool of OBS was complemented by ~60 terrestrial stations, installed on different islands in the western Indian Ocean, such as La Réunion, Madagascar, Mauritius, Seychelles, Mayotte and the Îles Éparses in the Mozambique channel. The OBS installation is a free-fall down to the seafloor, where they landed in an unknown orientation. Since seismologic investigations of crustal and upper mantle structure (e.g., receiver functions) and azimuthal anisotropy (e.g., SKS-splitting and Rayleigh waves) rely on the knowledge of the correct OBS orientation with respect to the geographic reference frame, it is of importance to determine the orientations of the OBS while recording on the seafloor. In an isotropic, horizontally homogeneous and non-dipping layered globe, the misorientation of each station refers to the offset between theoretical and recorded back-azimuth angle of a passive seismic event. Using large earthquakes (MW > 5.0), it is possible to establish multiple successful measurements per station and thus to determine with good confidence the

  14. Uniqueness in inverse elastic scattering with finitely many incident waves

    Elschner, Johannes [Weierstrass-Institut fuer Angewandte Analysis und Stochastik (WIAS) im Forschungsverbund Berlin e.V. (Germany); Yamamoto, Masahiro [Tokyo Univ. (Japan). Dept. of Mathematical Sciences


    We consider the third and fourth exterior boundary value problems of linear isotropic elasticity and present uniqueness results for the corresponding inverse scattering problems with polyhedral-type obstacles and a finite number of incident plane elastic waves. Our approach is based on a reflection principle for the Navier equation. (orig.)

  15. A mathematical framework for inverse wave problems in heterogeneous media

    Blazek, K.D.; Stolk, C.; Symes, W.W.


    This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The coefficients of these time-dependent partial differential equations re

  16. Applications of elastic full waveform inversion to shallow seismic surface waves

    Bohlen, Thomas; Forbriger, Thomas; Groos, Lisa; Schäfer, Martin; Metz, Tilman


    Shallow-seismic Rayleigh waves are attractive for geotechnical site investigations. They exhibit a high signal to noise ratio in field data recordings and have a high sensitivity to the S-wave velocity, an important lithological and geotechnical parameter to characterize the very shallow subsurface. Established inversion methods assume (local) 1-D subsurface models, and allow the reconstruction of the S-wave velocity as a function of depth by inverting the dispersion properties of the Rayleigh waves. These classical methods, however, fail if significant lateral variations of medium properties are present. Then the full waveform inversion (FWI) of the elastic wave field seems to be the only solution. Moreover, FWI may have the potential to recover multi-parameter models of seismic wave velocities, attenuation and eventually mass density. Our 2-D elastic FWI is a conjugate-gradient method where the gradient of the misfit function is calculated by the time-domain adjoint method. The viscoelastic forward modelling is performed with a classical staggered-grid 2-D finite-difference forward solver. Viscoelastic damping is implemented in the time-domain by a generalized standard linear solid. We use a multi-scale inversion approach by applying frequency filtering in the inversion. We start with the lowest frequency oft the field data and increase the upper corner frequency sequentially. Our modelling and FWI software is freely available under the terms of GNU GPL on In recent years we studied the applicability of two-dimensional elastic FWI using numerous synthetic reconstruction tests and several field data examples. Important pre-processing steps for the application of 2-D elastic FWI to shallow-seismic field data are the 3D to 2D correction of geometrical spreading and the estimation of a priori Q-values that must be used as a passive medium parameter during the FWI. Furthermore, a source-wavelet correction filter should be applied during the FWI

  17. Theoretical determination of Rayleigh wave acoustoelastic coefficients: comparison with experimental values.

    Duquennoy, Marc; Ouaftouh, Mohammadi; Ourak, Mohamed; Jenot, Frédéric


    The characterization of stress states in materials is often necessary in some industrial application. The ultrasonic methods can be potentially convenient since stress states inside materials can be obtained even if materials are opaque. Nevertheless, the knowledge of acousto-elastic coefficients is generally necessary to estimate residual stresses by ultrasonic methods, but the experimental determination of these acousto-elastic coefficients can be difficult in some cases. In this paper, Rayleigh wave (RW) acousto-elastic coefficients of an orthotropic material are theoretically determined according to its characteristics, i.e. the density and the secondand third-order elastic constants. Then, these RW acousto-elastic coefficients are directly measured during an experimental stage and a comparison between calculated and measured coefficients is realized. This study allows on the one hand to check the theoretical development and on the other hand to show that it is possible to calculate acousto-elastic coefficients theoretically from intrinsic characteristics of the material rather than measuring them directly during a calibration phase which is sometimes long and difficult to realize.

  18. Inversion of surface wave data for subsurface shear wave velocity profiles characterized by a thick buried low-velocity layer

    Farrugia, Daniela; Paolucci, Enrico; D'Amico, Sebastiano; Galea, Pauline


    The islands composing the Maltese archipelago (Central Mediterranean) are characterized by a four-layer sequence of limestones and clays. A common feature found in the western half of the archipelago is Upper Coralline Limestone (UCL) plateaus and hillcaps covering a soft Blue Clay (BC) layer which can be up to 75 m thick. The BC layer introduces a velocity inversion in the stratigraphy, implying that the VS30 (traveltime average sear wave velocity (VS) in the upper 30 m) parameter is not always suitable for seismic microzonation purposes. Such a layer may produce amplification effects, however might not be included in the VS30 calculations. In this investigation, VS profiles at seven sites characterized by such a lithological sequence are obtained by a joint inversion of the single-station Horizontal-to-Vertical Spectral Ratios (H/V or HVSR) and effective dispersion curves from array measurements analysed using the Extended Spatial Auto-Correlation technique. The lithological sequence gives rise to a ubiquitous H/V peak between 1 and 2 Hz. All the effective dispersion curves obtained exhibit a `normal' dispersive trend at low frequencies, followed by an inverse dispersive trend at higher frequencies. This shape is tentatively explained in terms of the presence of higher mode Rayleigh waves, which are commonly present in such scenarios. Comparisons made with the results obtained at the only site in Malta where the BC is missing below the UCL suggest that the characteristics observed at the other seven sites are due to the presence of the soft layer. The final profiles reveal a variation in the VS of the clay layer with respect to the depth of burial and some regional variations in the UCL layer. This study presents a step towards a holistic seismic risk assessment that includes the implications on the site effects induced by the buried clay layer. Such assessments have not yet been done for Malta.

  19. Elastic Wave-equation Reflection Traveltime Inversion Using Dynamic Warping and Wave Mode Decomposition

    Wang, T.


    Elastic full waveform inversion (EFWI) provides high-resolution parameter estimation of the subsurface but requires good initial guess of the true model. The traveltime inversion only minimizes traveltime misfits which are more sensitive and linearly related to the low-wavenumber model perturbation. Therefore, building initial P and S wave velocity models for EFWI by using elastic wave-equation reflections traveltime inversion (WERTI) would be effective and robust, especially for the deeper part. In order to distinguish the reflection travletimes of P or S-waves in elastic media, we decompose the surface multicomponent data into vector P- and S-wave seismogram. We utilize the dynamic image warping to extract the reflected P- or S-wave traveltimes. The P-wave velocity are first inverted using P-wave traveltime followed by the S-wave velocity inversion with S-wave traveltime, during which the wave mode decomposition is applied to the gradients calculation. Synthetic example on the Sigbee2A model proves the validity of our method for recovering the long wavelength components of the model.

  20. Computational study on full-wave inversion based on the elastic wave-equation; Dansei hado hoteishiki full wave inversion no model keisan ni yoru kento

    Uesaka, S. [Kyoto University, Kyoto (Japan). Faculty of Engineering; Watanabe, T.; Sassa, K. [Kyoto University, Kyoto (Japan)


    Algorithm is constructed and a program developed for a full-wave inversion (FWI) method utilizing the elastic wave equation in seismic exploration. The FWI method is a method for obtaining a physical property distribution using the whole observed waveforms as the data. It is capable of high resolution which is several times smaller than the wavelength since it can handle such phenomena as wave reflection and dispersion. The method for determining the P-wave velocity structure by use of the acoustic wave equation does not provide information about the S-wave velocity since it does not consider S-waves or converted waves. In an analysis using the elastic wave equation, on the other hand, not only P-wave data but also S-wave data can be utilized. In this report, under such circumstances, an inverse analysis algorithm is constructed on the basis of the elastic wave equation, and a basic program is developed. On the basis of the methods of Mora and of Luo and Schuster, the correction factors for P-wave and S-wave velocities are formulated directly from the elastic wave equation. Computations are performed and the effects of the hypocenter frequency and vibration transmission direction are examined. 6 refs., 8 figs.

  1. Experimental and theoretical study of Rayleigh-Lamb waves in a plate containing a surface-breaking crack

    Paffenholz, Joseph; Fox, Jon W.; Gu, Xiaobai; Jewett, Greg S.; Datta, Subhendu K.


    Scattering of Rayleigh-Lamb waves by a normal surface-breaking crack in a plate has been studied both theoretically and experimentally. The two-dimensionality of the far field, generated by a ball impact source, is exploited to characterize the source function using a direct integration technique. The scattering of waves generated by this impact source by the crack is subsequently solved by employing a Green's function integral expression for the scattered field coupled with a finite element representation of the near field. It is shown that theoretical results of plate response, both in frequency and time, are similar to those obtained experimentally. Additionally, implication for practical applications are discussed.

  2. Estimate of Rayleigh-to-Love wave ratio in the secondary microseism by a small array at Piñon Flat observatory, California

    Tanimoto, Toshiro; Lin, Chin-Jen; Hadziioannou, Céline; Igel, Heiner; Vernon, Frank


    Using closely located seismographs at Piñon Flat (PFO), California, for 1 year long record (2015), we estimated the Rayleigh-to-Love wave energy ratio in the secondary microseism (0.1-0.35 Hz) in four seasons. Rayleigh wave energy was estimated from a vertical component seismograph. Love wave energy was estimated from rotation seismograms that were derived from a small array at PFO. Derived ratios are 2-2.5, meaning that there is 2-2.5 times more Rayleigh wave energy than Love wave energy at PFO. In our previous study at Wettzell, Germany, this ratio was 0.9-1.0, indicating comparable energy between Rayleigh waves and Love waves. This difference suggests that the Rayleigh-to-Love wave ratios in the secondary microseism may differ greatly from region to region. It also implies that an assumption of the diffuse wavefield is not likely to be valid for this low frequency range as the equipartition of energy should make this ratio much closer.

  3. Seismic anisotropy of Precambrian lithosphere: Insights from Rayleigh wave tomography of the eastern Superior Craton

    Petrescu, Laura; Darbyshire, Fiona; Bastow, Ian; Totten, Eoghan; Gilligan, Amy


    The thick, seismically fast lithospheric keels underlying continental cores (cratons) are thought to have formed in the Precambrian and resisted subsequent tectonic destruction. A consensus is emerging from a variety of disciplines that keels are vertically stratified, but the processes that led to their development remain uncertain. Eastern Canada is a natural laboratory to study Precambrian lithospheric formation and evolution. It comprises the largest Archean craton in the world, the Superior Craton, surrounded by multiple Proterozoic orogenic belts. To investigate its lithospheric structure, we construct a frequency-dependent anisotropic seismic model of the region using Rayleigh waves from teleseismic earthquakes recorded at broadband seismic stations across eastern Canada. The joint interpretation of phase velocity heterogeneity and azimuthal anisotropy patterns reveals a seismically fast and anisotropically complex Superior Craton. The upper lithosphere records fossilized Archean tectonic deformation: anisotropic patterns align with the orientation of the main tectonic boundaries at periods ≤110 s. This implies that cratonic blocks were strong enough to sustain plate-scale deformation during collision at 2.5 Ga. Cratonic lithosphere with fossil anisotropy partially extends beneath adjacent Proterozoic belts. At periods sensitive to the lower lithosphere, we detect fast, more homogenous, and weakly anisotropic material, documenting postassembly lithospheric growth, possibly in a slow or stagnant convection regime. A heterogeneous, anisotropic transitional zone may also be present at the base of the keel. The detection of multiple lithospheric fabrics at different periods with distinct tectonic origins supports growing evidence that cratonization processes may be episodic and are not exclusively an Archean phenomenon.

  4. Determination of Rayleigh wave ellipticity across the Earthscope Transportable Array using single-station and array-based processing of ambient seismic noise

    Workman, Eli; Lin, Fan-Chi; Koper, Keith D.


    We present a single station method for the determination of Rayleigh wave ellipticity, or Rayleigh wave horizontal to vertical amplitude ratio (H/V) using Frequency Dependent Polarization Analysis (FDPA). This procedure uses singular value decomposition of 3-by-3 spectral covariance matrices over 1-hr time windows to determine properties of the ambient seismic noise field such as particle motion and dominant wave-type. In FPDA, if the noise is mostly dominated by a primary singular value and the phase difference is roughly 90° between the major horizontal axis and the vertical axis of the corresponding singular vector, we infer that Rayleigh waves are dominant and measure an H/V ratio for that hour and frequency bin. We perform this analysis for all available data from the Earthscope Transportable Array between 2004 and 2014. We compare the observed Rayleigh wave H/V ratios with those previously measured by multicomponent, multistation noise cross-correlation (NCC), as well as classical noise spectrum H/V ratio analysis (NSHV). At 8 s the results from all three methods agree, suggesting that the ambient seismic noise field is Rayleigh wave dominated. Between 10 and 30 s, while the general pattern agrees well, the results from FDPA and NSHV are persistently slightly higher (˜2 per cent) and significantly higher (>20 per cent), respectively, than results from the array-based NCC. This is likely caused by contamination from other wave types (i.e. Love waves, body waves, and tilt noise) in the single station methods, but it could also reflect a small, persistent error in NCC. Additionally, we find that the single station method has difficulty retrieving robust Rayleigh wave H/V ratios within major sedimentary basins, such as the Williston Basin and Mississippi Embayment, where the noise field is likely dominated by reverberating Love waves and tilt noise.

  5. Internal gravity waves: Analysis using the periodic, inverse scattering transform

    W. B. Zimmerman


    Full Text Available The discrete periodic inverse scattering transform (DPIST has been shown to provide the salient features of nonlinear Fourier analysis for surface shallow water waves whose dynamics are governed by the Korteweg-de Vries (KdV equation - (1 linear superposition of components with power spectra that are invariants of the motion of nonlinear dispersive waves and (2 nonlinear filtering. As it is well known that internal gravity waves also approximately satisfy the KdV equation in shallow stratified layers, this paper investigates the degree to which DPIST provides a useful nonlinear spectral analysis of internal waves by application to simulations and wave tank experiments of internal wave propagation from localized dense disturbances. It is found that DPIST analysis is sensitive to the quantity λ = (r/6s * (ε/μ2, where the first factor depends parametrically on the Richardson number and the background shear and density profiles and the second factor is the Ursell number-the ratio of the dimensionless wave amplitude to the dimensionless squared wavenumber. Each separate wave component of the decomposition of the initial disturbance can have a different value, and thus there is usually just one component which is an invariant of the motion found by DPIST analysis. However, as the physical applications, e.g. accidental toxic gas releases, are usually concerned with the propagation of the longest wavenumber disturbance, this is still useful information. In cases where only long, monochromatic solitary waves are triggered or selected by the waveguide, the entire DPIST spectral analysis is useful.

  6. Shear-wave Velocity Model from Rayleigh Wave Group Velocities Centered on the Sacramento/San Joaquin Delta

    Fletcher, Jon B.; Erdem, Jemile


    Rayleigh wave group velocities obtained from ambient noise tomography are inverted for an upper crustal model of the Central Valley, California, centered on the Sacramento/San Joaquin Delta. Two methods were tried; the first uses SURF96, a least squares routine. It provides a good fit to the data, but convergence is dependent on the starting model. The second uses a genetic algorithm, whose starting model is random. This method was tried at several nodes in the model and compared to the output from SURF96. The genetic code is run five times and the variance of the output of all five models can be used to obtain an estimate of error. SURF96 produces a more regular solution mostly because it is typically run with a smoothing constraint. Models from the genetic code are generally consistent with the SURF96 code sometimes producing lower velocities at depth. The full model, calculated using SURF96, employed a 2-pass strategy, which used a variable damping scheme in the first pass. The resulting model shows low velocities near the surface in the Central Valley with a broad asymmetrical sedimentary basin located close to the western edge of the Central Valley near 122°W longitude. At shallow depths, the Rio Vista Basin is found nestled between the Pittsburgh/Kirby Hills and Midland faults, but a significant basin also seems to exist to the west of the Kirby Hills fault. There are other possible correlations between fast and slow velocities in the Central Valley and geologic features such as the Stockton Arch, oil or gas producing regions and the fault-controlled western boundary of the Central Valley.

  7. Wave equation based microseismic source location and velocity inversion

    Zheng, Yikang; Wang, Yibo; Chang, Xu


    The microseismic event locations and velocity information can be used to infer the stress field and guide hydraulic fracturing process, as well as to image the subsurface structures. How to get accurate microseismic event locations and velocity model is the principal problem in reservoir monitoring. For most location methods, the velocity model has significant relation with the accuracy of the location results. The velocity obtained from log data is usually too rough to be used for location directly. It is necessary to discuss how to combine the location and velocity inversion. Among the main techniques for locating microseismic events, time reversal imaging (TRI) based on wave equation avoids traveltime picking and offers high-resolution locations. Frequency dependent wave equation traveltime inversion (FWT) is an inversion method that can invert velocity model with source uncertainty at certain frequency band. Thus we combine TRI with FWT to produce improved event locations and velocity model. In the proposed approach, the location and model information are interactively used and updated. Through the proposed workflow, the inverted model is better resolved and the event locations are more accurate. We test this method on synthetic borehole data and filed data of a hydraulic fracturing experiment. The results verify the effectiveness of the method and prove it has potential for real-time microseismic monitoring.

  8. On Short Wave Stability and Sufficient Conditions for Stability in the Extended Rayleigh Problem of Hydrodynamic Stability

    M Subbiah; V Ganesh


    We consider the extended Rayleigh problem of hydrodynamic stability dealing with the stability of inviscid homogeneous shear flows in sea straits of arbitrary cross section. We prove a short wave stability result, namely, if $k>0$ is the wave number of a normal mode then $k>k_c$ (for some critical wave number $k_c$) implies the stability of the mode for a class of basic flows. Furthermore, if $K(z)=\\frac{-({U''}_0-T_0{U'}_0)}{U_0-U_{0s}}$, where $U_0$ is the basic velocity, $T_0$ (a constant) the topography and prime denotes differentiation with respect to vertical coordinate then we prove that a sufficient condition for the stability of basic flow is $0 < K(z)≤\\left(\\frac{^2}{D^2}+\\frac{T^2_0}{4}\\right)$, where the flow domain is $0≤ z≤ D$.

  9. Inversion of Scattered Waves for Material Properties in Fractured Rock

    Gritto, Roland; Korneev, Valeri A.; Johnson, Lane R.


    The authors apply a recently developed low-frequency, non-linear inversion method which includes near and far field terms to a crosshole data set to determine the bulk and shear modulus, as well as the density for a fractured zone in a granitic rock mass. The method uses the scattered elastic wavefield which is extracted from the recorded data before the inversion is performed. The inversion result is appraised by investigating the resolution and standard deviation of the model estimates. The sensitivity of the three parameters to different features of the medium is revealed. While the bulk modulus appears to be sensitive to voids and welded contacts, the density is mostly affected by fractured zones. The shear modulus is least constrained due to the absence of S wave anisotropy information. It is shown that the three medium parameters are generally sensitive to other medium features than those determined by velocity inversions. Thus this method is viewed as a complimentary approach to travel time tomography which provides more insight into the material properties of inhomogeneous media.

  10. Computational study on full-wave inversion based on the acoustic wave-equation; Onkyoha hado hoteishiki full wave inversion no model keisan ni yoru kento

    Watanabe, T.; Sassa, K. [Kyoto University, Kyoto (Japan); Uesaka, S. [Kyoto University, Kyoto (Japan). Faculty of Engineering


    The effect of initial models on full-wave inversion (FWI) analysis based on acoustic wave-equation was studied for elastic wave tomography of underground structures. At present, travel time inversion using initial motion travel time is generally used, and inverse analysis is conducted using the concept `ray,` assuming very high wave frequency. Although this method can derive stable solutions relatively unaffected by initial model, it uses only the data of initial motion travel time. FWI calculates theoretical waveform at each receiver using all of observed waveforms as data by wave equation modeling where 2-D underground structure is calculated by difference calculus under the assumption that wave propagation is described by wave equation of P wave. Although it is a weak point that FWI is easily affected by noises in an initial model and data, it is featured by high resolution of solutions. This method offers very excellent convergence as a proper initial model is used, resulting in sufficient performance, however, it is strongly affected by initial model. 2 refs., 7 figs., 1 tab.

  11. Guided Wave Tomography Based on Full-Waveform Inversion.

    Rao, Jing; Ratassepp, Madis; Fan, Zheng


    In this paper, a guided wave tomography method based on Full Waveform Inversion (FWI) is developed for accurate and high resolu- tion reconstruction of the remaining wall thickness in isotropic plates. The forward model is computed in the frequency domain by solving a full-wave equation in a two-dimensional acoustic model, accounting for higher order eects such as diractions and multiple scattering. Both numerical simulations and experiments were carried out to obtain the signals of a dispersive guided mode propagating through defects. The inversion was based on local optimization of a waveform mist func- tion between modeled and measured data, and was applied iteratively to discrete frequency components from low to high frequencies. The resulting wave velocity maps were then converted to thickness maps by the dispersion characteristics of selected guided modes. The results suggest that the FWI method is capable to reconstruct the thickness map of a irregularly shaped defect accurately on a 10 mm thick plate with the thickness error within 0.5 mm.

  12. Inverse problem for multi-body interaction of nonlinear waves

    Marruzzo, Alessia; Antenucci, Fabrizio; Pagnani, Andrea; Leuzzi, Luca


    The inverse problem is studied in multi-body systems with nonlinear dynamics representing, e.g., phase-locked wave systems, standard multimode and random lasers. Using a general model for four-body interacting complex-valued variables we test two methods based on pseudolikelihood, respectively with regularization and with decimation, to determine the coupling constants from sets of measured configurations. We test statistical inference predictions for increasing number of sampled configurations and for an externally tunable {\\em temperature}-like parameter mimicing real data noise and helping minimization procedures. Analyzed models with phasors and rotors are generalizations of problems of real-valued spherical problems (e.g., density fluctuations), discrete spins (Ising and vectorial Potts) or finite number of states (standard Potts): inference methods presented here can, then, be straightforward applied to a large class of inverse problems.

  13. Weakly nonlinear models for internal waves: inverse scattering transform and solitary wave contents

    Chen, Shengqian


    The time evolution emanating from ``internal dam-break'' initial conditions is studied for a class of models of stratified Euler fluids in configurations close to two-homogeneous layers separated by a thin diffused interface. Direct numerical simulations and experiments in wave tanks show that such initial conditions eventually give rise to coherent structures that are close to solitary-wave solutions moving ahead of a region of dispersive wave motion and turbulent mixing close to the location of the initial dam step. A priori theoretical predictions of the main features of these solitary waves, such as their amplitudes and speeds, appear to be unavailable, even for simplified models of wave evolution in stratified fluids. With the aim of providing estimates of the existence, amplitude and speed of such solitary waves, an approach based on Inverse Scattering Transform (IST) for completely integrable models is developed here and tested against direct numerical simulations of Euler fluids and some of their mode...

  14. Seismic Tomography Around the Eastern Edge of the Alps From Ambient-Noise-Based Rayleigh Waves

    Zigone, Dimitri; Fuchs, Florian; Kolinsky, Petr; Gröschl, Gidera; Apoloner, Maria-Theresia; Qorbani, Ehsan; Schippkus, Sven; Löberich, Eric; Bokelmann, Götz; AlpArray Working Group


    Inspecting ambient noise Green's functions is an excellent tool for monitoring the quality of seismic data, and for swiftly detecting changes in the configuration of a seismological station. Those Green's functions readily provide stable information about structural variations near the Earth's surface. We apply the technique to a network consisting of about 40 broadband stations in the area of the Easternmost Alps, in particular those operated by the University of Vienna (AlpArrayAustria) and the Vienna University of Technology. Those data are used to estimate Green's functions between station pairs; the Green's function consist mainly of surface waves, and we use them to investigate crustal structure near the Eastern edge of the Alps. To obtain better signal-to-noise ratios in the noise correlation functions, we adopt a procedure using short time windows (2 hr). Energy tests are performed on the data to remove effects of transient sources and instrumental problems. The resulting 9-component correlation tensor is used to make travel time measurements on the vertical, radial and transverse components. Those measurements can be used to evaluate dispersion using frequency-time analysis for periods between 5-30 seconds. After rejecting paths without sufficient signal-to-noise ratio, we invert the velocity measurements using the Barmin et al. (2001) approach on a 10 km grid size. The obtained group velocity maps reveal complex structures with clear velocity contrasts between sedimentary basins and crystalline rocks. The Bohemian Massif and the Northern Calcareous Alps are associated with fast-velocity bodies. By contrast, the Vienna Basin presents clear low-velocity zones with group velocities down to 2 km/s at period of 7 s. The group velocities are then inverted to 3D images of shear wave speeds using the linear inversion method of Herrmann (2013). The results highlight the complex crustal structure and complement earthquake tomography studies in the region. Updated

  15. Effect of quantum corrections on Rayleigh-Taylor instability and internal waves in strongly coupled magnetized viscoelastic fluid

    Prajapati, Ramprasad


    The Rayleigh-Taylor (R-T) instability is recently investigated is strongly coupled plasma looking to its importance in dense stellar systems and Inertial Confinement Fusion [1-3]. In the present work, the effect of quantum corrections are studied on Rayleigh-Taylor (R-T) instability and internal wave propagation in a strongly coupled, magnetized, viscoelastic fluid. The modified generalized hydrodynamic model is used to derive the analytical dispersion relation. The internal wave mode and dispersion relation are modified due to the presence of quantum corrections and viscoelastic effects. We observe that strong coupling effects and quantum corrections significantly modifies the dispersion characteristics. The dispersion relation is also discussed in weakly coupled (hydrodynamic) and strongly coupled (kinetic) limits. The explicit expression of R-T instability criterion is derived which is influenced by shear velocity and quantum corrections. Numerical calculations are performed in astrophysical and experimental relevance and it is examined that both the shear and quantum effects suppresses the growth rate of R-T instability. The possible application of the work is discussed in Inertial Confinement Fusion (ICF) to discuss the suppression of R-T instability under considered situation. References: [1] R. P. Prajapati, Phys. Plasmas 23, 022106 (2016). [2] K. Avinash and A. Sen, Phys. Plasmas 22, 083707 (2015). [3] A. Das and P. Kaw, Phys. Plasmas 21 (2014) 062102.

  16. Integrated inversion using combined wave-equation tomography and full waveform inversion

    Wang, Haiyang; Singh, Satish C.; Calandra, Henri


    Wave-equation tomography (WT) and full waveform inversion (FWI) are combined through a hybrid misfit function to estimate high-resolution subsurface structures starting from a poorly constrained initial velocity model. Both methods share the same wavefield forward modelling and inversion schemes, while they differ only on the ways to calculate misfit functions and hence the ways to sample in the model space. Aiming at minimizing the cross-correlation phase delay between synthetic and real data, WT can be used to retrieve the long- and middle-wavelength model components, which are essential to FWI. Compared to ray-based traveltime tomography that is based on asymptotic high-frequency approximation, WT provides a better resolution by exploring the band-limited feature of seismic wavefield. On the other hand, FWI is capable of resolving the short-wavelength model component, complementing the WT. In this study, we apply WT to surface first-arrival refraction data, and apply FWI to both refraction and reflection data. We assign adaptive weights to the two different misfit measurements and build a progressive inversion strategy. To illustrate the advantage of our strategy over conventional `ray tomography + FWI' approach, we show in a synthetic lens test that WT can provide extra subsurface information that is critical for a successful FWI application. To further show the efficiency, we test our strategy on the 2-D Marmousi model where satisfactory inversion results are achieved without much manual intervention. Finally, we apply the inversion strategy to a deep-water seismic data set acquired offshore Sumatra with a 12-km-long streamer. In order to alleviate several practical problems posed by the deep-water setting, we apply downward continuation (DC) to generate a virtual ocean bottom experiment data set prior to inversion. The new geometry after DC boosts up the shallow refractions, as well as avoiding cumbersome modelling through the thick water column, thus

  17. Extracting the Group Velocity of Rayleigh Waves from the Cross Correlation of the Ambient Seismic Noise Between Two Seismic Stations

    Jin Xing; Li Jun; Lin Shu; Zhou Zhengrong; Kang Lanchi; Ou Yiping


    This paper uses the 8 broad-band stations' microseism data recorded by the Seismic Monitoring Network of Fujian Province to calculate the vertical correlation coefficient between two stationsat intervals of 5 minutes. According to the time intervals technique we obtain the different coefficients and then add the correlative coefficients. Depending on this, we extract the group velocity of Rayleigh waves from the cross correlation of the ambient seismic noise between two seismic stations and figure out the group velocity' spatial distribution. The results show that the signal noise ratio (SNR) increases proportionally to the superposition times, but the results from different days are similar to one another. Synchronously, the arrival-time is also stable and there is no obvious change when coming across typhoons. It is found the velocity of the surface wave is 2.9~3. 1km/s in Fujian Province, which is close to the observationally attained value.

  18. Rayleigh wave dispersion measurements reveal low-velocity zones beneath the new crust in the Gulf of California

    Persaud, Patricia; Di Luccio, Francesca; Clayton, Robert W.


    Rayleigh wave tomography provides images of the shallow mantle shear wave velocity structure beneath the Gulf of California. Low-velocity zones (LVZs) are found on axis between 26 and 50 km depth beneath the Guaymas Basin but mostly off axis under the other rift basins, with the largest feature underlying the Ballenas Transform Fault. We interpret the broadly distributed LVZs as regions of partial melting in a solid mantle matrix. The pathway for melt migration and focusing is more complex than an axis-centered source aligned above a deeper region of mantle melt and likely reflects the magmatic evolution of rift segments. We also consider the existence of solid lower continental crust in the Gulf north of the Guaymas Basin, where the association of the LVZs with asthenospheric upwelling suggests lateral flow assisted by a heat source. These results provide key constraints for numerical models of mantle upwelling and melt focusing in this young oblique rift.

  19. Parsimonious wave-equation travel-time inversion for refraction waves

    Fu, Lei


    We present a parsimonious wave-equation travel-time inversion technique for refraction waves. A dense virtual refraction dataset can be generated from just two reciprocal shot gathers for the sources at the endpoints of the survey line, with N geophones evenly deployed along the line. These two reciprocal shots contain approximately 2N refraction travel times, which can be spawned into O(N2) refraction travel times by an interferometric transformation. Then, these virtual refraction travel times are used with a source wavelet to create N virtual refraction shot gathers, which are the input data for wave-equation travel-time inversion. Numerical results show that the parsimonious wave-equation travel-time tomogram has about the same accuracy as the tomogram computed by standard wave-equation travel-time inversion. The most significant benefit is that a reciprocal survey is far less time consuming than the standard refraction survey where a source is excited at each geophone location.

  20. Improving Earthquake and Explosion Discrimination by Using Love and Rayleigh Wave Magnitudes (Postprint) Annual Report 3


    Seismology Data Management Center (DMC), corrected for the instrument response to displacement in nanometers, and rotated to transverse, radial, and...estimated in the a) Middle East, b) Korean Peninsula region, and in c) central Italy . Figure 3. Ms(VMAX)-Love versus Ms (VMAX)- Rayleigh for...earthquakes in the a) Middle East, b) Korean Peninsula region, and in c) central Italy . The third dataset focused on the damaging L’Aquila earthquake (6

  1. Tomographic Rayleigh-wave group velocities in the Central Valley, California centered on the Sacramento/San Joaquin Delta

    Fletcher, Jon Peter B.; Erdem, Jemile; Seats, Kevin; Lawrence, Jesse


    If shaking from a local or regional earthquake in the San Francisco Bay region were to rupture levees in the Sacramento/San Joaquin Delta then brackish water from San Francisco Bay would contaminate the water in the Delta: the source of fresh water for about half of California. As a prelude to a full shear-wave velocity model that can be used in computer simulations and further seismic hazard analysis, we report on the use of ambient noise tomography to build a fundamental-mode, Rayleigh-wave group velocity model for the region around the Sacramento/San Joaquin Delta in the western Central Valley, California. Recordings from the vertical component of about 31 stations were processed to compute the spatial distribution of Rayleigh wave group velocities. Complex coherency between pairs of stations were stacked over 8 months to more than a year. Dispersion curves were determined from 4 to about 18 seconds. We calculated average group velocities for each period and inverted for deviations from the average for a matrix of cells that covered the study area. Smoothing using the first difference is applied. Cells of the model were about 5.6 km in either dimension. Checkerboard tests of resolution, which is dependent on station density, suggest that the resolving ability of the array is reasonably good within the middle of the array with resolution between 0.2 and 0.4 degrees. Overall, low velocities in the middle of each image reflect the deeper sedimentary syncline in the Central Valley. In detail, the model shows several centers of low velocity that may be associated with gross geologic features such as faulting along the western margin of the Central Valley, oil and gas reservoirs, and large cross cutting features like the Stockton arch. At shorter periods around 5.5s, the model’s western boundary between low and high velocities closely follows regional fault geometry and the edge of a residual isostatic gravity low. In the eastern part of the valley, the boundaries

  2. Enhanced Rayleigh waves tomography of Mexico using ambient noise cross-correlations (C1) and correlations of coda of correlations (C3)

    Spica, Z. J.; Perton, M.; Calo, M.; Cordoba-Montiel, F.; Legrand, D.; Iglesias, A.


    Standard application of the seismic ambient noise tomography considers the existence of synchronous records at stations for green's functions retrieval. More recent theoretical and experimental observations showed the possibility to apply correlation of coda of noise correlation (C3) to obtain green's functions between stations of asynchronous seismic networks making possible to dramatically increase databases for imagining the Earth's interior. However, this possibility has not been fully exploited yet, and right now the data C3 are not included into tomographic inversions to refine seismic structures. Here we show for the first time how to incorporate the data of C1 and C3 to calculate dispersion maps of Rayleigh waves in the range period of 10-120s, and how the merging of these datasets improves the resolution of the structures imaged. Tomographic images are obtained for an area covering Mexico, the Gulf of Mexico and the southern U.S. We show dispersion maps calculated using both data of C1 and the complete dataset (C1+C3). The latter provide new details of the seismic structure of the region allowing a better understanding of their role on the geodynamics of the study area. The resolving power obtained in our study is several times higher than in previous studies based on ambient noise. This demonstrates the new possibilities for imaging the Earth's crust and upper mantle using this enlarged database.

  3. Inversion of the Chelyabinsk seismic surface waves and comparative constraints on the generation of seismic waves by atmospheric Impacts on Earth and Mars

    Karakostas, F. G.; Rakoto, V.; Lognonne, P. H.


    Meteor impacts are a very important seismic source for planetary seismology, since their locations and, in some cases, their occurence times can be accurately known from orbiters, tracking or optical observations. Their importance becomes greater in the case of a seismic experiment with one seismometer, as the SEIS (Seismic Experiment of Interior Structure) of the future Martian mission "InSight", as the known location allows a direct inversion of differential travel times and wave forms in terms of structure. Meteor impacts generate body and surface seismic waves when they reach the surface of a planet. But when they explode into the atmosphere, due to ablation, they generate shock waves, which are converted into linear, seismic waves in the solid part and acoustic waves in the atmosphere. This effect can be modeled when the amplitude of Rayleigh and other Spheroidal normal modes is made with the atmospheric/ground coupling effects. In this study, meteor impacts are modeled as seismic sources in a comparative analysis for the cases of Earth and Mars. Using the computed seismograms, calculated by the summation of the normal modes of the full planet (e.g. with atmosphere) the properties of the seismic source can be obtained. Its duration is typically associated to the radiation duration of shock waves until they reach the linear regime of propagation. These transition times are comparatively analyzed, for providing constraints on the seismic source duration on Earth and Mars. In the case of Earth, we test our approach with the Chelyabinsk superbolide. The computed seismograms are used in order to perform the inversion of the source, by comparison with the data of the Global Seismographic Network. The results are interpreted and compared with other observations. In the case of Mars, equivalent sources are similarly modeled in different atmospheric, impact size and lithospheric conditions.

  4. Inverse problem for multi-body interaction of nonlinear waves.

    Marruzzo, Alessia; Tyagi, Payal; Antenucci, Fabrizio; Pagnani, Andrea; Leuzzi, Luca


    The inverse problem is studied in multi-body systems with nonlinear dynamics representing, e.g., phase-locked wave systems, standard multimode and random lasers. Using a general model for four-body interacting complex-valued variables we test two methods based on pseudolikelihood, respectively with regularization and with decimation, to determine the coupling constants from sets of measured configurations. We test statistical inference predictions for increasing number of sampled configurations and for an externally tunable temperature-like parameter mimicing real data noise and helping minimization procedures. Analyzed models with phasors and rotors are generalizations of problems of real-valued spherical problems (e.g., density fluctuations), discrete spins (Ising and vectorial Potts) or finite number of states (standard Potts): inference methods presented here can, then, be straightforward applied to a large class of inverse problems. The high versatility of the exposed techniques also concerns the number of expected interactions: results are presented for different graph topologies, ranging from sparse to dense graphs.

  5. The viscous surface-internal wave problem: nonlinear Rayleigh-Taylor instability

    Wang, Yanjin


    We consider the free boundary problem for two layers of immiscible, viscous, incompressible fluid in a uniform gravitational field, lying above a rigid bottom in a three-dimensional horizontally periodic setting. The effect of surface tension is either taken into account at both free boundaries or neglected at both. We are concerned with the Rayleigh-Taylor instability, so we assume that the upper fluid is heavier than the lower fluid. When the surface tension at the free internal interface is below a critical value, which we identify, we establish that the problem under consideration is nonlinearly unstable.

  6. 3D-ambient noise Rayleigh wave tomography of Snæfellsjökull volcano, Iceland

    Obermann, Anne; Lupi, Matteo; Mordret, Aurélien; Jakobsdóttir, Steinunn S.; Miller, Stephen A.


    From May to September 2013, 21 seismic stations were deployed around the Snæfellsjökull volcano, Iceland. We cross-correlate the five months of seismic noise and measure the Rayleigh wave group velocity dispersion curves to gain more information about the geological structure of the Snæfellsjökull volcano. In particular, we investigate the occurrence of seismic wave anomalies in the first 6 km of crust. We regionalize the group velocity dispersion curves into 2-D velocity maps between 0.9 and 4.8 s. With a neighborhood algorithm we then locally invert the velocity maps to obtain accurate shear-velocity models down to 6 km depth. Our study highlights three seismic wave anomalies. The deepest, located between approximately 3.3 and 5.5 km depth, is a high velocity anomaly, possibly representing a solidified magma chamber. The second anomaly is also a high velocity anomaly east of the central volcano that starts at the surface and reaches approximately 2.5 km depth. It may represent a gabbroic intrusion or a dense swarm of inclined magmatic sheets (similar to the dike swarms found in the ophiolites), typical of Icelandic volcanic systems. The third anomaly is a low velocity anomaly extending up to 1.5 km depth. This anomaly, located directly below the volcanic edifice, may be interpreted either as a shallow magmatic reservoir (typical of Icelandic central volcanoes), or alternatively as a shallow hydrothermal system developed above the cooling magmatic reservoir.

  7. Rayleigh-wave phase-velocity maps and three-dimensional shear velocity structure of the western US from local non-plane surface wave tomography

    Pollitz, F.F.; Snoke, J. Arthur


    We utilize two-and-three-quarter years of vertical-component recordings made by the Transportable Array (TA) component of Earthscope to constrain three-dimensional (3-D) seismic shear wave velocity structure in the upper 200 km of the western United States. Single-taper spectral estimation is used to compile measurements of complex spectral amplitudes from 44 317 seismograms generated by 123 teleseismic events. In the first step employed to determine the Rayleigh-wave phase-velocity structure, we implement a new tomographic method, which is simpler and more robust than scattering-based methods (e.g. multi-plane surface wave tomography). The TA is effectively implemented as a large number of local arrays by defining a horizontal Gaussian smoothing distance that weights observations near a given target point. The complex spectral-amplitude measurements are interpreted with the spherical Helmholtz equation using local observations about a succession of target points, resulting in Rayleigh-wave phase-velocity maps at periods over the range of 18–125 s. The derived maps depend on the form of local fits to the Helmholtz equation, which generally involve the nonplane-wave solutions of Friederich et al. In a second step, the phase-velocity maps are used to derive 3-D shear velocity structure. The 3-D velocity images confirm details witnessed in prior body-wave and surface-wave studies and reveal new structures, including a deep (>100 km deep) high-velocity lineament, of width ∼200 km, stretching from the southern Great Valley to northern Utah that may be a relic of plate subduction or, alternatively, either a remnant of the Mojave Precambrian Province or a mantle downwelling. Mantle seismic velocity is highly correlated with heat flow, Holocene volcanism, elastic plate thickness and seismicity. This suggests that shallow mantle structure provides the heat source for associated magmatism, as well as thinning of the thermal lithosphere, leading to relatively high

  8. Experimental determination of wave function spread in Si inversion layers

    Majumdar, Amlan


    We have experimentally determined the extent of wave function spread TQM in Si inversion layers on (100)-oriented surface in metal-oxide-semiconductor field-effect transistors (MOSFETs) using the back gate bias sensitivity of front gate threshold voltage of planar fully depleted silicon-on-insulator (SOI) MOSFETs. We show that the sum of TQM for large positive and negative F is an electrically determined value of the SOI thickness TSI. We find that the electric field dependence of TQM for electrons and holes is given by TQM˜F-0.4 and F-0.6, respectively, at high electric fields with TQM being larger for holes at a given F. Larger TQM for holes can be explained by the fact that holes have a smaller effective mass along the confinement direction than electrons in (100) Si. The field dependences of TQM are, however, not consistent with the results of variational calculations that assume single-subband occupancy and predict TQM˜F-1/3. The discrepancy likely indicates that the effects of multiple-subband occupation are significant at room temperature, especially for holes.

  9. Imaging Crust and Mantle Structure beneath the D'Entrecasteaux Islands, Papua New Guinea, from Rayleigh Wave Tomography

    Jin, G.; Gaherty, J. B.; Abers, G. A.; Kim, Y.; Eilon, Z.; Buck, W. R.; Verave, R.


    The D'Entrecasteaux Islands and adjacent Papuan peninsula in eastern Papua New Guinea are home to the earliest stages of extension associated with the Woodlark Rift system. Very young (7-8 Ma) ultra-high pressure (coesite-eclogite facies) rocks within metamorphic core complexes (MCCs) on the D'Entrecasteaux Islands indicates exhumation from 100 km depths at plate-tectonic rates. We investigate the dynamic processes driving uplift and extension using seismic images of crustal and mantle structure derived from surface waves across the region. From March 2010 to July 2011, 31 on-shore and 8 off-shore broadband seismic stations deployed across the extensional region recorded 68 earthquakes with high signal-to-noise Rayleigh waves. We utilize a multi-channel cross-correlation technique to measure the phase delay and amplitude across the array in a period band between 20-80 sec, which images a depth range from lower crust to approximately 150 km depth. The phase difference of Rayleigh-wave arrivals between nearby stations is measured for each earthquake by fitting the narrow-band filtered cross-correlation between the observed seismograms. We then invert these intra-array phase measurements for a slowness vector map using the Eikonal equation to get the dynamic phase velocity and propagation direction. Averaging the dynamic phase velocity of all available events produces set of final phase velocity maps that can be inverted for shear-velocity structure, and the variations in phase-velocity as a function of azimuth provide constraints on anisotropy. For most of the frequency bands, the region beneath the MCCs on Goodenough Island and Fergusson Island, adjacent to the tip of the Woodlark spreading center, shows slow phase velocity, suggestive of high temperatures and/or partial melt, perhaps related to localized mantle upwelling. In contrast, the region near the Trobriand Island to the north, and the Papuan peninsula to the south, shows consistently higher phase velocity

  10. Influence of coupling with shear horizontal surface acoustic wave on lateral propagation of Rayleigh surface acoustic wave on 128°YX-LiNbO3

    Zhang, Benfeng; Han, Tao; Tang, Gongbin; Zhang, Qiaozhen; Omori, Tatsuya; Hashimoto, Ken-ya


    In this paper, we investigate the impact of the coupling with shear horizontal (SH) surface acoustic wave (SAW) on the propagation of Rayleigh SAW in periodic grating structures on 128°YX-LiNbO3. First, the frequency dispersion behavior with longitudinal and lateral wavenumbers of Rayleigh SAW is calculated using the finite element method (FEM) software COMSOL. It is shown that the coupling causes (1) the satellite stopband and (2) variation of the anisotropy factor. It is also shown these phenomena remain even when the electromechanical coupling factor of SH SAW is zero. Then, the extended thin plate model which can take coupling between two SAWs into account, is applied to simulate the result of FEM. Good agreement between these results indicated that the mechanical coupling is responsible for these two phenomena. Finally, including electrical excitation and detection, the model is applied to the infinitely long interdigital transducer (IDT) structure and the calculated result is compared with that obtained by the three-dimensional FEM. The excellent agreement of both results confirms the effectiveness of the extended thin plate model.

  11. Temperature Frequency Characteristics of Hexamethyldisiloxane (HMDSO Polymer Coated Rayleigh Surface Acoustic Wave (SAW Resonators for Gas-Phase Sensor Applications

    Ekaterina I. Radeva


    Full Text Available Temperature induced frequency shifts may compromise the sensor response of polymer coated acoustic wave gas-phase sensors operating in environments of variable temperature. To correct the sensor data with the temperature response of the sensor the latter must be known. This study presents and discusses temperature frequency characteristics (TFCs of solid hexamethyldisiloxane (HMDSO polymer coated sensor resonators using the Rayleigh surface acoustic wave (RSAW mode on ST-cut quartz. Using a RF-plasma polymerization process, RSAW sensor resonators optimized for maximum gas sensitivity have been coated with chemosensitive HMDSO films at 4 different thicknesses: 50, 100, 150 and 250 nm. Their TFCs have been measured over a (−100 to +110 °C temperature range and compared to the TFC of an uncoated device. An exponential 2,500 ppm downshift of the resonant frequency and a 40 K downshift of the sensor’s turn-over temperature (TOT are observed when the HMDSO thickness increases from 0 to 250 nm. A partial temperature compensation effect caused by the film is also observed. A third order polynomial fit provides excellent agreement with the experimental TFC curve. The frequency downshift due to mass loading by the film, the TOT and the temperature coefficients are unambiguously related to each other.

  12. Banquet Speech Some Sketches Of Rayleigh

    Howard, John N.


    Several short sketches are presented of Lord Rayleigh, to show his method of working and his interaction with his fellow scientists. The topics discussed are: his research on the blue of the sky (Rayleigh scattering); his rescue of Waterston from near-oblivion; his research on surface acoustic waves (Rayleigh waves); his collaboration with Agnes Pockels; his research on blackbody radiation (the Rayleigh-Jeans Law).

  13. Inverse method for the determination of elastic properties of coating layers by the surface ultrasonic waves

    CHANG Jun; YANG Zhen; XU Jin-quan


    As the coated materials are widely applied in engineering, estimation of the elastic properties of coating layers is of great practical importance. This paper presents an inversion algorithm for determining the elastic properties of coating layers from the given velocity dispersion of surface ultrasonic waves. Based on the dispersive equation of surface waves in layered half space,an objective function dependent on coating material parameters is introduced. The density and wave velocities, which make the object function minimum, are taken as the inversion results. Inverse analyses of two parameters (longitudinal and transverse velocities) and three parameters (the density, longitudinal and transverse velocities) of the coating layer were made.

  14. Crustal and upper mantle S-wave velocity structures across the Taiwan Strait from ambient seismic noise and teleseismic Rayleigh wave analyses

    Huang, Y.; Yao, H.; Wu, F. T.; Liang, W.; Huang, B.; Lin, C.; Wen, K.


    Although orogeny seems to have stopped in western Taiwan large and small earthquakes do occur in the Taiwan Strait. Limited studies have focused on this region before and were barely within reach for comprehensive projects like TAICRUST and TAIGER for logistical reasons; thus, the overall crustal structures of the Taiwan Strait remain unknown. Time domain empirical Green's function (TDEGF) from ambient seismic noise to determine crustal velocity structure allows us to study an area using station pairs on its periphery. This research aims to resolve 1-D average crustal and upper mantle S-wave velocity (Vs) structures alone paths of several broadband station-pairs across the Taiwan Strait; 5-120 s Rayleigh wave phase velocity dispersion data derived by combining TDEGF and traditional surface wave two-station method (TS). The average Vs structures show significant differences in the upper 15 km as expected. In general, the highest Vs are observed in the coastal area of Mainland China and the lowest Vs appear along the southwest offshore of the Taiwan Island; they differ by about 0.6-1.1 km/s. For different parts of the Strait, the Vs are lower in the middle by about 0.1-0.2 km/s relative to those in the northern and southern parts. The overall crustal thickness is approximately 30 km, much thinner and less variable than under the Taiwan Island.

  15. Rayleigh-Lamb wave propagation on a fractional order viscoelastic plate.

    Meral, F Can; Royston, Thomas J; Magin, Richard L


    A previous study of the authors published in this journal focused on mechanical wave motion in a viscoelastic material representative of biological tissue [Meral et al., J. Acoust. Soc. Am. 126, 3278-3285 (2009)]. Compression, shear and surface wave motion in and on a viscoelastic halfspace excited by surface and sub-surface sources were considered. It was shown that a fractional order Voigt model, where the rate-dependent damping component that is dependent on the first derivative of time is replaced with a component that is dependent on a fractional derivative of time, resulted in closer agreement with experiment as compared with conventional (integer order) models, such as those of Voigt and Zener. In the present study, this analysis is extended to another configuration and wave type: out-of-plane response of a viscoelastic plate to harmonic anti-symmetric Lamb wave excitation. Theoretical solutions are compared with experimental measurements for a polymeric tissue mimicking phantom material. As in the previous configurations the fractional order modeling assumption improves the match between theory and experiment over a wider frequency range. Experimental complexities in the present study and the reliability of the different approaches for quantifying the shear viscoelastic properties of the material are discussed.

  16. Ridge asymmetry and deep aqueous alteration at the trench observed from Rayleigh wave tomography of the Juan de Fuca plate

    Bell, Samuel; Ruan, Youyi; Forsyth, Donald W.


    Using Rayleigh wave tomography of noise-removed ocean bottom seismometer data from the Cascadia Initiative, we illuminate the structure of the upper mantle beneath the Juan de Fuca plate. Beneath the Juan de Fuca ridge, there is strong asymmetry, with a pronounced low-velocity zone in the 25-65 km depth range. Extending to the west from the spreading axis, this anomaly has velocities low enough to indicate the presence of melt. The asymmetry in velocity structure and the much greater abundance of seamounts on the west flank of the ridge suggest that dynamic, buoyant upwelling is important, perhaps triggered by thermal or compositional anomalies beneath Axial Seamount. In contrast, there is no evidence for asymmetry in the axial zone or lower than expected velocities beneath the Gorda ridge. On the eastern flank of the Juan de Fuca ridge, the shear velocity in the 25-65 depth range is higher than expected; the lithosphere appears to be colder and thicker than predicted by standard plate cooling models, perhaps caused by the downwelling counterpart of the upwelling on the west side of the ridge. Close to the trench, there is a sharp decrease in shear velocity. We interpret this as aqueous alteration caused by hydrothermal circulation through deep normal faults associated with bending of the plate. Beneath the Astoria and Nitinat fans, where abyssal plain sediment is thickest, the velocity decrease is much smaller, which is consistent with a thick sediment cap that prevents hydrothermal alteration of the plate.

  17. Acoustical breakdown of materials by focusing of laser-generated Rayleigh surface waves

    Veysset, David; Maznev, A. A.; Veres, István A.; Pezeril, Thomas; Kooi, Steven E.; Lomonosov, Alexey M.; Nelson, Keith A.


    Focusing of high-amplitude surface acoustic waves leading to material damage is visualized in an all-optical experiment. The optical setup includes a lens and an axicon that focuses an intense picosecond excitation pulse into a ring-shaped pattern at the surface of a gold-coated glass substrate. Optical excitation induces a surface acoustic wave (SAW) that propagates in the plane of the sample and converges toward the center. The evolution of the SAW profile is monitored using interferometry with a femtosecond probe pulse at variable time delays. The quantitative analysis of the full-field images provides direct information about the surface displacement profiles, which are compared to calculations. The high stress at the focal point leads to the removal of the gold coating and, at higher excitation energies, to damage of the glass substrate. The results open the prospect for testing material strength on the microscale using laser-generated SAWs.

  18. Graphene-mediated microfluidic transport and nebulization via high frequency Rayleigh wave substrate excitation.

    Ang, Kar M; Yeo, Leslie Y; Hung, Yew M; Tan, Ming K


    The deposition of a thin graphene film atop a chip scale piezoelectric substrate on which surface acoustic waves are excited is observed to enhance its performance for fluid transport and manipulation considerably, which can be exploited to achieve further efficiency gains in these devices. Such gains can then enable complete integration and miniaturization for true portability for a variety of microfluidic applications across drug delivery, biosensing and point-of-care diagnostics, among others, where field-use, point-of-collection or point-of-care functionality is desired. In addition to a first demonstration of vibration-induced molecular transport in graphene films, we show that the coupling of the surface acoustic wave gives rise to antisymmetric Lamb waves in the film which enhance molecular diffusion and hence the flow through the interstitial layers that make up the film. Above a critical input power, the strong substrate vibration displacement can also force the molecules out of the graphene film to form a thin fluid layer, which subsequently destabilizes and breaks up to form a mist of micron dimension aerosol droplets. We provide physical insight into this coupling through a simple numerical model, verified through experiments, and show several-fold improvement in the rate of fluid transport through the film, and up to 55% enhancement in the rate of fluid atomization from the film using this simple method.

  19. Influence of yielding base and rigid base on propagation of Rayleigh-type wave in a viscoelastic layer of Voigt type



    The present study aims to study the propagation of Rayleigh-type wave in a layer, composed of isotropic viscoelastic material of Voigt type, with the effect of yielding base and rigid base in two distinct cases.With the aid of an analytical treatment, closed-form expressions of phase velocity and damped velocity for both the cases are deduced. As a special case of the problem it is found that obtained results are in good agreement with the established standard results existing in the literature. It is established through the study that volume viscoelastic and shear-viscoelastic material parameter and yielding parameter have significant effect on phaseand damped velocities of Rayleigh-type wave in both the cases. Numerical calculations and graphical illustration have been carried out for both the considered cases in the presence and the absence of viscoelasticity. Acomparative study has been performed to analyse the effect of layer with yielding base, traction-free base and rigid base on the phase and damped velocities of Rayleigh-type wave.

  20. Group velocity distribution of Rayleigh waves and crustal and upper mantle velocity structure of the Chinese mainland and its vicinity

    何正勤; 丁志峰; 叶太兰; 孙为国; 张乃铃


    Based on the long period digital surface wave data recorded by 11 CDSN stations and 11 IRIS stations, the dispersion curves of the group velocities of fundamental mode Rayleigh waves along 647 paths, with the periods from 10 s to 92 s, were measured by multi-filter. Their distribution at 25 central periods within the region of 18((54(N, 70(~140(E was inverted by Dimtar-Yanovskaya method. Within the period from 10 s to 15.9 s, the group velocity distribution is laterally inhomogeneous and is closely related to geotectonic units, with two low velocity zones located in the Tarim basin and the East China Sea and its north regions, respectively. From 21 s to 33 s, the framework of tectonic blocks is revealed. From 36.6 s to 40 s, the lithospheric subdivision of the Chinese mainland is obviously uncovered, with distinct boundaries among the South-North seismic belt, the Tibetan plateau, the North China, the South China and the Northeast China. Four cross-sections of group velocity distribution with period along 30(N, 38(N, 90(E and 120(E, are discussed, respectively, which display the basic features of the crust and upper mantle of the Chinese mainland and its neighboring regions. There are distinguished velocity differences among the different tectonic blocks. There are low-velocity-zones (LVZ) in the middle crust of the eastern Tibetan plateau, high velocity featured as stable platform in the Tarim basin and the Yangtze platform, shallow and thick low-velocity-zone in the upper mantle of the North China. The upper mantle LVZ in the East China Sea and the Japan Sea is related to the frictional heat from the subduction of the Philippine slab and the strong extension since the Himalayan orogenic period.

  1. Ultrasonic Approach of Rayleigh Pitch-Catch Contact Ultrasound Waves on CFRP Laminated Composites

    In-Young Yang; Kwang-Hee Im; Uk Heo; David K Hsu; Je-Woong Park; Hak-Joon Kim; Sung-Jin Song


    CFRP (carbon fiber reinforced plastics) composite materials have wide applicability because of their inherent design flexibility and improved material properties. However, impacted composite structures have 50%-75% less strength than undamaged structures. In this work, a CFRP composite material was nondestructively characterized in order to ensure product quality and structural integrity of CFRP and one-sided pitch-catch technique was developed to measure impacted-damaged area by using an automated-data acquisition system in an immersion tank. A pitch-catch signal was found to be more sensitive than normal incidence backwall echo of longitudinal wave under defect conditions in the composite.

  2. Phase velocities of Rayleigh and Love waves in central and northern Europe from automated, broad-band, interstation measurements

    Soomro, R. A.; Weidle, C.; Cristiano, L.; Lebedev, S.; Meier, T.; Passeq Working Group


    The increasingly dense coverage of Europe with broad-band seismic stations makes it possible to image its lithospheric structure in great detail, provided that structural information can be extracted effectively from the very large volumes of data. We develop an automated technique for the measurement of interstation phase velocities of (earthquake-excited) fundamental-mode surface waves in very broad period ranges. We then apply the technique to all available broad-band data from permanent and temporary networks across Europe. In a new implementation of the classical two-station method, Rayleigh and Love dispersion curves are determined by cross-correlation of seismograms from a pair of stations. An elaborate filtering and windowing scheme is employed to enhance the target signal and makes possible a significantly broader frequency band of the measurements, compared to previous implementations of the method. The selection of acceptable phase-velocity measurements for each event is performed in the frequency domain, based on a number of fine-tuned quality criteria including a smoothness requirement. Between 5 and 3000 single-event dispersion measurements are averaged per interstation path in order to obtain robust, broad-band dispersion curves with error estimates. In total, around 63,000 Rayleigh- and 27,500 Love-wave dispersion curves between 10 and 350 s have been determined, with standard deviations lower than 2 per cent and standard errors lower than 0.5 per cent. Comparisons of phase-velocity measurements using events at opposite backazimuths and the examination of the variance of the phase-velocity curves are parts of the quality control. With the automated procedure, large data sets can be consistently and repeatedly measured using varying selection parameters. Comparison of average interstation dispersion curves obtained with different degrees of smoothness shows that rough perturbations do not systematically bias the average dispersion measurement. They

  3. Magnetic Helicity Conservation and Inverse Energy Cascade in Electron Magnetohydrodynamic Wave Packets

    Cho, Jungyeon


    Electron magnetohydrodynamics (EMHD) provides a fluid-like description of small-scale magnetized plasmas. An EMHD wave (also known as whistler wave) propagates along magnetic field lines. The direction of propagation can be either parallel or anti-parallel to the magnetic field lines. We numerically study propagation of 3-dimensional (3D) EMHD wave packets moving in one direction. We obtain two major results: 1. Unlike its magnetohydrodynamic (MHD) counterpart, an EMHD wave packet is dispersive. Because of this, EMHD wave packets traveling in one direction create opposite traveling wave packets via self-interaction and cascade energy to smaller scales. 2. EMHD wave packets traveling in one direction clearly exhibit inverse energy cascade. We find that the latter is due to conservation of magnetic helicity. We compare inverse energy cascade in 3D EMHD turbulence and 2-dimensional (2D) hydrodynamic turbulence.

  4. The diffraction of Rayleigh waves by a fluid-saturated alluvial valley in a poroelastic half-space modeled by MFS

    Liu, Zhongxian; Liang, Jianwen; Wu, Chengqing


    Two dimensional diffraction of Rayleigh waves by a fluid-saturated poroelastic alluvial valley of arbitrary shape in a poroelastic half-space is investigated using the method of fundamental solutions (MFS). To satisfy the free surface boundary conditions exactly, Green's functions of compressional (PI and PII) and shear (SV) wave sources buried in a fluid-saturated poroelastic half-space are adopted. Next, the procedure for solving the scattering wave field is presented. It is verified that the MFS is of excellent accuracy and numerical stability. Numerical results illustrate that the dynamic response strongly depends on such factors as the incident frequency, the porosity of alluvium, the boundary drainage condition, and the valley shape. There is a significant difference between the diffraction of Rayleigh waves for the saturated soil case and for the corresponding dry soil case. The wave focusing effect both on the displacement and pore pressure can be observed inside the alluvial valley and the amplification effect seems most obvious in the case of higher porosity and lower frequency. Additionally, special attention should also be paid to the concentration of pore pressure, which is closely related to the site liquefaction in earthquakes.

  5. Drag generation by interfacial waves at an inversion/thermocline in non-hydrostatic flow past an axisymmetric obstacle

    Teixeira, Miguel A. C.; Paci, Alexandre; Belleudy, Anne


    The drag associated with 3D trapped lee waves generated at a density interface by an axisymmetric obstacle is evaluated using a linear non-hydrostatic model. These waves propagate at temperature inversions capping the boundary layer in the atmosphere, or at the oceanic thermocline, generated by, for example, drifting ice keels. They are responsible for near-surface drag that may be misrepresented as turbulent form drag in numerical models. This drag receives contributions from a continuous wavenumber range forced by the obstacle, in contrast with 2D flow (where only discrete wave modes exist), as the waves are able to vary their angle of incidence with respect to the incoming flow to satisfy their dispersion relationship. Hence (and again in contrast with 2D linear flow), the drag is non-zero both for subcritical and supercritical flow, and attains a maximum for a value of the Froude number slightly smaller than 1. This drag maximum has lower magnitude than in the hydrostatic limit, due to the effect of wave dispersion. The drag calculated from the model is in good agreement with that obtained from experiments carried out in a laboratory water flume that use axisymmetric obstacles of different heights, especially for the lowest obstacle (as would be expected). The best agreement is achieved when the effects of both a rigid lid bounding the fluid layer further away from the obstacle, and friction (represented as a Rayleigh damping), are taken into account. The model is not as quantitatively accurate when the highest obstacle used in the experiments is considered, as this corresponds to stronger flow nonlinearity. But, even in that case, the model has a qualitatively correct behaviour, which is much more accurate than the 3D hydrostatic or 2D non-hydrostatic limits. This suggests that 3D and non-hydrostatic effects to a large extent determine the drag behaviour observed in the experiments. The wave signatures associated with this behaviour are dominated by transverse

  6. Nonlinear hydrodynamic effects induced by Rayleigh surface acoustic wave in sessile droplets.

    Alghane, M; Chen, B X; Fu, Y Q; Li, Y; Desmulliez, M P Y; Mohammed, M I; Walton, A J


    We report an experimental and numerical characterization of three-dimensional acoustic streaming behavior in small droplets of volumes (1-30 μl) induced by surface acoustic wave (SAW). We provide a quantitative evidence of the existence of strong nonlinear nature of the flow inertia in this SAW-driven flow over a range of the newly defined acoustic parameter F{NA}=Fλ/(σ/R_{d})≥0.01, which is a measure of the strength of the acoustic force to surface tension, where F is the acoustic body force, λ is the SAW wavelength, σ is the surface tension, and R{d} is the droplet radius. In contrast to the widely used Stokes model of acoustic streaming, which generally ignores such a nonlinearity, we identify that the full Navier-Stokes equation must be applied to avoid errors up to 93% between the computed streaming velocities and those from experiments as in the nonlinear case. We suggest that the Stokes model is valid only for very small acoustic power of ≤1 μW (F{NA}droplets.

  7. Skeletonized Wave Equation Inversion in VTI Media without too much Math

    Feng, Shihang


    We present a tutorial for skeletonized inversion of pseudo-acoustic anisotropic VTI data. We first invert for the anisotropic models using wave equation traveltime inversion. Here, the skeletonized data are the traveltimes of transmitted and/or reflected arrivals that lead to simpler misfit functions and more robust convergence compared to full waveform inversion. This provides a good starting model for waveform inversion. The effectiveness of this procedure is illustrated with synthetic data examples and a marine data set recorded in the Gulf of Mexico.

  8. Modeling of the attenuation of stress waves in concrete based on the Rayleigh damping model using time-reversal and PZT transducers

    Tian, Zhen; Huo, Linsheng; Gao, Weihang; Li, Hongnan; Song, Gangbing


    Wave-based concrete structural health monitoring has attracted much attention. A stress wave experiences significant attenuation in concrete, however there is a lack of a unified method for predicting the attenuation coefficient of the stress wave. In this paper, a simple and effective absorption attenuation model of stress waves in concrete is developed based on the Rayleigh damping model, which indicates that the absorption attenuation coefficient of stress waves in concrete is directly proportional to the square of the stress wave frequency when the damping ratio is small. In order to verify the theoretical model, related experiments were carried out. During the experiments, a concrete beam was designed in which the d33-model piezoelectric smart aggregates were embedded to detect the propagation of stress waves. It is difficult to distinguish direct stress waves due to the complex propagation paths and the reflection and scattering of stress waves in concrete. Hence, as another innovation of this paper, a new method for computing the absorption attenuation coefficient based on the time-reversal method is developed. Due to the self-adaptive focusing properties of the time-reversal method, the time-reversed stress wave focuses and generates a peak value. The time-reversal method eliminates the adverse effects of multipaths, reflection, and scattering. The absorption attenuation coefficient is computed by analyzing the peak value changes of the time-reversal focused signal. Finally, the experimental results are found to be in good agreement with the theoretical model.

  9. Magnetic helicity conservation and inverse energy cascade in electron magnetohydrodynamic wave packets.

    Cho, Jungyeon


    Electron magnetohydrodynamics (EMHD) provides a fluidlike description of small-scale magnetized plasmas. An EMHD wave propagates along magnetic field lines. The direction of propagation can be either parallel or antiparallel to the magnetic field lines. We numerically study propagation of three-dimensional (3D) EMHD wave packets moving in one direction. We obtain two major results. (1) Unlike its magnetohydrodynamic (MHD) counterpart, an EMHD wave packet is dispersive. Because of this, EMHD wave packets traveling in one direction create opposite-traveling wave packets via self-interaction and cascade energy to smaller scales. (2) EMHD wave packets traveling in one direction clearly exhibit inverse energy cascade. We find that the latter is due to conservation of magnetic helicity. We compare inverse energy cascade in 3D EMHD turbulence and two-dimensional (2D) hydrodynamic turbulence.

  10. Tutorial for Wave Equation Inversion of Skeletonized Data

    Lu, Kai


    Full waveform inversion of seismic data is often plagued by cycle skipping problems so that an iterative optimization method often gets stuck in a local minimum. To avoid this problem we simplify the objective function so that the iterative solution can quickly converge to a solution in the vicinity of the global minimum. The objective function is simplified by only using parsimonious and important portions of the data, which are defined as skeletonized data. We now present a mostly non-mathematical tutorial that explains the theory of skeletonized inversion. We also show its effectiveness with examples.

  11. Inverse energy cascade and emergence of large coherent vortices in turbulence driven by Faraday waves.

    Francois, N; Xia, H; Punzmann, H; Shats, M


    We report the generation of large coherent vortices via inverse energy cascade in Faraday wave driven turbulence. The motion of floaters in the Faraday waves is three dimensional, but its horizontal velocity fluctuations show unexpected similarity with two-dimensional turbulence. The inverse cascade is detected by measuring frequency spectra of the Lagrangian velocity, and it is confirmed by computing the third moment of the horizontal velocity fluctuations. This is observed in deep water in a broad range of wavelengths and vertical accelerations. The results broaden the scope of recent findings on Faraday waves in thin layers [A. von Kameke et al., Phys. Rev. Lett. 107, 074502 (2011)].

  12. Rayleigh surface wave modeling by finite difference method in biphasic media%双相介质瑞雷面波有限差分正演模拟

    张伟; 甘伏平; 刘伟; 郑智杰


    为了研究双相介质瑞雷面波的形成机制及传播规律,促进瑞雷面波资料处理方法的发展。文章根据弹性波动方程,采用交错网格有限差分算法,对二维各向同性弹性介质做解析解与数值解的对比,在此基础上,将PML吸收边界条件,改进的镜像法应用于双相介质波动方程中,并作了稳定性分析,对双相介质水平层状、起伏分界面等典型模型瑞雷面波及体波在内的全波场进行研究。结果表明:基于弹性介质解析解与数值解的对比,在误差接受范围内,研究双相介质是可行的;把稍作改进的镜像法应用于双相介质中,能够有效地处理瑞雷面波自由边界问题;通过详细分析双相介质瑞雷面波及体波在内的全波场的信息,对以双相介质为基础的地震波勘探有一定的指导作用。%In order to study the mechanism and propagation of Rayleigh surface wave in biphasic media and promote the development of data⁃processing method of Rayleigh surface wave, the authors applied finite difference method with staggered grids to simulate the 2D i⁃sotropic elastic media based on the elastic wave equation, and made a comparison between the analytical and numerical solutions. On such a basis, the PML absorbing boundary condition and improved image method can be applied to the two⁃phase medium wave equa⁃tion to simulate the typical media model including horizontal layer and undulating interface, analyze the full wave information including the Rayleigh surface wave and body wave, and make a stability analysis. The results show that, on the basis of the comparison between the numerical solution and the analytical solution of the elastic media within the acceptable range of the error, the study of biphasic me⁃dium is feasible. The slight improvement of the image method can be applied to biphasic media to deal with free boundary condition problem of the Rayleigh surface wave

  13. On the Contribution of Head Waves to Full Waveform Inversion

    Kazei, V.V.; Ponomarenko, A.V.; Troyan, V.N.; Kashtan, B.M.; Mulder, W.A.


    Full waveform inversion suffers from local minima, due to a lack of low frequencies in the data. A reflector below the zone of interest may, however, help in recovering the long-wavelength components of a velocity perturbation, as demonstrated in a paper by Mora. With the Born approximation for the

  14. On a technique for deriving the explicit secular equation of Rayleigh waves in an orthotropic half-space coated by an orthotropic layer

    Vinh, P. C.; Anh, V. T. N.; Linh, N. T. K.


    The secular equation of Rayleigh propagating in an orthotropic half-space coated by an orthotropic layer has been obtained by Sotiropolous [Sotiropolous, D. A. (1999), The e®ect of anisotropy on guided elastic waves in a layered half-space, Mechanics of Materials 31, 215-233] and by Sotiropolous & Tougelidis [Sotiropolous, D. A. and Tougelidis, G. (1998), Guided elastic waves in orthotropic surface layer, Ultrasonics 36, 371-374]. However, it is not totally explicit and some misprints have occurred in this secular equation in both papers. This secular equation was derived by expanding directly a six-order determinant originated from the traction-free conditions at the top surface of the layer and the continuity of displacements and stresses through the interface between the layer and the half-space. Since the expansion of this six-order determinant was not shown in both two papers, it has been difficult to readers to recognize these misprints. This paper presents a technique that provides a totally explicit secular equation of the wave. The technique makes clear the way from the traction-free and continuity conditions to the secular equation and enables us to recognize the misprints appearing in the reported secular equation. The technique can be employed to obtain explicit secular equations of Rayleigh waves for many other cases. Moreover, the paper introduces a transfer matrix in explicit form for an orthotropic layer that is much simpler in form than the one obtained previously.

  15. A new scheme for joint surface wave and earthquake travel-time inversion and resulting 3-D velocity model for the western North Island, New Zealand

    Eberhart-Phillips, Donna; Fry, Bill


    We have developed a joint inversion of surface wave group velocity (U) and local earthquake travel-time (LET) data and applied it to the North Island, New Zealand, to improve the existing New Zealand wide 3-D seismic velocity model. This approach takes full advantage of the differing sensitivities of surface and body waves. The data are complementary, particularly at shallow depths where LET tomography suffers from vertical smearing and surface wave tomography is susceptible to horizontal smearing. The employed U observations are 2-D models at discrete periods which were developed for Rayleigh wave dispersion curves measured from the 1744 interstation Green's Functions obtained by stacked cross-correlations of broadband ambient noise data. In the volume surrounding each U observation, we distribute numerous points for relating the U observation to the gridded 3-D tomography model, analogous to points along a raypath. The partial derivatives at the points are computed using the U sensitivity kernels for Vp and Vs, with Vs related to Vp and Vp/Vs perturbations. Thus, the U observations are included along with the travel-time observations in a joint inversion to best fit the data and the existing tomography model. The resulting model favors the U where there is little travel-time resolution. The combined inversion used 2949 U observations at 6-16 s period and LET from 1509 earthquakes that extend to 370 km depth, and improved the model fit by reducing the U residual data variance by 62% and the LET by 9%. The resulting model generally has better constrained depth of shallow anomalies, with decreased velocity in the upper 2 km in the western North Island, and slight focusing of crustal high velocity features at 8 km depth. Significantly, the increased resolution in the shallowest 5 km of the model improves the utility of the 3-D model for use in seismic hazard assessment, wave propagation studies, and studies comparing seismic velocities to geological mapping.

  16. On the application of Particle Swarm Optimization strategies on Scholte-wave inversion

    Wilken, D.; Rabbel, W.


    We investigate different aspects concerning the application of swarm intelligence optimization to the inversion of Scholte-wave phase-slowness frequency (p-f) spectra with respect to shear wave velocity structure. Besides human influence due to the dependence on a priori information for starting models and interpretation of p-f spectra as well as noise, the model resolution of the inversion problem is strongly influenced by the multimodality of the misfit function. We thus tested the efficiency of global, stochastic optimization approaches with focus on swarm intelligence methods that can explore the multiple minima of the misfit function. A comparison among different PSO schemes by applying them to synthetic Scholte-wave spectra led to a hybrid of Particle Swarm Optimization and Downhill Simplex providing the best resolution of inverted shear wave velocity depth models. The results showed a very low spread of best fitting solutions of 7 per cent in shear wave velocity and an average of 9 per cent for noisy synthetic data and a very good fit to the true synthetic model used for computation of the input data. To classify this method we also compared the probability of finding a good fit in synthetic spectra inversion with that of Evolutionary Algorithm, Simulated Annealing, Neighbourhood Algorithm and Artificial Bee Colony algorithm. Again the hybrid optimization scheme showed its predominance. The usage of stochastic algorithms furthermore allowed a new way of misfit definition in terms of dispersion curve slowness residuals making the inversion scheme independent on Scholte-wave mode identification and allowing joint inversion of fundamental mode and higher mode information. Finally we used the hybrid optimization scheme and the misfit calculation for the inversion of 2-D shear wave velocity profiles from two locations in the North- and Baltic Sea. The models show acceptable resolution and a very good structural correlation to high resolution reflection seismic

  17. Inverse determinations of the parameters of three-layered plate using angle probe generated Lamb waves

    LIUZhenqing; LIUXiao; TADe'an


    The study on the inverse problems in the ultrasonic nondestructive testing (NDT) has a wide application field in various industries. An error function based inversion algorithm is introduced to determine the parameters of three-layered plates from the measured velocity of multi-mode Lamb waves. A mixed-spectral estimation is proposed to combine FFT with AR model for exact determination of the ultrasonic phase velocity. Experiments are performed using two conventional angle probes as transmitter and receiver on the same surface of three-layered laminates. Inverse analyses of one parameter (thickness) and two parameters (longitudinal and transverse wave velocities in a layer, or thickness of two layers) of three-layered laminates are made. The experimental results show that the inverse approach is in good agreement with the actual value.

  18. Study on the electromechanical coupling coefficient of Rayleigh-type surface acoustic waves in semi-infinite piezoelectrics/non-piezoelectrics superlattices.

    Chen, Shi; Zhang, Yinhong; Lin, Shuyu; Fu, Zhiqiang


    The electromechanical coupling coefficient of Rayleigh-type surface acoustic waves in semi-infinite piezoelectrics/non-piezoelectrics superlattices is investigated by the transfer matrix method. Research results show the high electromechanical coupling coefficient can be obtained in these systems. The optimization design of it is also discussed fully. It is significantly influenced by electrical boundary conditions on interfaces, thickness ratios of piezoelectric and non-piezoelectric layers, and material parameters (such as velocities of pure longitudinal and transversal bulk waves in non-piezoelectric layers). In order to obtain higher electromechanical coupling coefficient, shorted interfaces, non-piezoelectric materials with large velocities of longitudinal and transversal bulk waves, and proper thickness ratios should be chosen.

  19. Solution of an inverse scattering problem for the acoustic wave equation in three-dimensional media

    Baev, A. V.


    A three-dimensional inverse scattering problem for the acoustic wave equation is studied. The task is to determine the density and acoustic impedance of a medium. A necessary and sufficient condition for the unique solvability of this problem is established in the form of an energy conservation law. The interpretation of the solution to the inverse problem and the construction of medium images are discussed.

  20. Background velocity inversion by phase along reflection wave paths

    Yu, Han


    A background velocity model containing the correct lowwavenumber information is desired for both the quality of the migration image and the success of waveform inversion. We propose to invert for the low-wavenumber part of the velocity model by minimizing the phase difference between predicted and observed reflections. The velocity update is exclusively along the reflection wavepaths and, unlike conventional FWI, not along the reflection ellipses. This allows for reconstructing the smoothly varying parts of the background velocity model. Tests with synthetic data show both the benefits and limitations of this method.

  1. Lithospheric structure of the westernmost Mediterranean inferred from finite frequency Rayleigh wave tomography S-velocity model.

    Palomeras, Imma; Villasenor, Antonio; Thurner, Sally; Levander, Alan; Gallart, Josep; Harnafi, Mimoun


    The Iberian Peninsula and Morocco, separated by the Alboran Sea and the Algerian Basin, constitute the westernmost Mediterranean. From north to south this region consists of the Pyrenees, the result of interaction between the Iberian and Eurasian plates; the Iberian Massif, a region that has been undeformed since the end of the Paleozoic; the Central System and Iberian Chain, regions with intracontinental Oligocene-Miocene deformation; the Gibraltar Arc (Betics, Rif and Alboran terranes) and the Atlas Mountains, resulting from post-Oligocene subduction roll-back and Eurasian-Nubian plate convergence. In this study we analyze data from recent broad-band array deployments and permanent stations on the Iberian Peninsula and in Morocco (Spanish IberArray and Siberia arrays, the US PICASSO array, the University of Munster array, and the Spanish, Portuguese, and Moroccan National Networks) to characterize its lithospheric structure. The combined array of 350 stations has an average interstation spacing of ~60 km, comparable to USArray. We have calculated the Rayleigh waves phase velocities from ambient noise for short periods (4 s to 40 s) and teleseismic events for longer periods (20 s to 167 s). We inverted the phase velocities to obtain a shear velocity model for the lithosphere to ~200 km depth. The model shows differences in the crust for the different areas, where the highest shear velocities are mapped in the Iberian Massif crust. The crustal thickness is highly variable ranging from ~25 km beneath the eastern Betics to ~55km beneath the Gibraltar Strait, Internal Betics and Internal Rif. Beneath this region a unique arc shaped anomaly with high upper mantle velocities (>4.6 km/s) at shallow depths (Gibraltar arc to ~55 km depth. Low upper mantle velocities (<4.2 km/s) are observed beneath the Atlas, the northeastern end of the Betic Mountains and the Late Cenozoic volcanic fields in Iberia and Morocco, indicative of high temperatures at relatively shallow depths

  2. Visco-elastic controlled-source full waveform inversion without surface waves

    Paschke, Marco; Krause, Martin; Bleibinhaus, Florian


    We developed a frequency-domain visco-elastic full waveform inversion for onshore seismic experiments with topography. The forward modeling is based on a finite-difference time-domain algorithm by Robertsson that uses the image-method to ensure a stress-free condition at the surface. The time-domain data is Fourier-transformed at every point in the model space during the forward modeling for a given set of frequencies. The motivation for this approach is the reduced amount of memory when computing kernels, and the straightforward implementation of the multiscale approach. For the inversion, we calculate the Frechet derivative matrix explicitly, and we implement a Levenberg-Marquardt scheme that allows for computing the resolution matrix. To reduce the size of the Frechet derivative matrix, and to stabilize the inversion, an adapted inverse mesh is used. The node spacing is controlled by the velocity distribution and the chosen frequencies. To focus the inversion on body waves (P, P-coda, and S) we mute the surface waves from the data. Consistent spatiotemporal weighting factors are applied to the wavefields during the Fourier transform to obtain the corresponding kernels. We test our code with a synthetic study using the Marmousi model with arbitrary topography. This study also demonstrates the importance of topography and muting surface waves in controlled-source full waveform inversion.

  3. An analytical model for the amplitude of lee waves forming on the boundary layer inversion

    Sachsperger, Johannes; Serafin, Stefano; Stiperski, Ivana; Grubišić, Vanda


    Lee waves are horizontally propagating gravity waves with a typical wavelength of 5-15 km that may be generated when stratified flow is lifted over a mountain. A frequently observed type of such waves is that of interfacial lee waves. Those develop, similar to surface waves on a free water surface, when the upstream flow features a density discontinuity. Such conditions are often present for example at the capping inversion in boundary layer flow. The dynamics of interfacial lee waves can be described concisely with linear interfacial gravity wave theory. However, while this theoretical framework accurately describes the wavelength, it fails to properly predict the amplitude of lee waves. It is well known that large amplitude lee waves may lead to low-level turbulence, which poses a potential hazard for aviation. Therefore, this property of interfacial lee waves deserves further attention. In this study, we develop a simple analytical model for the amplitude of lee waves forming on the boundary layer inversion. This model is based on the energetics of two-layer flow. We obtain an expression for the wave amplitude by equating the energy loss across an internal jump with the energy radiation through lee waves. The verification of the result with water tank experiments of density-stratified two-layer flow over two-dimensional topography from the HYDRALAB campaign shows good agreement between theory and observations. This new analytical model may be useful in determining potential hazards of interfacial lee waves with negligible computational cost as compared to numerical weather prediction models.

  4. Linearization Ill-Posedness for 2.5-D Wave Equation Inversion Model

    Ji-jun Liu


    For the weakly inhomogeneous acoustic medium in Ω={(x,y,z):z>0}, we consider the inverse problem of determining the density function ρ(x,y). The inversion input for our inverse problem is the wave field given on a line. We get an integral equation for the 2-D density perturbation from the linearization. By virtue of the integral transform, we prove the uniqueness and the instability of the solution to the integral equation. The degree of ill-posedness for this problem is also given.

  5. Structure of the deep Nazca slab from joint inversion of regional S wave trains and teleseismic S arrival times

    Lloyd, S. M.; van der Lee, S.; Assumpcao, M.; Rocha, M. P.; Vandecar, J. C.


    We combine receiver function constraints on crustal thickness, Rayleigh wave group velocities, regional S wave trains, and teleseismic S delays to jointly invert for the S-velocity structure of central South America. Previous studies using the teleseismic delay times have outlined 1) a long, strong high-velocity anomaly typical of subducting oceanic lithosphere beneath the central part of the Central Andes, and 2) a deeper, uppermost lower-mantle high-velocity anomalie beneath southeastern Brazil. Using the other above data sets, which constrain the upper mantle between the two regions, we connect the two tomographic models through the mentioned joint inversion of the combined data sets. We investigate whether the lower-mantle high velocity anomaly beneath southeastern Brazil is possibly the extension of the the high-velocity anomaly representing the subducting Nazca Plate between the Central Andes and whether any portion of the deep slab may be relatively flat around the mid-mantle transition region, allowing it to reach to beneath the continent's opposing, passive margin within the top 1000 km of the mantle. This reach could in turn lead to interesting mantle and passive-margin dynamics through the cycling of deeply subducted water. We will conclude with a comparison with North America, where past subduction at shallow dip angles (during the Laramide) may have led to flat slab segments in the transition zone. Thermo-kinetic modeling has shown that the same chunk of oceanic lithosphere was involved in both cases of "flatness", having slowed the slab's progression into the lower mantle and facilitating slab deformation within the transition zone.

  6. Power inversion design for ocean wave energy harvesting

    Talebani, Anwar N.

    The needs for energy sources are increasing day by day because of several factors, such as oil depletion, and global climate change due to the higher level of CO2, so the exploration of various renewable energy sources is very promising area of study. The available ocean waves can be utilized as free source of energy as the water covers 70% of the earth surface. This thesis presents the ocean wave energy as a source of renewable energy. By addressing the problem of designing efficient power electronics system to deliver 5 KW from the induction generator to the grid with less possible losses and harmonics as possible and to control current fed to the grid to successfully harvest ocean wave energy. We design an AC-DC full bridge rectifier converter, and a DC-DC boost converter to harvest wave energy from AC to regulated DC. In order to increase the design efficiency, we need to increase the power factor from (0.5-0.6) to 1. This is accomplished by designing the boost converter with power factor correction in continues mode with RC circuit as an input to the boost converter power factor correction. This design results in a phase shift between the input current and voltage of the full bridge rectifier to generate a small reactive power. The reactive power is injected to the induction generator to maintain its functionality by generating a magnetic field in its stator. Next, we design a single-phase pulse width modulator full bridge voltage source DC-AC grid-tied mode inverter to harvest regulated DC wave energy to AC. The designed inverter is modulated by inner current loop, to control current injected to the grid with minimal filter component to maintain power quality at the grid. The simulation results show that our design successfully control the current level fed to the grid. It is noteworthy that the simulated efficiency is higher than the calculated one since we used an ideal switch in the simulated circuit.

  7. Joint inversion of apparent resistivity and seismic surface and body wave data

    Garofalo, Flora; Sauvin, Guillaume; Valentina Socco, Laura; Lecomte, Isabelle


    A novel inversion algorithm has been implemented to jointly invert apparent resistivity curves from vertical electric soundings, surface wave dispersion curves, and P-wave travel times. The algorithm works in the case of laterally varying layered sites. Surface wave dispersion curves and P-wave travel times can be extracted from the same seismic dataset and apparent resistivity curves can be obtained from continuous vertical electric sounding acquisition. The inversion scheme is based on a series of local 1D layered models whose unknown parameters are thickness h, S-wave velocity Vs, P-wave velocity Vp, and Resistivity R of each layer. 1D models are linked to surface-wave dispersion curves and apparent resistivity curves through classical 1D forward modelling, while a 2D model is created by interpolating the 1D models and is linked to refracted P-wave hodograms. A priori information can be included in the inversion and a spatial regularization is introduced as a set of constraints between model parameters of adjacent models and layers. Both a priori information and regularization are weighted by covariance matrixes. We show the comparison of individual inversions and joint inversion for a synthetic dataset that presents smooth lateral variations. Performing individual inversions, the poor sensitivity to some model parameters leads to estimation errors up to 62.5 %, whereas for joint inversion the cooperation of different techniques reduces most of the model estimation errors below 5% with few exceptions up to 39 %, with an overall improvement. Even though the final model retrieved by joint inversion is internally consistent and more reliable, the analysis of the results evidences unacceptable values of Vp/Vs ratio for some layers, thus providing negative Poisson's ratio values. To further improve the inversion performances, an additional constraint is added imposing Poisson's ratio in the range 0-0.5. The final results are globally improved by the introduction of

  8. Realization of Arbitrary Inverse Unitary Transformation of Single Mode Fibre by Using Three Wave Plates

    WANG Shao-Kai; REN Ji-Gang; PENG Cheng-Zhi; JIANG Shuo; WANG Xiang-Bin


    We report a method to realize the arbitrary inverse unitary transformation imposed by a single-mode fibre on photon's polarization by the succession of two quarter-wave plates and a half-wave plate. The process of realization by polarization state vector. The method is meaningful in quantum communication experiment such as quantum teleportation, in which an unknown arbitrary quantum state should be kept to be unchanged in the case of using a single-mode fibre for time delay.

  9. Multi-Grid and Resolution Full-Wave Tomography and Moment Tensor Inversion (Postprint)


    number of discrete nodes in numerical methods, we adapt a multigrid/multilevel method ( Briggs , 1987) to solve the wave propagation and inversion...Monitoring Technologies 186 Approved for public release; distribution is unlimited. Antoun, T., D. Harris, T. Lay, S.C. Myers , M.E. Pasyanos, P...The current limits of resolution for surface wave tomography in North America, Eos Trans AGU, 81, F897. Briggs , W.L. (1987). A multigrid Tutorial

  10. A statistical assessment of seismic models of the U.S. continental crust using Bayesian inversion of ambient noise surface wave dispersion data

    Olugboji, T. M.; Lekic, V.; McDonough, W.


    We present a new approach for evaluating existing crustal models using ambient noise data sets and its associated uncertainties. We use a transdimensional hierarchical Bayesian inversion approach to invert ambient noise surface wave phase dispersion maps for Love and Rayleigh waves using measurements obtained from Ekström (2014). Spatiospectral analysis shows that our results are comparable to a linear least squares inverse approach (except at higher harmonic degrees), but the procedure has additional advantages: (1) it yields an autoadaptive parameterization that follows Earth structure without making restricting assumptions on model resolution (regularization or damping) and data errors; (2) it can recover non-Gaussian phase velocity probability distributions while quantifying the sources of uncertainties in the data measurements and modeling procedure; and (3) it enables statistical assessments of different crustal models (e.g., CRUST1.0, LITHO1.0, and NACr14) using variable resolution residual and standard deviation maps estimated from the ensemble. These assessments show that in the stable old crust of the Archean, the misfits are statistically negligible, requiring no significant update to crustal models from the ambient noise data set. In other regions of the U.S., significant updates to regionalization and crustal structure are expected especially in the shallow sedimentary basins and the tectonically active regions, where the differences between model predictions and data are statistically significant.

  11. Improved Shear Wave Motion Detection Using Pulse-Inversion Harmonic Imaging With a Phased Array Transducer.

    Pengfei Song; Heng Zhao; Urban, Matthew W; Manduca, Armando; Pislaru, Sorin V; Kinnick, Randall R; Pislaru, Cristina; Greenleaf, James F; Shigao Chen


    Ultrasound tissue harmonic imaging is widely used to improve ultrasound B-mode imaging quality thanks to its effectiveness in suppressing imaging artifacts associated with ultrasound reverberation, phase aberration, and clutter noise. In ultrasound shear wave elastography (SWE), because the shear wave motion signal is extracted from the ultrasound signal, these noise sources can significantly deteriorate the shear wave motion tracking process and consequently result in noisy and biased shear wave motion detection. This situation is exacerbated in in vivo SWE applications such as heart, liver, and kidney. This paper, therefore, investigated the possibility of implementing harmonic imaging, specifically pulse-inversion harmonic imaging, in shear wave tracking, with the hypothesis that harmonic imaging can improve shear wave motion detection based on the same principles that apply to general harmonic B-mode imaging. We first designed an experiment with a gelatin phantom covered by an excised piece of pork belly and show that harmonic imaging can significantly improve shear wave motion detection by producing less underestimated shear wave motion and more consistent shear wave speed measurements than fundamental imaging. Then, a transthoracic heart experiment on a freshly sacrificed pig showed that harmonic imaging could robustly track the shear wave motion and give consistent shear wave speed measurements of the left ventricular myocardium while fundamental imaging could not. Finally, an in vivo transthoracic study of seven healthy volunteers showed that the proposed harmonic imaging tracking sequence could provide consistent estimates of the left ventricular myocardium stiffness in end-diastole with a general success rate of 80% and a success rate of 93.3% when excluding the subject with Body Mass Index higher than 25. These promising results indicate that pulse-inversion harmonic imaging can significantly improve shear wave motion tracking and thus potentially

  12. Generalized Variational Principle for Long Water-Wave Equation by He's Semi-Inverse Method

    Weimin Zhang


    Full Text Available Variational principles for nonlinear partial differential equations have come to play an important role in mathematics and physics. However, it is well known that not every nonlinear partial differential equation admits a variational formula. In this paper, He's semi-inverse method is used to construct a family of variational principles for the long water-wave problem.

  13. Polarisation independent bi-directional four wave mixing for mid span spectral inversion

    Clausen, Anders; Buxens, Alvaro A.; Poulsen, Henrik Nørskov


    Polarisation independent Four Wave Mixing in a Semiconductor Optical Amplifier used for Mid Span Spectral Inversion (MSSI) is implemented and introduce only 0.9 dB penalty compared to polarisation dependent MSSI. The polarisation dependence in receiver sensitivity is 1 dB....

  14. Full-waveform inversion with reflected waves for 2D VTI media

    Pattnaik, Sonali


    Full-waveform inversion in anisotropic media using reflected waves suffers from the strong non-linearity of the objective function and trade-offs between model parameters. Estimating long-wavelength model components by fixing parameter perturbations, referred to as reflection-waveform inversion (RWI), can mitigate nonlinearity-related inversion issues. Here, we extend RWI to acoustic VTI (transversely isotropic with a vertical symmetry axis) media. To minimize trade-offs between the model parameters, we employ a new hierarchical two-stage approach that operates with the P-wave normal-moveout velocity and anisotropy coefficents ζ and η. First, is estimated using a fixed perturbation in ζ, and then we invert for η by fixing the updated perturbation in . The proposed 2D algorithm is tested on a horizontally layered VTI model.

  15. Upper mantle structure under western Saudi Arabia from Rayleigh wave tomography and the origin of Cenozoic uplift and volcanism on the Arabian Shield

    Park, Y; Nyblade, A; Rodgers, A; Al-Amri, A


    The shear velocity structure of the shallow upper mantle beneath the Arabian Shield has been modeled by inverting new Rayleigh wave phase velocity measurements between 45 and 140 s together with previously published Rayleigh wave group velocity measurement between 10 and 45 s. For measuring phase velocities, we applied a modified array method that minimizes the distortion of raypaths by lateral heterogeneity. The new shear velocity model shows a broad low velocity region in the lithospheric mantle across the Shield and a low velocity region at depths {ge} 150 km localized along the Red Sea coast and Makkah-Madinah-Nafud (MMN) volcanic line. The velocity reduction in the upper mantle corresponds to a temperature anomaly of {approx}250-330 K. These finding, in particular the region of continuous low velocities along the Red Sea and MMN volcanic line, do not support interpretations for the origin of the Cenozoic plateau uplift and volcanism on the Shield invoking two separate plumes. When combined with images of the 410 and 660 km discontinuities beneath the southern part of the Arabian Shield, body wave tomographic models, a S-wave polarization analysis, and SKS splitting results, our new model supports an interpretation invoking a thermal upwelling of warm mantle rock originating in the lower mantle under Africa that crosses through the transition zone beneath Ethiopia and moves to the north and northwest under the eastern margin of the Red Sea and the Arabian Shield. In this interpretation, the difference in mean elevation between the Platform and Shield can be attributed to isostatic uplift caused by heating of the lithospheric mantle under the Shield, with significantly higher region along the Red Sea possibly resulting from a combination of lithosphere thinning and dynamic uplift.

  16. High-resolution inverse Raman and resonant-wave-mixing spectroscopy

    Rahn, L.A. [Sandia National Laboratories, Livermore, CA (United States)


    These research activities consist of high-resolution inverse Raman spectroscopy (IRS) and resonant wave-mixing spectroscopy to support the development of nonlinear-optical techniques for temperature and concentration measurements in combustion research. Objectives of this work include development of spectral models of important molecular species needed to perform coherent anti-Stokes Raman spectroscopy (CARS) measurements and the investigation of new nonlinear-optical processes as potential diagnostic techniques. Some of the techniques being investigated include frequency-degenerate and nearly frequency-degenerate resonant four-wave-mixing (DFWM and NDFWM), and resonant multi-wave mixing (RMWM).

  17. Site effects in Mexico City: Constraints from surface wave inversion of shallow refraction data

    Ramos-Martínez, J.; Chávez-García, F. J.; Romero-Jiménez, E.; Rodríguez-Zúñiga, J. L.; Gómez-González, J. M.


    In order to understand and simulate site effects on strong ground motion records of recent earthquakes in Mexico City, it is fundamental to determine the in situ elastic and anelastic properties of the shallow stratigraphy of the basin. The main properties of interest are the shear wave velocities and Q-quality factors and their correlation with similar parameters in zones of the city. Despite population density and paved surfaces, it is feasible to gather shallow refraction data to obtain laterally homogeneous subsoil structures at some locations. We focused our analysis in the Texcoco Lake region of the northeastern Mexico City basin. This area consists of unconsolidated clay sediments, similar to those of the lake bed zone in Mexico City, where ground motion amplification and long duration disturbances are commonly observed. We recorded Rayleigh and Love waves using explosive and sledgehammer sources and 4.5 Hz vertical and horizontal geophones, respectively. Additionally, for the explosive source, we recorded three-component seismograms using 1 Hz seismometers. We obtained phase velocity dispersion curves from ray parameter-frequency domain analyses and inverted them for vertical distribution of S wave velocity. The initial model was obtained from a standard first-break refraction analysis. We also obtained an estimation of the QS shear wave quality factor for the uppermost stratigraphy. Results compare well with tilt and cone penetrometer resistance measurements at the same test site, emphasizing the importance of these studies for engineering purposes.

  18. Fast and accurate analytical model to solve inverse problem in SHM using Lamb wave propagation

    Poddar, Banibrata; Giurgiutiu, Victor


    Lamb wave propagation is at the center of attention of researchers for structural health monitoring of thin walled structures. This is due to the fact that Lamb wave modes are natural modes of wave propagation in these structures with long travel distances and without much attenuation. This brings the prospect of monitoring large structure with few sensors/actuators. However the problem of damage detection and identification is an "inverse problem" where we do not have the luxury to know the exact mathematical model of the system. On top of that the problem is more challenging due to the confounding factors of statistical variation of the material and geometric properties. Typically this problem may also be ill posed. Due to all these complexities the direct solution of the problem of damage detection and identification in SHM is impossible. Therefore an indirect method using the solution of the "forward problem" is popular for solving the "inverse problem". This requires a fast forward problem solver. Due to the complexities involved with the forward problem of scattering of Lamb waves from damages researchers rely primarily on numerical techniques such as FEM, BEM, etc. But these methods are slow and practically impossible to be used in structural health monitoring. We have developed a fast and accurate analytical forward problem solver for this purpose. This solver, CMEP (complex modes expansion and vector projection), can simulate scattering of Lamb waves from all types of damages in thin walled structures fast and accurately to assist the inverse problem solver.

  19. Time-domain full waveform inversion using the gradient preconditioning based on transmitted waves energy

    Zhang, Xiao-bo


    The gradient preconditioning approach based on seismic wave energy can effectively avoid the huge storage consumption in the gradient preconditioning algorithms based on Hessian matrices in time-domain full waveform inversion (FWI), but the accuracy is affected by the energy of reflected waves when strong reflectors are present in velocity model. To address this problem, we propose a gradient preconditioning method, which scales the gradient based on the energy of the “approximated transmitted wavefield” simulated by the nonreflecting acoustic wave equation. The method does not require computing or storing the Hessian matrix or its inverse. Furthermore, it can effectively eliminate the effects caused by geometric diffusion and non-uniformity illumination on gradient. The results of model experiments confirm that the time-domain FWI using the gradient preconditioning based on transmitted waves energy can achieve higher inversion precision for high-velocity body and the deep strata below when compared with using the gradient preconditioning based on seismic waves energy.

  20. Synthesis of anisotropic swirling surface acoustic waves by inverse filter, towards integrated generators of acoustical vortices

    Riaud, Antoine; Charron, Eric; Bussonnière, Adrien; Matar, Olivier Bou


    From radio-electronics signal analysis to biological samples actuation, surface acoustic waves (SAW) are involved in a multitude of modern devices. Despite this versatility, SAW transducers developed up to date only authorize the synthesis of the most simple standing or progressive waves such as plane and focused waves. In particular, acoustical integrated sources able to generate acoustical vortices (the analogue of optical vortices) are missing. In this work, we propose a flexible tool based on inverse filter technique and arrays of SAW transducers enabling the synthesis of prescribed complex wave patterns at the surface of anisotropic media. The potential of this setup is illustrated by the synthesis of a 2D analog of 3D acoustical vortices, namely "swirling surface acoustic waves". Similarly to their 3D counterpart, they appear as concentric structures of bright rings with a phase singularity in their center resulting in a central dark spot. Swirling SAW can be useful in fragile sensors whose neighborhood...

  1. Regularization strategy for an inverse problem for a 1 + 1 dimensional wave equation

    Korpela, Jussi; Lassas, Matti; Oksanen, Lauri


    An inverse boundary value problem for a 1 + 1 dimensional wave equation with a wave speed c(x) is considered. We give a regularization strategy for inverting the map { A } :c\\mapsto {{Λ }}, where Λ is the hyperbolic Neumann-to-Dirichlet map corresponding to the wave speed c. That is, we consider the case when we are given a perturbation of the Neumann-to-Dirichlet map \\tilde{{{Λ }}}={{Λ }}+{ E }, where { E } corresponds to the measurement errors, and reconstruct an approximative wave speed \\tilde{c}. We emphasize that \\tilde{{{Λ }}} may not be in the range of the map { A }. We show that the reconstructed wave speed \\tilde{c} satisfies \\parallel \\tilde{c}-c\\parallel ≤slant C\\parallel { E }{\\parallel }1/54. Our regularization strategy is based on a new formula to compute c from Λ.

  2. Photoacoustic clutter reduction by inversion of a linear scatter model using plane wave ultrasound measurements.

    Schwab, Hans-Martin; Beckmann, Martin F; Schmitz, Georg


    Photoacoustic imaging aims to visualize light absorption properties of biological tissue by receiving a sound wave that is generated inside the observed object as a result of the photoacoustic effect. In clinical applications, the strong light absorption in human skin is a major problem. When high amplitude photoacoustic waves that originate from skin absorption propagate into the tissue, they are reflected back by acoustical scatterers and the reflections contribute to the received signal. The artifacts associated with these reflected waves are referred to as clutter or skin echo and limit the applicability of photoacoustic imaging for medical applications severely. This study seeks to exploit the acoustic tissue information gained by plane wave ultrasound measurements with a linear array in order to correct for reflections in the photoacoustic image. By deriving a theory for clutter waves in k-space and a matching inversion approach, photoacoustic measurements compensated for clutter are shown to be recovered.

  3. Joint inversion of surface waves and teleseismic body waves across the Tibetan collision zone: the fate of subducted Indian lithosphere

    Nunn, Ceri; Roecker, Steven W.; Priestley, Keith F.; Liang, Xiaofeng; Gilligan, Amy


    This is the version of record, which can also be found on the publisher's website at: © The Authors 2014. Published by Oxford University Press on behalf of The Royal Astronomical Society We carry out a joint inversion of surface wave dispersion curves and teleseismic shear wave arrival times across the Tibetan collision zone, from just south of the Himalaya to the Qaidam Basin at the northeastern margin of the plateau, and from the ...


    Fahmi ben Hassen; Jijun Liu; Roland Potthast


    We study wave splitting procedures for acoustic or electromagnetic scattering problems. The idea of these procedures is to split some scattered field into a sum of fields coming from different spatial regions such that this information can be used either for inversion algorithms or for active noise control. Splitting algorithms can be based on general boundary layer potential representation or Green's representation formula. We will prove the unique decomposition of scattered wave outside the specified reference domain G and the unique decomposition of far-field pattern with respect to different reference domain G. Further, we employ the splitting technique for field reconstruction for a scatterer with two or more separate components, by combining it with the point source method for wave recovery. Using the decomposition of scattered wave as well as its far-field pattern, the wave splitting procedure proposed in this paper gives an efficient way to the computation of scattered wave near the obstacle, from which the multiple obstacles which cause the far-field pattern can be reconstructed separately. This considerably extends the range of the decomposition methods in the area of inverse scattering. Finally, we will provide numerical examples to demonstrate the feasibility of the splitting method.

  5. Acoustoelastic analysis of reflected waves in nearly incompressible, hyper-elastic materials: forward and inverse problems.

    Kobayashi, Hirohito; Vanderby, Ray


    Many materials (e.g., rubber or biologic tissues) are "nearly" incompressible and often assumed to be incompressible in their constitutive equations. This assumption hinders realistic analyses of wave motion including acoustoelasticity. In this study, this constraint is relaxed and the reflected waves from nearly incompressible, hyper-elastic materials are examined. Specifically, reflection coefficients are considered from the interface of water and uni-axially prestretched rubber. Both forward and inverse problems are experimentally and analytically studied with the incident wave perpendicular to the interface. In the forward problem, the wave reflection coefficient at the interface is evaluated with strain energy functions for nearly incompressible materials in order to compute applied strain. For the general inverse problem, mathematical relations are derived that identify both uni-axial strains and normalized material constants from reflected wave data. The validity of this method of analysis is demonstrated via an experiment with stretched rubber. Results demonstrate that applied strains and normalized material coefficients can be simultaneously determined from the reflected wave data alone if they are collected at several different (but unknown) levels of strain. This study therefore indicates that acoustoelasticity, with an appropriate constitutive formulation, can determine strain and material properties in hyper-elastic, nearly incompressible materials.

  6. Parallel Inversion Arithmetic for 3D Multi-Wave Pre-stack Elasticity Parameters and Its Application

    Luo, S.; Li, L.


    Multi-wave seismic prospect is an elastic wave prospect by which all wave fields can be achieved. We can inverse the stratum lithological parameters and elastic parameters by the multi-wave amplitude characteristics in order to get the information of the reservoirs and fluids. At present, the main methods of multi-wave inversion are post-stack inversion and single component partial-stack inversion, which are based on the approximative expressions and isotropy media. Widely known, the post-stack inversion can only be used to inverse the impedance, three lithological parameters(P wave velocity,S wave velocity and density)can not be obtained independently in this kind of method. The single component is not the whole elastic wave inversion, and the theory formula of the isotropy media is unfit for the anisotropy media inversion. Therefore, based on the anisotropy media, the method of the multi-wave associated pre-stack inversion is studied by using of the precise AVA formulae in this paper. To the questions of the lithology identification and the prediction of reservoirs, the authors studied the associated inversion of 3D lithological parameters for the anisotropy media with 3D3C data. The basic processes of the parameter inversion are as follows: (1) create the velocity model and produce the NMO gathers, (2) match the layers of the P wave with the same layers of P-SV wave, and convert AVO gathers into AVA gathers, (3) inverse the lithology parameters and anisotropy coefficients with the NMO gather, and (4) compute the elastic parameters, elastic impedance, elastic impedance grads based on the inversed parameters. Because of the huge amount of computing work of 3D pre-stack parameter inversion, the parallel arithmetic of the 3D pre-stack parameter inversion is utilized to improve the computing efficiency. Via the 3D real data processing, it is proved that this method is effective and can be applied in the oil and gas prediction of the reservoirs.

  7. Angle-domain Migration Velocity Analysis using Wave-equation Reflection Traveltime Inversion

    Zhang, Sanzong


    The main difficulty with an iterative waveform inversion is that it tends to get stuck in a local minima associated with the waveform misfit function. This is because the waveform misfit function is highly non-linear with respect to changes in the velocity model. To reduce this nonlinearity, we present a reflection traveltime tomography method based on the wave equation which enjoys a more quasi-linear relationship between the model and the data. A local crosscorrelation of the windowed downgoing direct wave and the upgoing reflection wave at the image point yields the lag time that maximizes the correlation. This lag time represents the reflection traveltime residual that is back-projected into the earth model to update the velocity in the same way as wave-equation transmission traveltime inversion. The residual movemout analysis in the angle-domain common image gathers provides a robust estimate of the depth residual which is converted to the reflection traveltime residual for the velocity inversion. We present numerical examples to demonstrate its efficiency in inverting seismic data for complex velocity model.

  8. Dispersion of Rayleigh, Scholte, Stoneley and Love waves in a model consisting of a liquid layer overlying a two-layer transversely isotropic solid medium

    Bagheri, Amirhossein; Greenhalgh, Stewart; Khojasteh, Ali; Rahimian, Mohammad


    The dispersion of interface waves is studied theoretically in a model consisting of a liquid layer of finite thickness overlying a transversely isotropic solid layer which is itself underlain by a transversely isotropic solid of dissimilar elastic properties. The method of potential functions and Hankel transformation was utilized to solve the equations of motion. Two frequency equations were developed: one for Love waves and the other for the remaining surface and interface waves. Numerical group and phase velocity dispersion curves were computed for four different classes of model, in which the substratum is stiffer or weaker than the overlying layer, and for various thickness combinations of the layers. Dispersion curves are presented for generalized Rayleigh, Scholte, Stoneley and Love waves, each of which are possible in all proposed models. They show the dependence of the velocity on layer thicknesses and material properties (elastic constants). Special cases involving zero thickness for the water layer or the solid layer, and/or isotropic material properties for the solid exhibit interesting features and agree favourably with previously published results for these simpler cases, thus validating the new formulation.

  9. A trade-off solution between model resolution and covariance in surface-wave inversion

    Xia, J.; Xu, Y.; Miller, R.D.; Zeng, C.


    Regularization is necessary for inversion of ill-posed geophysical problems. Appraisal of inverse models is essential for meaningful interpretation of these models. Because uncertainties are associated with regularization parameters, extra conditions are usually required to determine proper parameters for assessing inverse models. Commonly used techniques for assessment of a geophysical inverse model derived (generally iteratively) from a linear system are based on calculating the model resolution and the model covariance matrices. Because the model resolution and the model covariance matrices of the regularized solutions are controlled by the regularization parameter, direct assessment of inverse models using only the covariance matrix may provide incorrect results. To assess an inverted model, we use the concept of a trade-off between model resolution and covariance to find a proper regularization parameter with singular values calculated in the last iteration. We plot the singular values from large to small to form a singular value plot. A proper regularization parameter is normally the first singular value that approaches zero in the plot. With this regularization parameter, we obtain a trade-off solution between model resolution and model covariance in the vicinity of a regularized solution. The unit covariance matrix can then be used to calculate error bars of the inverse model at a resolution level determined by the regularization parameter. We demonstrate this approach with both synthetic and real surface-wave data. ?? 2010 Birkh??user / Springer Basel AG.

  10. Inverse four-wave-mixing and self-parametric amplification effect in optical fibre.

    Turitsyn, Sergei K; Bednyakova, Anastasia E; Fedoruk, Mikhail P; Papernyi, Serguei B; Clements, Wallace R L


    An important group of nonlinear processes in optical fibre involves the mixing of four waves due to the intensity dependence of the refractive index. It is customary to distinguish between nonlinear effects that require external/pumping waves (cross-phase modulation and parametric processes such as four-wave mixing) and self-action of the propagating optical field (self-phase modulation and modulation instability). Here, we present a new nonlinear self-action effect, self-parametric amplification (SPA), which manifests itself as optical spectrum narrowing in normal dispersion fibre, leading to very stable propagation with a distinctive spectral distribution. The narrowing results from an inverse four-wave mixing, resembling an effective parametric amplification of the central part of the spectrum by energy transfer from the spectral tails. SPA and the observed stable nonlinear spectral propagation with random temporal waveform can find applications in optical communications and high power fibre lasers with nonlinear intra-cavity dynamics.

  11. Skeletonized wave-equation Qs tomography using surface waves

    Li, Jing


    We present a skeletonized inversion method that inverts surface-wave data for the Qs quality factor. Similar to the inversion of dispersion curves for the S-wave velocity model, the complicated surface-wave arrivals are skeletonized as simpler data, namely the amplitude spectra of the windowed Rayleigh-wave arrivals. The optimal Qs model is then found that minimizes the difference in the peak frequencies of the predicted and observed Rayleigh wave arrivals using a gradient-based wave-equation optimization method. Solutions to the viscoelastic wave-equation are used to compute the predicted Rayleigh-wave arrivals and the misfit gradient at every iteration. This procedure, denoted as wave-equation Qs tomography (WQs), does not require the assumption of a layered model and tends to have fast and robust convergence compared to Q full waveform inversion (Q-FWI). Numerical examples with synthetic and field data demonstrate that the WQs method can accurately invert for a smoothed approximation to the subsur-face Qs distribution as long as the Vs model is known with sufficient accuracy.

  12. Sliding without slipping under Coulomb friction: opening waves and inversion of frictional force

    Yastrebov, Vladislav A


    An elastic layer slides on a rigid flat governed by Coulomb's friction law. We demonstrate that if the coefficient of friction is high enough, the sliding localizes within stick-slip pulses, which transform into opening waves propagating at intersonic speed in the direction of sliding or, for high Poisson's ratios, at supersonic speed in the opposite one. This sliding mode, characterized by small frictional dissipation, rapidly relaxes the shear elastic energy via stress waves and enables the contact surface slide ahead of the top one, resulting in inversion of the frictional force direction.

  13. Simultaneous inversion of layered compressional velocity and shear velocity by using plane wave seismogram

    宋海斌; 马在田; 张关泉


    A layer-stripping method is presented for simultaneous inversion of compressional velocity and shear velocity in layered medium from single precritical-incident-angle data of P-P and P-SV plane wave seismogram. A finite bandwidth algorithm is provided and results obviously better than previous research work are obtained by the numerical experiments for band-limited seismogram and synthetic data including noise.

  14. Waves and vortices in the inverse cascade regime of stratified turbulence with or without rotation

    Herbert, Corentin; Rosenberg, Duane; Pouquet, Annick


    We study the partition of energy between waves and vortices in stratified turbulence, with or without rotation, for a variety of parameters, focusing on the behavior of the waves and vortices in the inverse cascade of energy towards the large scales. To this end, we use direct numerical simulations in a cubic box at a Reynolds number Re=1000, with the ratio between the Brunt-V\\"ais\\"al\\"a frequency N and the inertial frequency f varying from 1/4 to 20, together with a purely stratified run. The Froude number, measuring the strength of the stratification, varies within the range 0.02 < Fr < 0.32. We find that the inverse cascade is dominated by the slow quasi-geostrophic modes. Their energy spectra and fluxes exhibit characteristics of an inverse cascade, even though their energy is not conserved. Surprisingly, the slow vortices still dominate when the ratio N/f increases, also in the stratified case, although less and less so. However, when N/f increases, the inverse cascade of the slow modes becomes we...

  15. Rayleigh/Raman lidar observations of gravity wave activity from 15 to 70 km altitude over Syowa (69°S, 40°E), the Antarctic

    Kogure, Masaru; Nakamura, Takuji; Ejiri, Mitsumu K.; Nishiyama, Takanori; Tomikawa, Yoshihiro; Tsutsumi, Masaki; Suzuki, Hidehiko; Tsuda, Takuo T.; Kawahara, Takuya D.; Abo, Makoto


    The potential energy of gravity waves (GWs) per unit mass (Ep), at altitudes of 15-70 km, has been examined from temperature profiles obtained by a Rayleigh/Raman lidar at Syowa Station (69°S, 40°E) from May 2011 to October 2013, with the exception of the summer months. The GWs with ground-based wave periods longer than 2 h and vertical wavelengths between 1.8 and 16 km were extracted from the temperature profiles. Ep was larger in winter than in spring and fall, although in 2012, at altitudes below 30 km, Ep was larger in spring than in winter and fall. Ep increased with a mean scale height of 11.3 km. Ep profiles showed a local maximum at an altitude of 20 km and a minimum at 25 km in almost every month, which has not been reported by previous studies observed by radiosondes. The values of Ep in October of 2012 were smaller at 35-60 km and larger at 20-35 km than those in October of 2011 and 2013. This difference in the Ep profile is most probably caused by different seasonal variations of zonal winds. The larger and smaller Ep values seem to be observed both below and above the altitude at which the zonal wind speed reached 0 m s-1. This result suggests that wind filtering of gravity waves with small phase speeds is significantly important in early spring.

  16. Shot- and angle-domain wave-equation traveltime inversion of reflection data: Theory

    Zhang, Sanzong


    The main difficulty with iterative waveform inversion is that it tends to get stuck in local minima associated with the waveform misfit function. To mitigate this problem and avoid the need to fit amplitudes in the data, we have developed a wave-equation method that inverts the traveltimes of reflection events, and so it is less prone to the local minima problem. Instead of a waveform misfit function, the penalty function was a crosscorrelation of the downgoing direct wave and the upgoing reflection wave at the trial image point. The time lag, which maximized the crosscorrelation amplitude, represented the reflection-traveltime residual (RTR) that was back projected along the reflection wavepath to update the velocity. Shot- and angle-domain crosscorrelation functions were introduced to estimate the RTR by semblance analysis and scanning. In theory, only the traveltime information was inverted and there was no need to precisely fit the amplitudes or assume a high-frequency approximation. Results with synthetic data and field records revealed the benefits and limitations of wave-equation reflection traveltime inversion.

  17. Frequency-Dependent Spherical-Wave Reflection in Acoustic Media: Analysis and Inversion

    Li, Jingnan; Wang, Shangxu; Wang, Jingbo; Dong, Chunhui; Yuan, Sanyi


    Spherical-wave reflectivity (SWR), which describes the seismic wave reflection in real subsurface media more accurately than plane-wave reflectivity (PWR), recently, again attracts geophysicists' attention. The recent studies mainly focus on the amplitude variation with offset/angle (AVO/AVA) attributes of SWR. For a full understanding of the reflection mechanism of spherical wave, this paper systematically investigates the frequency-dependent characteristics of SWR in a two-layer acoustic medium model with a planar interface. Two methods are used to obtain SWR. The first method is through the calculation of classical Sommerfeld integral. The other is by 3D wave equation numerical modeling. To enhance computation efficiency, we propose to perform wave equation simulation in cylindrical coordinates, wherein we for the first time implement unsplit convolutional perfectly matched layer as the absorbing boundary. Both methods yield the same results, which demonstrate the validity and accuracy of the computation. From both the numerical tests and the theoretical demonstration, we find that the necessary condition when frequency dependence of SWR occurs is that the upper and lower media have different velocities. At the precritical small angle, the SWR exhibits complicated frequency-dependent characteristics for varying medium parameters. Especially when the impedance of upper medium equals that of lower one, the PWR is zero according to geometric seismics. Whereas the SWR is nonzero: the magnitude of SWR decreases with growing frequency, and approaches that of the corresponding PWR at high frequency; the phase of SWR increases with growing frequency, but approaches 90° or -90° at high frequency. At near- and post-critical angles, large difference exists between SWR and PWR, and the difference is particularly great at low frequencies. Finally, we propose a nonlinear inversion method to estimate physical parameters and interface depth of media by utilizing the frequency

  18. Characterizing the parent Hamiltonians for a complete set of orthogonal wave functions: An inverse quantum problem

    Ramezanpour, A.


    We study the inverse problem of constructing an appropriate Hamiltonian from a physically reasonable set of orthogonal wave functions for a quantum spin system. Usually, we are given a local Hamiltonian and our goal is to characterize the relevant wave functions and energies (the spectrum) of the system. Here, we take the opposite approach; starting from a reasonable collection of orthogonal wave functions, we try to characterize the associated parent Hamiltonians, to see how the wave functions and the energy values affect the structure of the parent Hamiltonian. Specifically, we obtain (quasi) local Hamiltonians by a complete set of (multilayer) product states and a local mapping of the energy values to the wave functions. On the other hand, a complete set of tree wave functions (having a tree structure) results to nonlocal Hamiltonians and operators which flip simultaneously all the spins in a single branch of the tree graph. We observe that even for a given set of basis states, the energy spectrum can significantly change the nature of interactions in the Hamiltonian. These effects can be exploited in a quantum engineering problem optimizing an objective functional of the Hamiltonian.

  19. Iterative methods for solving coefficient inverse problems of wave tomography in models with attenuation

    Goncharsky, Alexander V.; Romanov, Sergey Y.


    We develop efficient iterative methods for solving inverse problems of wave tomography in models incorporating both diffraction effects and attenuation. In the inverse problem the aim is to reconstruct the velocity structure and the function that characterizes the distribution of attenuation properties in the object studied. We prove mathematically and rigorously the differentiability of the residual functional in normed spaces, and derive the corresponding formula for the Fréchet derivative. The computation of the Fréchet derivative includes solving both the direct problem with the Neumann boundary condition and the reversed-time conjugate problem. We develop efficient methods for numerical computations where the approximate solution is found using the detector measurements of the wave field and its normal derivative. The wave field derivative values at detector locations are found by solving the exterior boundary value problem with the Dirichlet boundary conditions. We illustrate the efficiency of this approach by applying it to model problems. The algorithms developed are highly parallelizable and designed to be run on supercomputers. Among the most promising medical applications of our results is the development of ultrasonic tomographs for differential diagnosis of breast cancer.

  20. On an inverse source problem for enhanced oil recovery by wave motion maximization in reservoirs

    Karve, Pranav M.


    © 2014, Springer International Publishing Switzerland. We discuss an optimization methodology for focusing wave energy to subterranean formations using strong motion actuators placed on the ground surface. The motivation stems from the desire to increase the mobility of otherwise entrapped oil. The goal is to arrive at the spatial and temporal description of surface sources that are capable of maximizing mobility in the target reservoir. The focusing problem is posed as an inverse source problem. The underlying wave propagation problems are abstracted in two spatial dimensions, and the semi-infinite extent of the physical domain is negotiated by a buffer of perfectly-matched-layers (PMLs) placed at the domain’s truncation boundary. We discuss two possible numerical implementations: Their utility for deciding the tempo-spatial characteristics of optimal wave sources is shown via numerical experiments. Overall, the simulations demonstrate the inverse source method’s ability to simultaneously optimize load locations and time signals leading to the maximization of energy delivery to a target formation.

  1. High-resolution global tomography: A full-wave technique for forward and inverse modeling

    Nissen-Meyer, Tarje; Sigloch, Karin; Fournier, Alexandre


    In recent years, seismology has greatly benefitted from significant progress in digital data collection and processing, accurate numerical methods for wave propagation, and high-performance computing to explore crucial scales of interest in both data and model spaces. We will present a full-wave technique to address the seismic forward and inverse problem at the global scale, with a specific focus on diffracted waves in the lowermost mantle: Our 2D spectral-element method tackles 3D wave propagation through spherically symmetric background models down to seismic frequencies of 1 Hz and delivers the wavefields necessary to construct sensitivity kernels. This specific approach distinguishes itself from the adjoint method in that it requires no knowledge about data structure or observables at the time of forward modeling by means of storing entire reference space-time wavefields. To obtain a direct view of the interconnection between surface displacements and earth structure, we examine the time-dependent sensitivity of the seismic signal to 3D model perturbations. Being highly sensitive to such parameters as epicentral distance, earthquake radiation pattern, depth, frequency, receiver components and time windows, this effort suggests criteria for data selection to optimally illuminate a specific region within the earth. As shown with core-diffracted P-waves, we measure and model our observables (e.g. traveltimes, amplitudes) in multiple-frequency passbands, thereby increasing robustness of the inverse problem and path coverage. This allows us to selectively draw only upon frequency bands with high signal-to-noise ratio. We discuss the selection and usability of data for such a Pdiff tomographic setting, coverage maps and target regions. We also touch upon the validity of a 1D reference model and quantify the applicability range of the first-order Born approximation.

  2. Direct and inverse cascades of energy, momentum and wave action in spectra of wind-driven waves

    Badulin, S. I.; Pushkarev, A. N.; Resio, D.; Zakharov, V. E.


    The time-dependent, spatially uniform Hasselmann's kinetic equation for surface gravity waves in presence of wind forcing and white-capping dissipation is studied numerically. We use conventional parameterizations of wind wave input (Snyder et al. 1981; Plant 1982; Hsiao &Shemdin 1983; Donelan, Pierson 1987) that are consistent with weakly nonlinear scaling. We assume that strong dissipation due to white-capping is essential for short waves only (with frequencies above 1Hz) belonging to the spectral tail and can be neglected near the spectral peak. We compare our numerical results with the predictions of the theory of weak turbulence and found a very good coincidence. It is shown that asymptotic behavior of wave spectra is in perfect agreement with stationary solutions of the Hasselmann equation -- Kolmogorov's solutions for direct (Zakharov & Filonenko 1966) and inverse (Zakharov &Zaslavskii 1982) cascades. This asymptotic behavior appears at rather early stages of wind wave evolution (physical time of order of few hours in our experiments); A strong tendency of solutions to self-similar behavior of duration limited solutions is found for rather wide range of initial conditions and external forcing; Good quantitative coincidence with recapitulative experimental data for duration limited wind wave growth (Young 1999, p.111) and for fetch-limited (JONSWAP) spectra parameterized by wave age C_p/Uwind is found. The findings here are quite robust and hopefully will be applied to the practical problems. Present wave prediction models are based on fairly crude parameterizations of the nonlinear energy transfers. In large part due to inaccuracies in these parameterizations, these models have had to rely on empirical fitting of general growth equation as a basis for constraining additional source-sink terms in the detailed balance equations. Results from this study could be used to reformulate a complete energy balance equation for wave generation, propagation and decay

  3. Inverse hydrograph routing optimization model based on the kinematic wave approach

    Saghafian, B.; Jannaty, M. H.; Ezami, N.


    This article presents and validates the inverse flood hydrograph routing optimization model under kinematic wave (KW) approximation in order to produce the upstream (inflow) hydrograph, given the downstream (outflow) hydrograph of a river reach. The cost function involves minimization of the error between the observed outflow hydrograph and the corresponding directly routed outflow hydrograph. Decision variables are the inflow hydrograph ordinates. The KW and genetic algorithm (GA) are coupled, representing the selected methods of direct routing and optimization, respectively. A local search technique is also enforced to achieve better agreement of the routed outflow hydrograph with the observed hydrograph. Computer programs handling the direct flood routing, cost function and local search are linked with the optimization model. The results show that the case study inflow hydrographs obtained by the GA were reconstructed with accuracy. It was also concluded that the coupled KW-GA model framework can perform inverse hydrograph routing with numerical stability.

  4. The tropical tropopause inversion layer: variability and modulation by equatorial waves

    Pilch Kedzierski, Robin; Matthes, Katja; Bumke, Karl


    The tropical tropopause layer (TTL) acts as a transition layer between the troposphere and the stratosphere over several kilometers, where air has both tropospheric and stratospheric properties. Within this region, a fine-scale feature is located: the tropopause inversion layer (TIL), which consists of a sharp temperature inversion at the tropopause and the corresponding high static stability values right above, which theoretically affect the dispersion relations of atmospheric waves like Rossby or inertia-gravity waves and hamper stratosphere-troposphere exchange (STE). Therefore, the TIL receives increasing attention from the scientific community, mainly in the extratropics so far. Our goal is to give a detailed picture of the properties, variability and forcings of the tropical TIL, with special emphasis on small-scale equatorial waves and the quasi-biennial oscillation (QBO).We use high-resolution temperature profiles from the COSMIC satellite mission, i.e., ˜ 2000 measurements per day globally, between 2007 and 2013, to derive TIL properties and to study the fine-scale structures of static stability in the tropics. The situation at near tropopause level is described by the 100 hPa horizontal wind divergence fields, and the vertical structure of the QBO is provided by the equatorial winds at all levels, both from the ERA-Interim reanalysis.We describe a new feature of the equatorial static stability profile: a secondary stability maximum below the zero wind line within the easterly QBO wind regime at about 20-25 km altitude, which is forced by the descending westerly QBO phase and gives a double-TIL-like structure. In the lowermost stratosphere, the TIL is stronger with westerly winds. We provide the first evidence of a relationship between the tropical TIL strength and near-tropopause divergence, with stronger (weaker) TIL with near-tropopause divergent (convergent) flow, a relationship analogous to that of TIL strength with relative vorticity in the

  5. An Adaptive Observer-Based Algorithm for Solving Inverse Source Problem for the Wave Equation

    Asiri, Sharefa M.


    Observers are well known in control theory. Originally designed to estimate the hidden states of dynamical systems given some measurements, the observers scope has been recently extended to the estimation of some unknowns, for systems governed by partial differential equations. In this paper, observers are used to solve inverse source problem for a one-dimensional wave equation. An adaptive observer is designed to estimate the state and source components for a fully discretized system. The effectiveness of the algorithm is emphasized in noise-free and noisy cases and an insight on the impact of measurements’ size and location is provided.

  6. Interpreting Ulysses data using inverse scattering theory: Oblique Alfv\\'en waves

    Wheeler, Harry R; Hamilton, R L


    Solitary wave structures observed by the Ulysses spacecraft in the solar wind were analyzed using both inverse scattering theory as well as direct numerical integration of the derivative nonlinear Schr\\"odinger (DNLS) equation. Several of these structures were found to be consistent with soliton solutions of the DNLS equation. Such solitary structures have been commonly observed in the space plasma environment and may, in fact, be long-lived solitons. While the generation of these solitons may be due to an instability mechanism, e.g., the mirror instability, they may be observable far from the source region due to their coherent nature.

  7. Prognostic Implications of Newly Developed T-Wave Inversion After Primary Percutaneous Coronary Intervention in Patients With ST-Segment Elevation Myocardial Infarction.

    Lee, Man-Jong; Jang, Ji-Hoon; Lee, Myung-Dong; Kwon, Sung Woo; Shin, Sung-Hee; Park, Sang-Don; Woo, Seong-Ill; Kim, Dae-Hyeok; Kwan, Jun; Park, Keum-Soo


    We investigated the prognostic value of newly developed T-wave inversion after primary percutaneous coronary intervention (PCI) in patients with ST-segment elevation myocardial infarction. New T-wave inversion was defined as new onset of T-wave inversion after the primary PCI, without negative T waves on the presenting electrocardiogram. The primary end point was the occurrence of major adverse cardiac events (MACE), which consisted of cardiovascular mortality, nonfatal myocardial infarction, and rehospitalization for heart failure. A total of 271 patients were analyzed and followed up for 24 months in this study. New T-wave inversion was observed in 194 patients (72%), whereas the remaining 77 patients (28%) did not show T-wave inversion after the index PCI. Post-PCI Thrombolysis In Myocardial Infarction flow grade 2 or 3 was observed more frequently in patients with new T-wave inversion (97% vs 90%; p = 0.011). The cumulative MACE rate was significantly lower in patients with new T-wave inversion than in those without new T-wave inversion (8% vs 30%; odds ratio 0.197, 95% confidential interval 0.096 to 0.403; p wave inversion was an independent prognostic factor for MACE (hazard ratio 0.297, 95% confidential interval 0.144 to 0.611; p = 0.001). In conclusion, newly developed T-wave inversion after primary PCI was associated with favorable long-term outcome.

  8. An Inverse Source Problem for a One-dimensional Wave Equation: An Observer-Based Approach

    Asiri, Sharefa M.


    Observers are well known in the theory of dynamical systems. They are used to estimate the states of a system from some measurements. However, recently observers have also been developed to estimate some unknowns for systems governed by Partial differential equations. Our aim is to design an observer to solve inverse source problem for a one dimensional wave equation. Firstly, the problem is discretized in both space and time and then an adaptive observer based on partial field measurements (i.e measurements taken form the solution of the wave equation) is applied to estimate both the states and the source. We see the effectiveness of this observer in both noise-free and noisy cases. In each case, numerical simulations are provided to illustrate the effectiveness of this approach. Finally, we compare the performance of the observer approach with Tikhonov regularization approach.

  9. Joint Inversion of Body-Wave Arrival Times and Surface-Wave Dispersion Data in the Wavelet Domain Constrained by Sparsity Regularization

    Zhang, H.; Fang, H.; Yao, H.; Maceira, M.; van der Hilst, R. D.


    Recently, Zhang et al. (2014, Pure and Appiled Geophysics) have developed a joint inversion code incorporating body-wave arrival times and surface-wave dispersion data. The joint inversion code was based on the regional-scale version of the double-difference tomography algorithm tomoDD. The surface-wave inversion part uses the propagator matrix solver in the algorithm DISPER80 (Saito, 1988) for forward calculation of dispersion curves from layered velocity models and the related sensitivities. The application of the joint inversion code to the SAFOD site in central California shows that the fault structure is better imaged in the new model, which is able to fit both the body-wave and surface-wave observations adequately. Here we present a new joint inversion method that solves the model in the wavelet domain constrained by sparsity regularization. Compared to the previous method, it has the following advantages: (1) The method is both data- and model-adaptive. For the velocity model, it can be represented by different wavelet coefficients at different scales, which are generally sparse. By constraining the model wavelet coefficients to be sparse, the inversion in the wavelet domain can inherently adapt to the data distribution so that the model has higher spatial resolution in the good data coverage zone. Fang and Zhang (2014, Geophysical Journal International) have showed the superior performance of the wavelet-based double-difference seismic tomography method compared to the conventional method. (2) For the surface wave inversion, the joint inversion code takes advantage of the recent development of direct inversion of surface wave dispersion data for 3-D variations of shear wave velocity without the intermediate step of phase or group velocity maps (Fang et al., 2014, Geophysical Journal International). A fast marching method is used to compute, at each period, surface wave traveltimes and ray paths between sources and receivers. We will test the new joint

  10. Tropopause inversion layer formation and stratosphere-troposphere exchange during idealized baroclinic wave life cycle experiments

    Kunkel, Daniel; Wirth, Volkmar; Hoor, Peter


    Recent simulations of baroclinic wave life cycles revealed that the tropopause inversion layer (TIL), commonly situated just above the thermal tropopause, is evident in such experiments and emerges after the onset of wave breaking. Furthermore, bidirectional stratosphere-troposphere exchange (STE) occurs during this non-linear stage of the wave evolution and might be affected by the appearance of the TIL. We study the evolution and the impact of the TIL on STE by using the COSMO model in an idealized mid-latitude channel geometry configuration without physical sub-grid scale parameterizations. We initialize the model with a geostrophically balanced upper level jet stream which is disturbed by an anomaly of potential vorticity to trigger the evolution of the baroclinic waves. Moreover, we use passive tracers of tropospheric or stratospheric origin to identify regions of potential STE. Our results show that the static stability is low in regions of stratosphere to troposphere exchange (STT), while it is high in regions dominated by exchange in the opposite direction (TST). Furthermore, inertia gravity waves, originating from regions with strong ageostrophic wind components, modulate the static stability as well as the vertical shear of the horizontal wind near and above the tropopause. While propagating away from their source, the inertia gravity waves lead to large values of the squared Brunt Vaisala frequency in regions which are simultaneously characterized by low bulk Richardson numbers. Thus, these regions are statically stable and turbulent at the same time and might be crucial for TST, thereby explaining tropospheric mixing ratio changes of e.g. CO across the tropopause which commonly change from tropospheric to stratospheric values a few hundred meters above the local thermal tropopause.

  11. Genetic algorithms-based inversion of multimode guided waves for cortical bone characterization

    Bochud, N.; Vallet, Q.; Bala, Y.; Follet, H.; Minonzio, J.-G.; Laugier, P.


    Recent progress in quantitative ultrasound has exploited the multimode waveguide response of long bones. Measurements of the guided modes, along with suitable waveguide modeling, have the potential to infer strength-related factors such as stiffness (mainly determined by cortical porosity) and cortical thickness. However, the development of such model-based approaches is challenging, in particular because of the multiparametric nature of the inverse problem. Current estimation methods in the bone field rely on a number of assumptions for pairing the incomplete experimental data with the theoretical guided modes (e.g. semi-automatic selection and classification of the data). The availability of an alternative inversion scheme that is user-independent is highly desirable. Thus, this paper introduces an efficient inversion method based on genetic algorithms using multimode guided waves, in which the mode-order is kept blind. Prior to its evaluation on bone, our proposal is validated using laboratory-controlled measurements on isotropic plates and bone-mimicking phantoms. The results show that the model parameters (i.e. cortical thickness and porosity) estimated from measurements on a few ex vivo human radii are in good agreement with the reference values derived from x-ray micro-computed tomography. Further, the cortical thickness estimated from in vivo measurements at the third from the distal end of the radius is in good agreement with the values delivered by site-matched high-resolution x-ray peripheral computed tomography.

  12. A pile-soil-bridge structure with dynamic interaction under Rayleigh wave excitation%Rayleigh波作用下桩-土-桥梁结构动力相互作用问题研究

    谷音; 于志敏


    A 2D finite element model for a semi-infinite space with layered media and Rayleigh wave input was built by using equivalent viscous-elastic artificial boundary elements. The responses in free-field of even and layered media were computed. The results indicated that the finite element method has excellent estimation precision compared with the theore tical solutions. The dynamic response of a pile-soil-bridge structure with dynamic interaction under Rayleigh waves was analyzed. A typical rigid frame bridge was included in this case study. The influence of different site conditions, changes of location of soft interlayer, different Rayleigh wave input and pile length on Rayleigh wave propagation and the seismic response were considered. The influencing factors of the rigid frame bridge structure were also discussed.%基于等效粘弹性人工边界单元建立了可考虑成层介质及Rayleigh波输入的二维有限元时域模型,计算了Sayleih波作用下成层介质与均匀介质的自由场反应,与理论解比较表明有限元计算结果具有较好的工程精度.针对Rayleigh波作用下桩-土-典型刚构桥梁结构动力反应进行了分析,考虑了场地条件的不同、软夹层位置的改变、不同频率Rayleigh波的输入以及桩长对Rayleigh波传播与场地地震反应的影响,对影响因素进行了讨论.

  13. Incorporating Love- and Rayleigh-Wave Magnitudes, Unequal Earthquake and Explosion Variance Assumptions, and Intrastation Complexity for Improved Event Screening


    formulation of the teleseismic explosion identification problem with multiple discriminants, Bull. Seism . Soc.Am.9T. 1730-1741. Bonner, J.L., D...Application at Regional and Teleseismic Distances, Part II: Application and Ms-mh Performance. Bull. Seism . Soc. Am. 96: 678-696 Bonner, J. L., R. B...Herrmann, D. Harkrider, and M. Pasyanos (2008). The surface wave magnitude for the 9 October 2006 North Korean nuclear explosion. Bull. Seism . Soc

  14. Subsurface images of the Eastern Rift, Africa, from the joint inversion of body waves, surface waves and gravity: investigating the role of fluids in early-stage continental rifting

    Roecker, S.; Ebinger, C.; Tiberi, C.; Mulibo, G.; Ferdinand-Wambura, R.; Mtelela, K.; Kianji, G.; Muzuka, A.; Gautier, S.; Albaric, J.; Peyrat, S.


    The Eastern Rift System (ERS) of northern Tanzania and southern Kenya, where a cratonic lithosphere is in the early stages of rifting, offers an ideal venue for investigating the roles of magma and other fluids in such an environment. To illuminate these roles, we jointly invert arrival times of locally recorded P and S body waves, phase delays of ambient noise generated Rayleigh waves and Bouguer anomalies from gravity observations to generate a 3-D image of P and S wave speeds in the upper 25 km of the crust. While joint inversion of gravity and arrival times requires a relationship between density and wave speeds, the improvement in resolution obtained by the combination of these disparate data sets serves to further constrain models, and reduce uncertainties. The most significant features in the 3-D model are (1) P and S wave speeds that are 10-15 per cent lower beneath the rift zone than in the surrounding regions, (2) a relatively high wave speed tabular feature located along the western edge of the Natron and Manyara rifts, and (3) low (˜1.71) values of Vp/Vs throughout the upper crust, with the lowest ratios along the boundaries of the rift zones. The low P and S wave speeds at mid-crustal levels beneath the rift valley are an expected consequence of active volcanism, and the tabular, high-wave speed feature is interpreted to be an uplifted footwall at the western edge of the rift. Given the high levels of CO2 outgassing observed at the surface along border fault zones, and the sensitivity of Vp/Vs to pore-fluid compressibility, we infer that the low Vp/Vs values in and around the rift zone are caused by the volcanic plumbing in the upper crust being suffused by a gaseous CO2 froth on top of a deeper, crystalline mush. The repository for molten rock is likely located in the lower crust and upper mantle, where the Vp/Vs ratios are significantly higher.

  15. Measuring the linear and nonlinear elastic properties of brain tissue with shear waves and inverse analysis.

    Jiang, Yi; Li, Guoyang; Qian, Lin-Xue; Liang, Si; Destrade, Michel; Cao, Yanping


    We use supersonic shear wave imaging (SSI) technique to measure not only the linear but also the nonlinear elastic properties of brain matter. Here, we tested six porcine brains ex vivo and measured the velocities of the plane shear waves induced by acoustic radiation force at different states of pre-deformation when the ultrasonic probe is pushed into the soft tissue. We relied on an inverse method based on the theory governing the propagation of small-amplitude acoustic waves in deformed solids to interpret the experimental data. We found that, depending on the subjects, the resulting initial shear modulus [Formula: see text] varies from 1.8 to 3.2 kPa, the stiffening parameter [Formula: see text] of the hyperelastic Demiray-Fung model from 0.13 to 0.73, and the third- [Formula: see text] and fourth-order [Formula: see text] constants of weakly nonlinear elasticity from [Formula: see text]1.3 to [Formula: see text]20.6 kPa and from 3.1 to 8.7 kPa, respectively. Paired [Formula: see text] test performed on the experimental results of the left and right lobes of the brain shows no significant difference. These values are in line with those reported in the literature on brain tissue, indicating that the SSI method, combined to the inverse analysis, is an efficient and powerful tool for the mechanical characterization of brain tissue, which is of great importance for computer simulation of traumatic brain injury and virtual neurosurgery.

  16. Research and application of spectral inversion technique in frequency domain to improve resolution of converted PS-wave

    Zhang, Hua; He, Zhen-Hua; Li, Ya-Lin; Li, Rui; He, Guamg-Ming; Li, Zhong


    Multi-wave exploration is an effective means for improving precision in the exploration and development of complex oil and gas reservoirs that are dense and have low permeability. However, converted wave data is characterized by a low signal-to-noise ratio and low resolution, because the conventional deconvolution technology is easily affected by the frequency range limits, and there is limited scope for improving its resolution. The spectral inversion techniques is used to identify λ/8 thin layers and its breakthrough regarding band range limits has greatly improved the seismic resolution. The difficulty associated with this technology is how to use the stable inversion algorithm to obtain a high-precision reflection coefficient, and then to use this reflection coefficient to reconstruct broadband data for processing. In this paper, we focus on how to improve the vertical resolution of the converted PS-wave for multi-wave data processing. Based on previous research, we propose a least squares inversion algorithm with a total variation constraint, in which we uses the total variance as a priori information to solve under-determined problems, thereby improving the accuracy and stability of the inversion. Here, we simulate the Gaussian fitting amplitude spectrum to obtain broadband wavelet data, which we then process to obtain a higher resolution converted wave. We successfully apply the proposed inversion technology in the processing of high-resolution data from the Penglai region to obtain higher resolution converted wave data, which we then verify in a theoretical test. Improving the resolution of converted PS-wave data will provide more accurate data for subsequent velocity inversion and the extraction of reservoir reflection information.

  17. Mrg: A Magnitude Scale for 1 s Rayleigh Waves at Local Distances with Focus on Yield Estimation


    Bache, T. (1982), Estimating the yield of underground nuclear explosions, Bull. Seism . Soc. Am., 72, pp. S131-S168. Cho, K. H., R. B. Herrmann, C. J...Ammon, and K. Lee (2007), Imaging the upper crust of the Korean peninsula by surface-wave tomography, Bull. Seism . Soc. Am., 97, pp. 198-207. Denny...Monitoring the earthquake source process in North America, Bull. Seism . Soc. Am., 101, pp. 2609-2625. Kennett, B.L.N., E. R. Engdahl, and R. Buland

  18. Exact Wave Solutions to Inverse-KdV Equation%Inverse-KdV方程的精确行波解




  19. Estimation of underground structure using phase velocities of Love-and Rayleigh-waves from three-component microtremor array observation at Morioka city; Moriokashi ni okeru sanseibun are bido kansoku ni yoru reiri-ha rabu-ha no ryoiso sokudo wo mochiita chika kozo suitei

    Yamamoto, Hidekazu; Saito, Tokumi; Ohashi, Hiromasa [Iwate University, Iwate (Japan)


    In conventional microtremor prospecting methods, underground structure is estimated using the phase velocity of Rayleigh-wave only. However, it is considered that the underground structure can be estimated at a higher accuracy by using two phase velocities of Rayleigh-wave and Love-wave that directly reflects S-wave velocity structure. Therefore, three-component microtremor array observation of a circle (equilateral triangle) with the maximum radius of 40 to 250 m was carried out at the center of Morioka city. Analysis was carried out by means of extended space with autocorrelation to obtain phase velocities of Love- and Rayleigh-waves. The frequency zone of the obtained Rayleigh-wave phase velocity is 1.5 Hz to 8.6 Hz, and the phase velocity is 2670 m/s to 733 m/s. The frequency zone of the obtained Love-wave phase velocity is 3 Hz to 8.6 Hz, and the phase velocity is 2100 m/s to 412 m/s. The underground structure obtained by using two observed phase velocities is clarified under a depth of 116 m. A stratum deemed to be the basement exists from a depth of 21 m (Vs=1100 m). As a result, the underground structure can be estimated at a higher accuracy if two phase velocities of Love-and Rayleigh-waves are used. (translated by NEDO)

  20. Layering ratios: a systematic approach to the inversion of surface wave data in the absence of a priori information

    Cox, Brady R.; Teague, David P.


    Surface wave methods provide a cost effective means of developing shear wave velocity (Vs) profiles for applications such as dynamic site characterization and seismic site response analyses. However, the inverse problem involved in obtaining a realistic layered earth model from surface wave dispersion data is inherently ill-posed, non-linear and mix-determined, without a unique solution. When available, a priori information such as geotechnical boreholes or geologic well logs should be used to aid in constraining site-specific inversion parameters. Unfortunately, a priori information is often unavailable, particularly at significant depths, and a `blind analysis' must be performed. In these situations, the analyst must decide on an appropriate number of layers and ranges for their corresponding inversion parameters (i.e. trial number of layers and ranges in their respective thicknesses, shear wave velocities, compression wave velocities and mass densities). Selection of these parameters has been shown to significantly impact the results of an inversion. This paper presents a method for conducting multiple inversions utilizing systematically varied inversion layering parametrizations in order to identify and encompass the most reasonable layered earth models for a site. Each parametrization is defined by a unique layering ratio, which represents a multiplier that systemically increases the potential thickness of each layer in the inversion parametrization based on the potential thickness of the layer directly above it. The layering ratio method is demonstrated at two sites associated with the InterPacific Project, wherein it is shown to significantly aid in selecting reasonable Vs profiles that are close representations of the subsurface. While the goal of the layering ratio inversion methodology is not necessarily to find the `optimal' or `best' Vs profile for a site, it may be successful at doing so for certain sites/datasets. However, the primary reason for using

  1. One-channel inverse filter: Spatio-temporal control of a complex wave-field from a single point

    Rupin, Matthieu; Roux, Philippe; Catheline, Stefan


    Can we make good use of the degrees of freedom of a wave-field trapped in a cavity to perform complete spatio-temporal inversion from a single emitter? To answer these questions, we used experiments conducted in the ultrasonic regime to investigate the wave-field in a water cavity where the energy was not homogeneously distributed over all of the degrees of freedom. While the time reversal from a single emitter gives poor results, we show the possibility to recover optimal spatio-temporal focusing by converting the multi-channel focusing technique of the spatio-temporal inverse filter into a single-channel method that we call the one-channel inverse filter. In particular, this method has the advantage of leaving the choice open for the duration of the time window for the inversion of the wave-field. We, thus, demonstrate that the shorter the time window, the better optimized the inversion. We believe that in addition to demonstrating the possibility of controlling the waves in a cavity, this method might have an interesting role in the improvement of solid imaging devices that are based on the exploitation of reverberations in cavities.

  2. S-wave velocity structure inferred from receiver function inversion in Tengchong volcanic area

    贺传松; 王椿镛; 吴建平


    Tengchong volcanic area is located near the impinging and underthrust margin of India and Eurasia plates. The volcanic activity is closely related to the tectonic environment. The deep structure characteristics are inferred from the receiver function inversion with the teleseismic records in the paper. The results show that the low velocity zone is influenced by the NE-trending Dayingjiang fault. The S-wave low velocity structure occurs obviously in the southern part of the fault, but unobviously in its northern part. There are low velocity zones in the shallow position, which coincides with the seismicity. It also demonstrates that the low velocity zone is directly related to the thermal activity in the volcanic area. Therefore, we consider that the volcano may be alive again.

  3. Bootstrap inversion for Pn wave velocity in North-Western Italy

    C. Eva


    Full Text Available An inversion of Pn arrival times from regional distance earthquakes (180-800 km, recorded by 94 seismic stations operating in North-Western Italy and surrounding areas, was carried out to image lateral variations of P-wave velocity at the crust-mantle boundary, and to estimate the static delay time at each station. The reliability of the obtained results was assessed using both synthetic tests and the bootstrap Monte Carlo resampling technique. Numerical simulations demonstrated the existence of a trade-off between cell velocities and estimated station delay times along the edge of the model. Bootstrap inversions were carried out to determine the standard deviation of velocities and time terms. Low Pn velocity anomalies are detected beneath the outer side of the Alps (-6% and the Western Po plain (-4% in correspondence with two regions of strong crustal thickening and negative Bouguer anomaly. In contrast, high Pn velocities are imaged beneath the inner side of the Alps (+4% indicating the presence of high velocity and density lower crust-upper mantle. The Ligurian sea shows high Pn velocities close to the Ligurian coastlines (+3% and low Pn velocities (-1.5% in the middle of the basin in agreement with the upper mantle velocity structure revealed by seismic refraction profiles.

  4. Reconstruction of multiple gastric electrical wave fronts using potential-based inverse methods.

    Kim, J H K; Pullan, A J; Cheng, L K


    One approach for non-invasively characterizing gastric electrical activity, commonly used in the field of electrocardiography, involves solving an inverse problem whereby electrical potentials on the stomach surface are directly reconstructed from dense potential measurements on the skin surface. To investigate this problem, an anatomically realistic torso model and an electrical stomach model were used to simulate potentials on stomach and skin surfaces arising from normal gastric electrical activity. The effectiveness of the Greensite-Tikhonov or the Tikhonov inverse methods were compared under the presence of 10% Gaussian noise with either 84 or 204 body surface electrodes. The stability and accuracy of the Greensite-Tikhonov method were further investigated by introducing varying levels of Gaussian signal noise or by increasing or decreasing the size of the stomach by 10%. Results showed that the reconstructed solutions were able to represent the presence of propagating multiple wave fronts and the Greensite-Tikhonov method with 204 electrodes performed best (correlation coefficients of activation time: 90%; pacemaker localization error: 3 cm). The Greensite-Tikhonov method was stable with Gaussian noise levels up to 20% and 10% change in stomach size. The use of 204 rather than 84 body surface electrodes improved the performance; however, for all investigated cases, the Greensite-Tikhonov method outperformed the Tikhonov method.

  5. Gravitational waves from first order phase transitions as a probe of an early matter domination era and its inverse problem

    Barenboim, Gabriela, E-mail:; Park, Wan-Il, E-mail:


    We investigate the gravitational wave background from a first order phase transition in a matter-dominated universe, and show that it has a unique feature from which important information about the properties of the phase transition and thermal history of the universe can be easily extracted. Also, we discuss the inverse problem of such a gravitational wave background in view of the degeneracy among macroscopic parameters governing the signal.

  6. Inverse procedure for simultaneous evaluation of viscosity and density of Newtonian liquids from dispersion curves of Love waves

    Kiełczyński, P.; Szalewski, M.; Balcerzak, A.


    Simultaneous determination of the viscosity and density of liquids is of great importance in the monitoring of technological processes in the chemical, petroleum, and pharmaceutical industry, as well as in geophysics. In this paper, the authors present the application of Love waves for simultaneous inverse determination of the viscosity and density of liquids. The inversion procedure is based on measurements of the dispersion curves of phase velocity and attenuation of ultrasonic Love waves. The direct problem of the Love wave propagation in a layered waveguide covered by a viscous liquid was formulated and solved. Love waves propagate in an elastic layered waveguide covered on its surface with a viscous (Newtonian) liquid. The inverse problem is formulated as an optimization problem with appropriately constructed objective function that depends on the material properties of an elastic waveguide of the Love wave, material parameters of a liquid (i.e., viscosity and density), and the experimental data. The results of numerical calculations show that Love waves can be efficiently applied to determine simultaneously the physical properties of liquids (i.e., viscosity and density). Sensors based on this method can be very attractive for industrial applications to monitor on-line the parameters (density and viscosity) of process liquid during the course of technological processes, e.g., in polymer industry.

  7. Rayleigh-wave imaging of upper-mantle shear velocities beneath the Malawi Rift; Preliminary results from the SEGMeNT experiment

    Accardo, N. J.; Gaherty, J. B.; Shillington, D. J.; Nyblade, A.; Ebinger, C. J.; Mbogoni, G. J.; Chindandali, P. R. N.; Mulibo, G. D.; Ferdinand-Wambura, R.; Kamihanda, G.


    The Malawi Rift (MR) is an immature rift located at the southern tip of the Western branch of the East African Rift System (EARS). Pronounced border faults and tectonic segmentation are seen within the upper crust. Surface volcanism in the region is limited to the Rungwe volcanic province located north of Lake Malawi (Nyasa). However, the distribution of extension and magma at depth in the crust and mantle lithosphere is unknown. As the Western Rift of the EARS is largely magma-poor except for discrete volcanic provinces, the MR presents the ideal location to elucidate the role of magmatism in early-stage rifting and the manifestation of segmentation at depth. This study investigates the shear velocity of the crust and mantle lithosphere beneath the MR to constrain the thermal structure, the amount of total crustal and lithospheric thinning, and the presence and distribution of magmatism beneath the rift. Utilizing 55 stations from the SEGMeNT (Study of Extension and maGmatism in Malawi aNd Tanzania) passive-source seismic experiment operating in Malawi and Tanzania, we employed a multi-channel cross-correlation algorithm to obtain inter-station phase and amplitude information from Rayleigh wave observations between 20 and 80 s period. We retrieve estimates of phase velocity between 9-20 s period from ambient noise cross-correlograms in the frequency domain via Aki's formula. We invert phase velocity measurements to obtain estimates of shear velocity (Vs) between 50-200 km depth. Preliminary results reveal a striking low-velocity zone (LVZ) beneath the Rungwe volcanic province with Vs ~4.2-4.3 km/s in the uppermost mantle. Low velocities extend along the entire strike of Lake Malawi and to the west where a faster velocity lid (~4.5 km/s) is imaged. These preliminary results will be extended by incorporating broadband data from seven "lake"-bottom seismometers (LBS) to be retrieved from Lake Malawi in October of this year. The crust and mantle modeling will be

  8. North American Mantle Heterogeneity from Joint Inversion of Body and Surface Waves

    Lou, X.; Van der Lee, S.


    We have developed a Python/Matplotlib tool to measure teleseismic body wave arrival times. A graphic user interface is built to visualize seismograms and facilitate quality control. Seismic data from IRIS PASSCAL arrays and EarthScope's Transportable Array were processed with this tool to get teleseismic P and S relative delay times sampling both western and eastern North America. Distributions of delay times corrected for crustal structures show that the mantle east of the Rocky Mountains is at least as hetergeneous as that west of the Rocky Mountains. To better understand the heterogeneity within active and stable North America, we have simultaneously inverted relative S wave delay times and NA07's regional waveform fitting constraints for a new S velocity model. This joint inversion combines the complementary resolving powers of body and surface waves. The Rocky Mountains is a surface geological boundary separating active western and stable eastern US. But the actual boundary within the mantle does not necessary coincide with the location of the mountain front at the surface. At 150 km depth, high velocity Wyoming craton extends to west of the Rockies while low velocity anomalies in east Colorado and New Mexico extend to east of the Rockies. In western US, a dipping high velocity Juan de Fuca Slab extends continuously to the Transition Zone east of which are possibly older fragments of Farallon Plate. We do see a slab window beneath west central Oregon at about 150 km depth. Along the Snake River Plain, there are strong low velocities of up to 5% above 300 km depth. Low velocity of about 1% resides below 600 km depth, suggesting that the plume conduit beneath Yellowstone is not continuous.

  9. Global upper-mantle tomography with the automated multimode inversion of surface and S-wave forms

    Lebedev, S.; Hilst, R.D. van der


    We apply the Automated Multimode Inversion of surface and S-wave forms to a large global data set, verify the accuracy of the method and assumptions behind it, and compute an Sv-velocity model of the upper mantle (crust–660 km). The model is constrained with ~51 000 seismograms recorded at 368

  10. Bivariate Rayleigh Distribution and its Properties

    Ahmad Saeed Akhter


    Full Text Available Rayleigh (1880 observed that the sea waves follow no law because of the complexities of the sea, but it has been seen that the probability distributions of wave heights, wave length, wave induce pitch, wave and heave motions of the ships follow the Rayleigh distribution. At present, several different quantities are in use for describing the state of the sea; for example, the mean height of the waves, the root mean square height, the height of the “significant waves” (the mean height of the highest one-third of all the waves the maximum height over a given interval of the time, and so on. At present, the ship building industry knows less than any other construction industry about the service conditions under which it must operate. Only small efforts have been made to establish the stresses and motions and to incorporate the result of such studies in to design. This is due to the complexity of the problem caused by the extensive variability of the sea and the corresponding response of the ships. Although the problem appears feasible, yet it is possible to predict service conditions for ships in an orderly and relatively simple manner Rayleigh (1980 derived it from the amplitude of sound resulting from many independent sources. This distribution is also connected with one or two dimensions and is sometimes referred to as “random walk” frequency distribution. The Rayleigh distribution can be derived from the bivariate normal distribution when the variate are independent and random with equal variances. We try to construct bivariate Rayleigh distribution with marginal Rayleigh distribution function and discuss its fundamental properties.

  11. An inversion scheme to model subsurface fracture systems using shear wave splitting polarization and delay time observations simultaneously

    Yang, Ming; Elkibbi, Maya; Rial, José A.


    Shear wave splitting polarization (p) and delay time (Δt) observations are used to invert for fracture orientation and intensity of fracturing, simultaneously. By addressing the different levels of uncertainty involved in measurements of these two parameters, as well as their dissimilar relationships to fracture configuration, we have developed an inversion algorithm which reduces the primary double-response inversion to two connected single-response ones. We show that its inherent non-linearity complicates this problem, which therefore requires a more sophisticated attack than conventional inversion schemes. It will be shown that the construction of residue function contours in the model plane and the generation of surrogate data by simulation process are essential to this approach. We illustrate the capabilities of this technique by inverting shear wave splitting data from The Geysers geothermal reservoir in California. In principle the method should be useful for characterizing fractured reservoirs, whether geothermal or hydrocarbon.

  12. CORRIGENDUM: Atoms riding Rayleigh waves Atoms riding Rayleigh waves

    Benedek, G.; Echenique, P. M.; Toennies, J. P.; Traeger, F.


    In the original paper the affiliation list is incorrect. The correct address list is as follows: G Benedek1, 5, P M Echenique1, 2, J P Toennies3 and F Traeger4 1 Donostia International Physics Center (DIPC), Paseo Manuel de Lardizábal 4, 20018 Donostia—San Sebastián, Spain 2 Departamento de Física de Materiales and CFM (CSIC-UPV/EHU), Universidad del País Vasco/Euskal Herriko Unibertsitatea, E-20018 San Sebastián/Donostia, Spain 3 Max Planck-Institut für Dynamik und Selbstorganisation, Bunsenstraße 10 D-37073 Göttingen, Germany 4 Fakultät für Chemie und Biochemie, Ruhr-Universität Bochum Universitätsstraße 150, 44801 Bochum, Germany 5 Permanent address: Dipartimento di Scienza dei Materiali, Universitá di Milano-Bicocca, Via Cozzi 53, 20125 Milano, Italy

  13. Monte Carlo search techniques applied to the measurement of higher mode phase velocities and anisotropic surface wave tomography. Geologica Ultraiectina (285)

    Visser, K.


    In this thesis we present all three stages of the inversion approach proposed by Kennett and Yoshizawa (2002). The three stage inversion approach consists of obtaining fundamental and higher mode Love and Rayleigh wave phase velocity measurements through waveform fitting in the first stage, combinin

  14. Source parameter inversion for wave energy focusing to a target inclusion embedded in a three-dimensional heterogeneous halfspace

    Karve, Pranav M.


    We discuss a methodology for computing the optimal spatio-temporal characteristics of surface wave sources necessary for delivering wave energy to a targeted subsurface formation. The wave stimulation is applied to the target formation to enhance the mobility of particles trapped in its pore space. We formulate the associated wave propagation problem for three-dimensional, heterogeneous, semi-infinite, elastic media. We use hybrid perfectly matched layers at the truncation boundaries of the computational domain to mimic the semi-infiniteness of the physical domain of interest. To recover the source parameters, we define an inverse source problem using the mathematical framework of constrained optimization and resolve it by employing a reduced-space approach. We report the results of our numerical experiments attesting to the methodology\\'s ability to specify the spatio-temporal description of sources that maximize wave energy delivery. Copyright © 2016 John Wiley & Sons, Ltd.

  15. T-wave inversions related to left ventricular basal hypertrophy and myocardial fibrosis in non-apical hypertrophic cardiomyopathy: A cardiovascular magnetic resonance imaging study

    Chen, Xiuyu, E-mail: [Department of Radiology, State Key Laboratory of Cardiovascular Disease, Fuwai Hospital, National Center for Cardiovascular Diseases, Chinese Academy of Medical Sciences and Peking Union Medical College, Beijing 100037 (China); Zhao, Shihua, E-mail: [Department of Radiology, State Key Laboratory of Cardiovascular Disease, Fuwai Hospital, National Center for Cardiovascular Diseases, Chinese Academy of Medical Sciences and Peking Union Medical College, Beijing 100037 (China); Zhao, Tao, E-mail: [Department of Radiology, State Key Laboratory of Cardiovascular Disease, Fuwai Hospital, National Center for Cardiovascular Diseases, Chinese Academy of Medical Sciences and Peking Union Medical College, Beijing 100037 (China); Lu, Minjie, E-mail: [Department of Radiology, State Key Laboratory of Cardiovascular Disease, Fuwai Hospital, National Center for Cardiovascular Diseases, Chinese Academy of Medical Sciences and Peking Union Medical College, Beijing 100037 (China); Yin, Gang, E-mail: [Department of Radiology, State Key Laboratory of Cardiovascular Disease, Fuwai Hospital, National Center for Cardiovascular Diseases, Chinese Academy of Medical Sciences and Peking Union Medical College, Beijing 100037 (China); Jiang, Shiliang, E-mail: [Department of Radiology, State Key Laboratory of Cardiovascular Disease, Fuwai Hospital, National Center for Cardiovascular Diseases, Chinese Academy of Medical Sciences and Peking Union Medical College, Beijing 100037 (China); Prasad, Sanjay, E-mail: [NIHR Biomedical Research Unit, Royal Brompton Hospital Sydney Street, London, SW3 6NP (United Kingdom)


    Objectives: To investigate the relationship between T-wave inversions and left ventricular (LV) segmental hypertrophy and myocardial fibrosis assessed by cardiovascular magnetic resonance (CMR) in patients with non-apical hypertrophic cardiomyopathy (HCM). Methods: 196 consecutive patients with non-apical HCM underwent late gadolinium enhancement (LGE) CMR and 12-lead electrocardiogram. The distribution and magnitude of LV segmental hypertrophy and LGE were assessed according to the AHA 17-segment model and analyzed in relation to T-wave inversions. Results: Of 196 HCM patients, 144 (73%) exhibited T-wave inversions. 144 (73%) patients had evidence of myocardial fibrosis as defined by LGE, and the prevalence of LGE was significantly higher in patients with T-wave inversions compared with those without T-wave inversions (78% vs. 59%, P = 0.008). T-wave inversions were related to basal anterior and basal anteroseptal LGE (20% vs. 10%, P = 0.04 and 68% vs. 46%, P = 0.005, respectively). In addition, T-wave inversions were associated with greater basal anteroseptal and basal inferior wall thickness (19.5 ± 4.7 mm vs. 16.7 ± 4.5 mm, P < 0.001 and 10.9 ± 3.3 mm vs. 9.6 ± 3.0 mm, P = 0.01, respectively). By logistic regression analysis, basal anteroseptal wall thickness and LGE were independent determinants of T-wave inversions (P = 0.005, P = 0.01, respectively). Conclusions: T-wave inversions in HCM are associated with LGE and wall thickness of the left ventricular basal segments. Moreover, basal anteroseptal wall thickness and LGE are independent determinants of T-wave inversions.

  16. Stroh formalism and Rayleigh waves

    Tanuma, Kazumi


    Introduces a powerful and elegant mathematical method for the analysis of anisotropic elasticity equationsThe reader can grasp the essentials as quickly as possibleCan be used as a textbook, which presents compactly introduction and applications of the Stroh formalismAppeals to the people not only in mathematics but also in mechanics and engineering sciencePrerequisites are only basic linear algebra, calculus and fundamentals of differential equations

  17. Isolated T Wave Inversion in Lead aVL: An ECG Survey and a Case Report

    Getaw Worku Hassen


    Full Text Available Background. Computerized electrocardiogram (ECG analysis has been of tremendous help for noncardiologists, but can we rely on it? The importance of ST depression and T wave inversions in lead aVL has not been emphasized and not well recognized across all specialties. Objective. This study’s goal was to analyze if there is a discrepancy of interpretation by physicians from different specialties and a computer-generated ECG reading in regard to a TWI in lead aVL. Methods. In this multidisciplinary prospective study, a single ECG with isolated TWI in lead aVL that was interpreted by the computer as normal was given to all participants to interpret in writing. The readings by all physicians were compared by level of education and by specialty to one another and to the computer interpretation. Results. A total of 191 physicians participated in the study. Of the 191 physicians 48 (25.1% identified and 143 (74.9% did not identify the isolated TWI in lead aVL. Conclusion. Our study demonstrated that 74.9% did not recognize the abnormality. New and subtle ECG findings should be emphasized in their training so as not to miss significant findings that could cause morbidity and mortality.

  18. T-wave inversions on ECG as primary manifestation of Hashimoto's disease.

    Araque, Katherine A; Smith, Michael J; Walsh, Brooks M


    A middle-aged Hispanic woman presented to the emergency department (ED) reporting of acute new onset pressure-like chest pain developed at rest. It was radiated to the right arm and associated with malaise. Initial ECG demonstrated T-wave inversions (TWIs) in all anterior and lateral leads. Electrolytes, serial cardiac troponin and D-dimer were all normal. Comprehensive transthoracic echocardiogram and nuclear stress test did not reveal a cardiac cause of her symptoms.Serum thyroid-stimulating hormone was markedly elevated (207 mIU/L) and free thyroxine was low (FT4 0.07 ng/dL), consistent with severe primary hypothyroidism. Thyroperoxidase (TPO) antibodies were positive. Therapy with levothyroxine was started. No other cause of the TWIs was identified. A repeat ECG obtained 8 weeks later showed partial resolution of the TWIs. Our observations indicate that Hashimoto's disease is the most likely primary cause of this patient's extensive and profound TWI, which improved after thyroid replacement therapy. 2016 BMJ Publishing Group Ltd.

  19. Statistical flaw characterization through Bayesian shape inversion from scattered wave observations

    McMahan, Jerry A.; Criner, Amanda K.


    A method is discussed to characterize the shape of a flaw from noisy far-field measurements of a scattered wave. The scattering model employed is a two-dimensional Helmholtz equation which quantifies scattering due to interrogating signals from various physical phenomena such as acoustics or electromagnetics. The well-known inherent ill-posedness of the inverse scattering problem is addressed via Bayesian regularization. The method is loosely related to the approach described in [1] which uses the framework of [2] to prove the well-posedness of the infinite-dimensional problem and derive estimates of the error for a particular discretization approach. The method computes the posterior probability density for the flaw shape from the scattered field observations, taking into account prior assumptions which are used to describe any a priori knowledge of the flaw. We describe the computational approach to the forward problem as well as the Markov chain Monte Carlo (MCMC) based approach to approximating the posterior. We present simulation results for some hypothetical flaw shapes with varying levels of observation error and arrangement of observation points. The results show how the posterior probability density can be used to visualize the shape of the flaw taking into account the quantitative confidence in the quality of the estimation and how various arrangements of the measurements and interrogating signals affect the estimation

  20. Joint inversion of P-wave velocity and Vp-Vs ratio:imaging the deep structure in NE Japan

    Wang Zhi


    A new inversion scheme is presented to obtain three-dimensional images of P-wave velocity (Vp) and P-S-wave velocity ratio (Vp/Vs) using P- and S-phase pairs, i.e., the same source-receiver pairs for the P- and S-wave arrival-time data. The S-wave velocity (Vs) was separately inverted using the S-phase arrival times. The earthquake hypocenters were simultaneously relocated in the joint inversion. The method considers the Vp/Vs anomaly as a model parameter in the inversion. The proposed method thus provides a more robust calculation of the Vp/Vs anomaly than the conventional method of dividing Vp by Vs. The method also takes into account the ray path difference between P- and S-waves, and hence yields a less biased Vp-Vs ratio than the method of inverting S-P-wave data for Vp and Vp/Vs anomalies under the assumption of identical P and S ray paths. The proposed method was used to image the crust and upper mantle in northeastern (NE) Japan taking advantage of a large number of high-quality arrival times of P- and S-wave source-receiver pairs. The inverted structures suggest that the subducting slab of the Pacifi c plate is an inclined zone of high-Vp and Vs anomalies with low Vp/Vs perturbation. The mantle wedge is characterized by low-Vp, low-Vs, and high-Vp/Vs anomalies at shallow depths beneath active volcanoes. These features are also observed at greater depths in the back-arc region. Although these features have been previously reported, the Vp/Vs anomaly pattern obtained in this study shows much less scatter and is much better correlated with the seismic velocity perturbation patterns than previous studies. The proposed method can be used, in conjunction with velocity anomaly patterns, to quantify thermal processes associated with plate subduction.

  1. Satellite-based RAR performance simulation for measuring directional ocean wave spectrum based on SAR inversion spectrum

    REN Lin; MAO Zhihua; HUANG Haiqing; GONG Fang


    Some missions have been carried out to measure wave directional spectrum by synthetic aperture radar (SAR) and airborne real aperture radar (RAR) at a low incidence. Both them have their own advantages and limitations. Scientists hope that SAR and satellite-based RAR can complement each other for the research on wave properties in the future. For this study, the authors aim to simulate the satellite-based RAR system to validate performance for measuring the directional wave spectrum. The principal measurements are introduced and the simulation methods based on the one developed by Hauser are adopted and slightly modified. To enhance the authenticity of input spectrum and the wave spectrum measuring consistency for SAR and satellite-based RAR, the wave height spectrum inversed from Envisat ASAR data by cross spectrum technology is used as the input spectrum of the simulation system. In the process of simulation, the sea surface, backscattering signal, modulation spectrum and the estimated wave height spectrum are simulated in each look direction. Directional wave spectrum are measured based on the simulated observations from 0° to 360~. From the estimated wave spectrum, it has an 180° ambiguity like SAR, but it has no special high wave number cut off in all the direction. Finally, the estimated spectrum is compared with the input one in terms of the dominant wave wavelength, direction and SWH and the results are promising. The simulation shows that satellite-based RAR should be capable of measuring the directional wave properties. Moreover, it indicates satellite-based RAR basically can measure waves that SAR can measure.

  2. Rayleigh reflections and nonlinear acoustics of solids

    Breazeale, M. A.


    Schlierken studies of ultrasonic waves, and nonlinear acoustics of solids are addressed. A goniometer for use in a Schlieren system for visualization of ultrasonic waves in liquids is described. The goniometer is used to obtain Schlieren photographs of leaky Rayleigh waves excited on an Al2O3 layer on a stainless steel reflector immersed in water, showing that the Rayleigh wave velocity in this case is less than that of either a water Al203 layer or a water stainless steel layer. Also investigated are: (1) nonlinearity parameters and third order elastic constants of copper between 300 and 3 K; (2) measurement of nonlinearity parameters in small solid samples by the harmonic generation technique; (3) relationship between solid nonlinearity parameters and thermodynamic Gruneisen parameters; and (4) quantum mechanical theory of nonlinear interaction of ultrasonic waves.

  3. Shot- and angle-domain wave-equation traveltime inversion of reflection data: Synthetic and field data examples

    Zhang, Sanzong


    Full-waveform inversion requires the accurate simulation of the dynamics and kinematics of wave propagation. This is difficult in practice because the amplitudes cannot be precisely reproduced for seismic waves in the earth. Wave-equation reflection traveltime tomography (WT) is proposed to avoid this problem by directly inverting the reflection-traveltime residuals without the use of the high-frequency approximation. We inverted synthetic traces and recorded seismic data for the velocity model by WT. Our results demonstrated that the wave-equation solution overcame the high-frequency approximation of ray-based tomography, was largely insensitive to the accurate modeling of amplitudes, and mitigated problems with ambiguous event identification. The synthetic examples illustrated the effectiveness of the WT method in providing a highly resolved estimate of the velocity model. A real data example from the Gulf of Mexico demonstrated these benefits of WT, but also found the limitations in traveltime residual estimation for complex models.

  4. 3D elastic full-waveform inversion for OBC data using the P-wave excitation amplitude

    Oh, Ju-Won


    We suggest a fast and efficient 3D elastic full waveform inversion (FWI) algorithm based on the excitation amplitude (maximum energy arrival) of the P-wave in the source wavefield. It evaluates the gradient direction significantly faster than its conventional counterpart. In addition, it removes the long-wavelength artifacts from the gradient, which are often originated from SS correlation process. From these advantages, the excitation approach offers faster convergence not only for the S wave velocity, but also for the entire process of multi-parameter inversion, compared to the conventional FWI. The feasibility of the proposed method is demonstrated through the synthetic Marmousi and a real OBC data from North Sea.

  5. Design of A Hydraulic Power Take-off System for the Wave Energy Device with An Inverse Pendulum

    张大海; 李伟; 赵海涛; 鲍经纬; 林勇刚


    This paper describes a dual-stroke acting hydraulic power take-off (PTO) system employed in the wave energy converter (WEC) with an inverse pendulum. The hydraulic PTO converts slow irregular reciprocating wave motions to relatively smooth, fast rotation of an electrical generator. The design of the hydraulic PTO system and its control are critical to maximize the generated power. A time domain simulation study and the laboratory experiment of the full-scale beach test are presented. The results of the simulation and laboratory experiments including their comparison at full-scale are also presented, which have validated the rationality of the design and the reliability of some key components of the prototype of the WEC with an inverse pendulum with the dual-stroke acting hydraulic PTO system.

  6. Rayleigh-Taylor mixing in supernova experiments

    Swisher, N. C.; Abarzhi, S. I., E-mail: [Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 (United States); Kuranz, C. C. [University of Michigan, Ann Arbor, Michigan 48109 (United States); Arnett, D. [University of Arizona, Tucson, Arizona 85721 (United States); Hurricane, O.; Remington, B. A.; Robey, H. F. [Lawrence Livermore National Laboratory, Livermore, California 94550 (United States)


    We report a scrupulous analysis of data in supernova experiments that are conducted at high power laser facilities in order to study core-collapse supernova SN1987A. Parameters of the experimental system are properly scaled to investigate the interaction of a blast-wave with helium-hydrogen interface, and the induced Rayleigh-Taylor instability and Rayleigh-Taylor mixing of the denser and lighter fluids with time-dependent acceleration. We analyze all available experimental images of the Rayleigh-Taylor flow in supernova experiments and measure delicate features of the interfacial dynamics. A new scaling is identified for calibration of experimental data to enable their accurate analysis and comparisons. By properly accounting for the imprint of the experimental conditions, the data set size and statistics are substantially increased. New theoretical solutions are reported to describe asymptotic dynamics of Rayleigh-Taylor flow with time-dependent acceleration by applying theoretical analysis that considers symmetries and momentum transport. Good qualitative and quantitative agreement is achieved of the experimental data with the theory and simulations. Our study indicates that in supernova experiments Rayleigh-Taylor flow is in the mixing regime, the interface amplitude contributes substantially to the characteristic length scale for energy dissipation; Rayleigh-Taylor mixing keeps order.

  7. Fast Inversion of Air-Coupled Spectral Analysis of Surface Wave (SASW Using in situ Particle Displacement

    Yifeng Lu


    Full Text Available Spectral Analysis of Surface Wave (SASW is widely used in nondestructive subsurface profiling for geological sites. The air-coupled SASW is an extension from conventional SASW methods by replacing ground-mounted accelerometers with non-contact microphones, which acquire a leaky surface wave instead of ground vibration. The air-coupled SASW is a good candidate for fast inspection in shallow geological studies. Especially for pavement maintenance, minimum traffic interference might be induced. One issue that restrains SASW from fast inspection is the traditional slow inversion which relies on guess-and-check iteration techniques including a forward analysis. In this article, a fast inversion analysis algorithm is proposed to estimate the shear velocity profile without performing conventional forward simulation. By investigating the attenuation of particle displacement along penetrating depths, a weighted combination relationship is derived to connect the dispersion curve with the shear velocity profile directly. Using this relationship, the shear velocity profile could be estimated from a given/measured dispersion curve. The proposed procedure allows the surface wave-based method to be fully automatic and even operated in real-time for geological site and pavement assessment. The method is verified by the forward analysis with stiffness matrix method. It is also proved by comparing with other published results using various inversion methods.

  8. Asymptotic Rayleigh instantaneous unit hydrograph

    Troutman, B.M.; Karlinger, M.R.


    The instantaneous unit hydrograph for a channel network under general linear routing and conditioned on the network magnitude, N, tends asymptotically, as N grows large, to a Rayleigh probability density function. This behavior is identical to that of the width function of the network, and is proven under the assumption that the network link configuration is topologically random and the link hydraulic and geometric properties are independent and identically distributed random variables. The asymptotic distribution depends only on a scale factor, {Mathematical expression}, where ?? is a mean link wave travel time. ?? 1988 Springer-Verlag.

  9. High resolution imaging of lithospheric structures beneath the Pyrenees by full waveform inversion of shortperiod teleseismic P waves

    Wang, Yi; Chevrot, Sébastien; Komatitsch, Dimitri; Monteiller, Vadim; Durochat, Clément


    Thanks to the deployment of permanent and temporary broadband arrays, coverage and data quality have dramatically improved in the last decade, especially for regional-scale studies. In addition, owing to the progress of high-performance resources and numerical simulation techniques, waveform inversion approaches nowadays become a viable alternative to classical asymptotic ray based tomographic approaches. Exploiting full waveforms in seismic tomography requires an efficient and precise method to solve the elastic wave equation in 3D inhomogeneous media. Since resolution of waveform inversion is limited by the seismic wavelength as well as the wavefield sampling density, it is crucial to exploit short-period teleseismic waves recorded by dense regional arrays. However, modeling the propagation of short-period body waves in heterogeneous media is still very challenging, even on the largest modern supercomputers. For this reason, we have developed a hybrid method that couples a global wave propagation method in a 1D Earth to a 3D spectral-element method in a regional domain. This hybrid method restricts the costly 3D computations to inside the regional domain, which dramatically decreases the computational cost, allows us to compute teleseismic wavefields down to 1s period, thus accounting for the complexities that affect the propagation of seismic waves in the regional domain. We present the first application of this new waveform inversion approach to broadband data coming from two dense transects deployed during the PYROPE experiment across the Pyrenees mountains. We obtain the first high-resolution lithospheric section of compressional and shear velocities across an orogenic belt. The tomographic model provides clear evidence for the under-thrusting of the thinned Iberian crust beneath the European plate and for the important role of rift-inherited mantle structures during the formation of the Pyrenees.

  10. Elastic-wave-mode separation in TTI media with inverse-distance weighted interpolation involving position shading

    Wang, Jian; Meng, Xiaohong; Zheng, Wanqiu


    The elastic-wave reverse-time migration of inhomogeneous anisotropic media is becoming the hotspot of research today. In order to ensure the accuracy of the migration, it is necessary to separate the wave mode into P-wave and S-wave before migration. For inhomogeneous media, the Kelvin–Christoffel equation can be solved in the wave-number domain by using the anisotropic parameters of the mesh nodes, and the polarization vector of the P-wave and S-wave at each node can be calculated and transformed into the space domain to obtain the quasi-differential operators. However, this method is computationally expensive, especially for the process of quasi-differential operators. In order to reduce the computational complexity, the wave-mode separation of mixed domain can be realized on the basis of a reference model in the wave-number domain. But conventional interpolation methods and reference model selection methods reduce the separation accuracy. In order to further improve the separation effect, this paper introduces an inverse-distance interpolation method involving position shading and uses the reference model selection method of random points scheme. This method adds the spatial weight coefficient K, which reflects the orientation of the reference point on the conventional IDW algorithm, and the interpolation process takes into account the combined effects of the distance and azimuth of the reference points. Numerical simulation shows that the proposed method can separate the wave mode more accurately using fewer reference models and has better practical value.

  11. 多道瞬态瑞雷波在隧道超前探测中的应用%Application of Multi-channel Transient Rayleigh Wave Method on the Advanced Detecting Technology to Tunnel

    吴腾飞; 吴荣新; 张平松; 程刚



  12. Laboratory Generation of Solitary Waves:An Inversion Technique to Improve Available Methods

    A.Romano; M.Guerrini; G.Bellotti; 琚烈红


    Solitary waves are often used in laboratory experiments to study tsunamis propagation and interaction with coasts. However, the experimental shape of the waves may differ from the theoretical one. In this paper, a correction technique aiming at minimizing the discrepancies between the two profiles is presented. Laboratory experiments reveal their effectiveness in correcting the experimental shape of solitary waves, mainly for low nonlinearities.

  13. The Modularized Software Package ASKI - Full Waveform Inversion Based on Waveform Sensitivity Kernels Utilizing External Seismic Wave Propagation Codes

    Schumacher, F.; Friederich, W.


    We present the modularized software package ASKI which is a flexible and extendable toolbox for seismic full waveform inversion (FWI) as well as sensitivity or resolution analysis operating on the sensitivity matrix. It utilizes established wave propagation codes for solving the forward problem and offers an alternative to the monolithic, unflexible and hard-to-modify codes that have typically been written for solving inverse problems. It is available under the GPL at The Gauss-Newton FWI method for 3D-heterogeneous elastic earth models is based on waveform sensitivity kernels and can be applied to inverse problems at various spatial scales in both Cartesian and spherical geometries. The kernels are derived in the frequency domain from Born scattering theory as the Fréchet derivatives of linearized full waveform data functionals, quantifying the influence of elastic earth model parameters on the particular waveform data values. As an important innovation, we keep two independent spatial descriptions of the earth model - one for solving the forward problem and one representing the inverted model updates. Thereby we account for the independent needs of spatial model resolution of forward and inverse problem, respectively. Due to pre-integration of the kernels over the (in general much coarser) inversion grid, storage requirements for the sensitivity kernels are dramatically reduced.ASKI can be flexibly extended to other forward codes by providing it with specific interface routines that contain knowledge about forward code-specific file formats and auxiliary information provided by the new forward code. In order to sustain flexibility, the ASKI tools must communicate via file output/input, thus large storage capacities need to be accessible in a convenient way. Storing the complete sensitivity matrix to file, however, permits the scientist full manual control over each step in a customized procedure of sensitivity/resolution analysis and full

  14. On Rayleigh's Principle

    Andersen, Kurt Munk


    Rayleigh's principle expresses that the smallest eigenvalue of a regular Sturm-Liouville problem with regular boundary conditions is the minimum value of a certain functional, the so called Rayleigh's quotient, and that this value is attained at the corresponding eigenfunctions only. This can...... be proved by means of more advanced methods. However, it turns out that there is an elementary proof, which is presented in the report....

  15. Terahertz Wide-Angle Imaging and Analysis on Plane-wave Criteria Based on Inverse Synthetic Aperture Techniques

    Gao, Jing Kun; Qin, Yu Liang; Deng, Bin; Wang, Hong Qiang; Li, Jin; Li, Xiang


    This paper presents two parts of work around terahertz imaging applications. The first part aims at solving the problems occurred with the increasing of the rotation angle. To compensate for the nonlinearity of terahertz radar systems, a calibration signal acquired from a bright target is always used. Generally, this compensation inserts an extra linear phase term in the intermediate frequency (IF) echo signal which is not expected in large-rotation angle imaging applications. We carried out a detailed theoretical analysis on this problem, and a minimum entropy criterion was employed to estimate and compensate for the linear-phase errors. In the second part, the effects of spherical wave on terahertz inverse synthetic aperture imaging are analyzed. Analytic criteria of plane-wave approximation were derived in the cases of different rotation angles. Experimental results of corner reflectors and an aircraft model based on a 330-GHz linear frequency-modulated continuous wave (LFMCW) radar system validated the necessity and effectiveness of the proposed compensation. By comparing the experimental images obtained under plane-wave assumption and spherical-wave correction, it also showed to be highly consistent with the analytic criteria we derived.

  16. Influence of the condensate and inverse cascade on the direct cascade in wave turbulence

    Korotkevich, A O


    During direct numerical simulation of the isotropic turbulence of surface gravity waves in the framework of Hamiltonian equations formation of the long wave background or condensate was observed. Exponents of the direct cascade spectra at the different levels of an artificial condensate suppression show a tendency to become closer to the prediction of the wave turbulence theory at lower levels of condensate. A simple qualitative explanation of the mechanism of this phenomenon is proposed.

  17. 山西地区面波相速度分布图像%Rayleigh-wave phase velocity distribution in Shanxi region

    宋美琴; 何正勤; 郑勇; 吕芳; 刘春; 梁向军; 苏燕; 李丽


    In this work,seismic datas are taken from seismograms of over 100 earthquakes which are recorded from Feburary in 2009 to November in 2011 at 31 stations in Shanxi Province and other 6 broadband stations in adjacent areas,including Hebei,Henan,Shanxi and Neimeng Province.We obtained 350 high-quality Rayleigh wave phase velocity dispersion curves of fundamental mode by removing the duplicate paths and low quality data.The periods of the dispersion curves range from 8 to 75 seconds.Based on the method of Ditmar & Yanovskaya,we obtained phase velocity dispersion maps in 33 periods with resolution ranges from 40 to 50 km.We analyzed the phase velocity distribution maps at four representative periods and the phase velocity section maps along three profiles.The phase velocity maps reveal the lateral heterogeneity of the velocity structure and the phase speed variation with depth in the crust and the upper mantle of the Shanxi fault depression zone.The phase velocity map at 10 s clearly shows the spatial differences between the rift zone and the uplift zones in the two sides,presenting low phase velocity anomalies in the maximum depression regions near the centers of several basins inside the rift zone Moderate to strong earthquakes(M≥6)in Shanxi are mostly concentrated in the transitional zones where dramatic phase velocity changes occur at 15 s.At 20~26 s period,significant phase velocity difference can be observed across the latitude of 38°N,where phase velocity is higher in the south side than that in the north,which is in consistent with the variation pattern of Moho depth in the depression zone.This kind of velocity pattern keeps constant with the increase of period,which is consistent with the feature that the blocks in the north Shanxi is relatively weaker than those in the south.Along 113°E,the phase velocities at periods of 25~75 s are higher in the north side of latitude 38°N than in the south.This is consistent with the result of the lithospheric

  18. Surface wave scattering theory : with applications to forward and inverse problems in seismology

    Snieder, R.K.


    Scattering of surface waves in a three dimensional layered elastic medium with embedded heterogeneities is described in this thesis with the Born approximation. The dyadic decomposition of the surface wave Green's function provides the crucial element for an efficient application of Born theory to s

  19. A New Wave Equation Based Source Location Method with Full-waveform Inversion

    Wu, Zedong


    Locating the source of a passively recorded seismic event is still a challenging problem, especially when the velocity is unknown. Many imaging approaches to focus the image do not address the velocity issue and result in images plagued with illumination artifacts. We develop a waveform inversion approach with an additional penalty term in the objective function to reward the focusing of the source image. This penalty term is relaxed early to allow for data fitting, and avoid cycle skipping, using an extended source. At the later stages the focusing of the image dominates the inversion allowing for high resolution source and velocity inversion. We also compute the source location explicitly and numerical tests show that we obtain good estimates of the source locations with this approach.

  20. Imaging earth`s interior: Tomographic inversions for mantle P-wave velocity structure

    Pulliam, R.J.


    A formalism is developed for the tomographic inversion of seismic travel time residuals. The travel time equations are solved both simultaneously, for velocity model terms and corrections to the source locations, and progressively, for each set of terms in succession. The methods differ primarily in their treatment of source mislocation terms. Additionally, the system of equations is solved directly, neglecting source terms. The efficacy of the algorithms is explored with synthetic data as we perform simulations of the general procedure used to produce tomographic images of Earth`s mantle from global earthquake data. The patterns of seismic heterogeneity in the mantle that would be returned reliably by a tomographic inversion are investigated. We construct synthetic data sets based on real ray sampling of the mantle by introducing spherical harmonic patterns of velocity heterogeneity and perform inversions of the synthetic data.

  1. Imaging earth's interior: Tomographic inversions for mantle P-wave velocity structure

    Pulliam, R.J.


    A formalism is developed for the tomographic inversion of seismic travel time residuals. The travel time equations are solved both simultaneously, for velocity model terms and corrections to the source locations, and progressively, for each set of terms in succession. The methods differ primarily in their treatment of source mislocation terms. Additionally, the system of equations is solved directly, neglecting source terms. The efficacy of the algorithms is explored with synthetic data as we perform simulations of the general procedure used to produce tomographic images of Earth's mantle from global earthquake data. The patterns of seismic heterogeneity in the mantle that would be returned reliably by a tomographic inversion are investigated. We construct synthetic data sets based on real ray sampling of the mantle by introducing spherical harmonic patterns of velocity heterogeneity and perform inversions of the synthetic data.

  2. Illuminating heterogeneous anisotropic upper mantle: testing a new anisotropic teleseismic body-wave tomography code - part II: Inversion mode

    Munzarova, Helena; Plomerova, Jaroslava; Kissling, Edi


    necessary step before AniTomo is applied to real datasets. We examine various aspects coming along with anisotropic tomography such as setting a starting anisotropic model and parameters controlling the inversion, and particularly influence of a ray coverage on resolvability of individual anisotropic parameters. Synthetic testing also allows investigation of the well-known trade-off between effects of P-wave anisotropy and isotropic heterogeneities. Therefore, the target synthetic models are designed to represent schematically different heterogeneous anisotropic structures of the upper mantle. Testing inversion mode of the AniTomo code, considering an azimuthally quasi-equal distribution of rays and teleseismic P-wave incidences, shows that a separation of seismic anisotropy and isotropic velocity heterogeneities is plausible and that the correct orientation of the symmetry axes in a model can be found within three iterations for well-tuned damping factors.

  3. Inversion of single-station teleseismic P-wave polarization-data for the velocity structure of Beijing area

    LIU; Futian; (


    [1]Pavlis, G. L., Booker, J. R., Progressive multiple event location (PMEL), Bull. Seismol. Soc. Am., 1983, 73: 1753.[2]Dziewonski, A. M., Anderson, D. L., Travel times and station corrections for P-waves at teleseismic distances, J. Geophys. Res., 1983, 88: 3295.[3]Hu Ge, Menke, W., Formal inversion of laterally heterogeneous velocity structure from P-wave polarization data, Geophys. J. Int., 1992. 110: 63.[4]Menke, W., Lerner-Lam, A., Transition from linear to complex polarization in short period compressional waves, Bull. Seismol. Soc. Am., 1991, 81: 611.[5]Hu Ge, Menke, W., Rognvaldsson, S., A demonstration of the joint use of p-wave polarization and travel-time data in tomographic inversion: crustal velocity structure near the south Iceland Lowland network, Geophys. Res. Letters, 1993, 20(13): 1407.[6]Teng, J., Yao, H., Chou, H., Crustal structure in the Beijing-Tianjin-Tangshan-Zhangjiakou region, Acta Geophysica Sinica(in Chinese), 1979, 22(3): 218.[7]Shao, X., Zhang, J., Chen, X. et al., The results of deep sounding by using converted waves of earthquakes in the Beijing-Tianjin-Tangshan region, Seismology and Geology(in Chinese), 1980: 2(2): 12.[8]Wei, M., Shi, Z., Yin, X. et al., The basic configuration of crustal structure in North China region and its relation to the earthquakes from gravimetric date, Seismology and Geology(in Chinese), 1980, 2(2): 55.[9]Jin Anshu, Liu Futian, Sun Yongzhi, Three-dimensional P velocity structure of the crust and upper Mantle under Beijing region, Acta Geophysica Sinica(in Chinese), 1980, 23(2): 172.[10]Vidale, J.E., Complex polarization analysis of particle motion, Bull. Seismol. Soc. Am., 1986, 76: 1393.[11]Jurkevics, A., Polarization analysis of three-component array data, Bull, Seismol. Soc. Am., 1988, 78: 1725.[12]Park, J., Vernon, F. L., Lindberg, C.R., Frequency dependent polarization analysis of high-frequency seismograms, J. Geophys. Res., 1987, 92: 12664.[13

  4. Diagnostic Value of Electrocardiographic T Wave Inversion in Lead aVL in Diagnosing Coronary Artery Disease in Patients with Chronic Stable Angina

    Hatem L. Farhan


    Full Text Available Objectives: The clinical value of T wave inversion in lead aVL in diagnosing coronary artery disease (CAD remains unclear. This study aims to investigate the correlation between aVL T wave inversion and CAD in patients with chronic stable angina.Methods: Electrocardiograms (ECGs of 257 consecutive patients undergoing coronary angiography were analyzed. All patients had chronic stable angina. All patients with secondary T wave inversion had been excluded (66 patients. The remaining 191 patients constituted the study population. Detailed ECG interpretation and coronary angiographic findings were conducted by experienced cardiologists.Results: T wave inversion in aVL was identified in 89 ECGs (46.8% with definite ischemic Q-ST-T changes in different leads in 97 ECGs (50.8%. Stand alone aVL T wave inversion was found in 27 ECGs (14.1% while ischemic changes in other leads with normal aVL were identified in 36 ECGs (18.8%. The incidence of CAD was 86.3%. Single, two- and multi-vessel CAD were found in 38.8%, 28.5% and 32.7% of cases respectively. The prevalence of left main, left anterior descending, left circumflex and right coronary arteries were 4.7%, 61.2%, 29.3% and 44.5%, respectively. T wave inversion in aVL was found to be the only ECG variable significantly predicting mid segment left anterior descending artery (LAD lesions (Odds Ratio 2.93, 95% Confidence Interval 1.59-5.37, p=0.001.Conclusion: This study provides new information relating to T wave inversion in lead aVL to mid segment LAD lesions. Implication of this simple finding may help in bedside diagnosis of CAD typically mid LAD lesions. However, further studies are needed to corroborate this finding.

  5. Time-domain full waveform inversion using the gradient preconditioning based on seismic wave energy: Application to the South China Sea

    Mengxuan, Zhong


    The gradient preconditioning algorithms based on Hessian matrices in time-domain full waveform inversion (FWI) are widely used now, but consume a lot of memory and do not fit the FWI of large models or actual seismic data well. To avoid the huge storage consumption, the gradient preconditioning approach based on seismic wave energy has been proposed it simulates the “approximated wave field” with the acoustic wave equation and uses the energy of the simulated wavefield to precondition the gradient. The method does not require computing and storing the Hessian matrix or its inverse and can effectively eliminate the effect caused by geometric diffusion and uneven illumination on gradient. The result of experiments in this article with field data from South China Sea confirms that the time-domain FWI using the gradient preconditioning based on seismic wave energy (GPWE) can achieve higher inversion accuracy for the deep high-velocity model and its underlying strata.

  6. Estimation of the p-wave velocity profile of elastic real data based on surface wave inversion

    Ponomarenko, A.V.; Kashtan, B.M.; Troyan, V.N.; Mulder, W.A.


    Recently, we proposed an analytical approach to invert for a smoothly varying near-surface P-wave velocity profile that has a squared slowness linearly decreasing with depth. The exact solution for such a velocity profile in the acoustic approximation can be expressed in terms of Airy functions and

  7. Evidence for serpentinization of the Ionian upper mantle from simultaneous inversion of P- and S-wave arrival times

    D'Alessandro, Antonino; Mangano, Giorgio; D'Anna, Giuseppe; Scudero, Salvatore


    Simultaneous inversion of P- and S-wave arrival times, collected during a 3-years Ocean Bottom Seismometer with Hydrophone (OBS/H) monitoring campaign, yields 1D P- and S-wave velocity models for the Ionian lithosphere (Central Mediterranean). The 1D model highlights the presence, in the Ionian upper mantle, of two layers characterized by high seismic P-wave velocity (S1 and S2, 6.3-6.7 and 7.5 km/s, respectively). These two layers, with thicknesses of about 3.3 km and 5 km, respectively, and ranging from ∼8 to ∼16 km in depth, are characterized by low S-wave velocity (S1 = 3.05-3.2 km/s, S2 = 3.85 km/s) and high values of VP/VS (S1 = 2.06-2.09, S2 = 1.95). This is a characteristic feature, often encountered in passive margins and is generally interpreted as partly serpentinized peridotite. The VP, VS and VP/VS values of S1 are consistent with 55-65% of serpentinization of the upper mantle, while the S2 ones are consistent with 15-25% of serpentinization. This research provides a crucial hint about the debated nature of the Ionian crust, suggesting its oceanic structure.

  8. The diagonalator: An alternative cost functional for wave-equation inversion

    Poor Moghaddam, P.; Mulder, W.A.


    The classic least-squares cost functional for full waveform inversion suffers from local minima due to loop skipping in the absence of low frequencies in the seismic data. Velocity model building based on subsurface spatial or temporal shifts may break down in the presence of multiples in the data.

  9. Inversion of single-station teleseismic P-wave polarization-data for the velocity structure of Beijing area


    Broadband three-component seismic data recorded by Beijingstation (BJI) of CDSN were used to calculate P-wave polarization of teleseismic events. These polarization data were then used in the inversion for the underground structure around the Beijing station, especially for the details of velocity discontinuities. The result shows that a conspicuous low velocity zone exists in the crust on the west of the station, which is in good agreement with previous studies. It proves the theory that polarization data could be applied to inversion for velocity structures, especially for boundaries with large velocity gradient. It also demonstrates the feasibility of velocity structure inversion with polarization data from high-quality broadband data recorded by a single station. Therefore, travel-times and polarization data can be jointly used to study velocity structure. Polarization data are more suitable for delineating the boundary of velocity anomalies. Moreover, if the polarization method is combined with receiver function method to fully exploit their complementarity, it is possible to obtain the lateral velocity variation around the station as well as the detailed vertical variation below the station.

  10. Large-scale inhomogeneity in sapphire test masses revealed by Rayleigh scattering imaging

    Yan, Zewu; Ju, Li; Eon, François; Gras, Slawomir; Zhao, Chunnong; Jacob, John; Blair, David G.


    Rayleigh scattering in test masses can introduce noise and reduce the sensitivity of laser interferometric gravitational wave detectors. In this paper, we present laser Rayleigh scattering imaging as a technique to investigate sapphire test masses. The system provides three-dimensional Rayleigh scattering mapping of entire test masses and quantitative evaluation of the Rayleigh scattering coefficient. Rayleigh scattering mapping of two sapphire samples reveals point defects as well as inhomogeneous structures in the samples. We present results showing significant non-uniform scattering within two 4.5 kg sapphire test masses manufactured by the heat exchanger method.

  11. Cardiac and non-cardiac causes of T-wave inversion in the precordial leads in adult subjects: A Dutch case series and review of the literature

    Salah; AM; Said; Rene; Bloo; Ramon; de; Nooijer; Andries; Slootweg


    AIM: To describe the electrocardiographic(ECG) phenomena characterized by T-wave inversion in the precordial leads in adults and to highlight its differential diagnosis. METHODS: A retrospective chart review of 8 adult patients who were admitted with ECG T-wave inversion in the anterior chest leads with or without prolongation of corrected QT(QTc) interval. They had different clinical conditions. Each patient underwent appropriate clinical assessment including investigation for myocardial involvement. Single and multimodality noninvasive, semi-invasive and invasive diagnostic approach were used to ascertain the diagnosis. The diagnostic assessment included biochemical investigation, cardiac and abdominal ultrasound, cerebral and chest computed tomography, nuclear medicine and coronary angiography.RESULTS: Eight adult subjects(5 females) with a mean age of 66 years(range 51 to 82) are analyzed. The etiology of T-wave inversion in the precordial leads were diverse. On admission, all patients had normal blood pressure and the ECG showed sinus rhythm. Five patients showed marked prolongation of the QTc interval. The longest QTc interval(639 ms) was found in the patient with pheochromocytoma. Giant T-wave inversion(≥ 10 mm) was found in pheochromocytoma followed by electroconvulsive therapy and finally ischemic heart disease. The deepest T-wave was measured in lead V3(5 ×). In 3 patients presented with mild T-wave inversion(patients 1, 5 and 4 mm), the QTc interval was not prolonged(432, 409 and 424 msec), respectively.CONCLUSION: T-wave inversion associated with or without QTc prolongation requires meticulous history taking, physical examination and tailored diagnostic modalities to reach rapid and correct diagnosis to establish appropriate therapeutic intervention.

  12. Determining surface wave arrival angle anomalies

    Larson, Erik W. F.; Ekström, Göran


    A new method for measuring arrival angles of teleseismic Love and Rayleigh waves is developed. The new method utilizes estimates of surface wave dispersion to create a phase-matched filter to isolate the Love or Rayleigh wave in three-component recordings. The polarization of the filtered wave group is determined in the time domain by application of a variation of the complex polarization method of Vidale [1986]. Orientation, linearity, and ellipticity of particle motion are estimated in several frequency bands to determine the frequency-dependent polarization. The method employs an iterative scheme, by which a predicted Love wave, based on the estimated dispersion and polarization, is subtracted from the three-component data prior to the estimation of Rayleigh wave polarization, and vice versa. The method is applied to an extensive set of Global Seismographic Network data covering the years 1989-1998. Between 4244 and 15,075 measurements are collected for fundamental mode Love and Rayleigh waves at nine different periods (37 to 150 s). Measurement uncertainties are estimated using the statistics of observations for pairwise similar paths and are generally of the order of 15-50% of the total signal, depending on the period and the wave type. Large and azimuthally invariant angle anomalies are documented for several stations and are consistent with misorientation of the horizontal seismometers. Two schemes are employed to determine the misorientations: (1) an azimuthally weighted average at each station, and (2) a joint inversion for seismometer misorientation and globally heterogeneous phase velocities. The determined corrections are robust and correlate well with those reported in earlier studies. Azimuthally varying arrival angle anomalies are shown to agree qualitatively with predictions of wave refraction calculated for recent phase velocity maps, which explain up to 30% of the variance in the new measurements.

  13. Numerical Approximation of Boundary Control for the Wave Equation - with Application to an Inverse Problem

    Mariegaard, Jesper Sandvig

    We consider a control problem for the wave equation: Given the initial state, find a specific boundary condition, called a control, that steers the system to a desired final state. The Hilbert uniqueness method (HUM) is a mathematical method for the solution of such control problems. It builds...... on the duality between the control system and its adjoint system, and these systems are connected via a so-called controllability operator. In this project, we are concerned with the numerical approximation of HUM control for the one-dimensional wave equation. We study two semi-discretizations of the wave...... equation: a linear finite element method (L-FEM) and a discontinuous Galerkin-FEM (DG-FEM). The controllability operator is discretized with both L-FEM and DG-FEM to obtain a HUM matrix. We show that formulating HUM in a sine basis is beneficial for several reasons: (i) separation of low and high frequency...

  14. Directional infrared emission resulting from cascade population inversion and four-wave mixing in Rb vapor.

    Akulshin, Alexander; Budker, Dmitry; McLean, Russell


    Directional infrared emission at 1.37 and 5.23 μm is generated in Rb vapors that are stepwise excited by low-power cw resonant light. The radiation at 5.23 μm originating from amplified spontaneous emission on the 5D(5/2)→6P(3/2) transition and wave mixing consists of forward- and backward-directed components with distinctive spectral and spatial properties. Diffraction-limited light at 1.37 μm generated in the copropagating direction only is a product of parametric wave mixing around the 5P(3/2)→5D(5/2)→6P(3/2)→6S(1/2)→5P(3/2) transition loop. This highly nondegenerate mixing process involves one externally applied and two internally generated optical fields. Similarities between wave mixing generated blue and 1.37 μm light are demonstrated.

  15. 南海瑞雷面波群速度层析成像及其地球动力学意义%Group velocity tomography of Rayleigh waves in South China Sea and its geodynamic implications

    陈立; 薛梅; Le Khanh Phon; 杨挺


    complex geological structures. In this study, we give a 3D shear wave velocity structure of South China Sea deduced from surface wave tomography and analyze its geodynamic implications. Due to the newly deployed seismic stations in western and southern South China Sea, we have a better ray path coverage when using the single station method. This is especially true for the coastal region of southern China, where earthquakes occur less frequently and the newly added stations can increase the ray density in this region. We used earthquakes distributed on the periphery of South China Sea and collected earthquake data from 48 stations. We first calculated the group velocity dispersion curves of fundamental mode for Rayleigh waves with periods from 14 s to 130 s using multiple filter technique. Then we conducted subspace inversion to get group velocity distributions for different periods in the region. Finally, on the basis of the relationship between shear wave velocity and group velocity under certain layer structure of the Earth, we obtained the 3D shear wave structures in the form of depth slices and vertical profiles by using a damped least square algorithm. The results show: ①High velocities exist in sea basins where velocity image delineates the shape of sea basins: the high velocities in shallow parts may indicate oceanic characteristics of the sea basin crust, while high velocities in deeper parts may come from high velocity materials which remained after the formation of oceanic crust at expanding ocean ridge. The velocity differences among sea basins are consistent with their heat flow values as well as their ages. The high velocities disappear at depths greater than 60 km, and are replaced by a low-velocity zone in a certain depth range. Beneath the low-velocity zone, a NE-SW high-velocity belt is observed at a depth of 200 km, and may be related to the ancient subduction in this region. ②Surrounding the South China Sea, there are obvious high velocities

  16. PS-wave moveout inversion for tilted TI media: A physical modeling study

    Dewangan, P.; Tsvankin, I.; Batzle, M.; Van Wijk, K.; Haney, M.

    -waves can be inverted for the parameters of a horizontal TI layer with a tilted symmetry axis. The 2D multicomponent reflection data are acquired over a phenolic sample manufactured to simulate the effective medium formed by steeply dipping fracture sets...

  17. Multichannel analysis of surface waves

    Park, C.B.; Miller, R.D.; Xia, J.


    The frequency-dependent properties of Rayleigh-type surface waves can be utilized for imaging and characterizing the shallow subsurface. Most surface-wave analysis relies on the accurate calculation of phase velocities for the horizontally traveling fundamental-mode Rayleigh wave acquired by stepping out a pair of receivers at intervals based on calculated ground roll wavelengths. Interference by coherent source-generated noise inhibits the reliability of shear-wave velocities determined through inversion of the whole wave field. Among these nonplanar, nonfundamental-mode Rayleigh waves (noise) are body waves, scattered and nonsource-generated surface waves, and higher-mode surface waves. The degree to which each of these types of noise contaminates the dispersion curve and, ultimately, the inverted shear-wave velocity profile is dependent on frequency as well as distance from the source. Multichannel recording permits effective identification and isolation of noise according to distinctive trace-to-trace coherency in arrival time and amplitude. An added advantage is the speed and redundancy of the measurement process. Decomposition of a multichannel record into a time variable-frequency format, similar to an uncorrelated Vibroseis record, permits analysis and display of each frequency component in a unique and continuous format. Coherent noise contamination can then be examined and its effects appraised in both frequency and offset space. Separation of frequency components permits real-time maximization of the S/N ratio during acquisition and subsequent processing steps. Linear separation of each ground roll frequency component allows calculation of phase velocities by simply measuring the linear slope of each frequency component. Breaks in coherent surface-wave arrivals, observable on the decomposed record, can be compensated for during acquisition and processing. Multichannel recording permits single-measurement surveying of a broad depth range, high levels of

  18. A goal-oriented reduced basis method for the wave equation in inverse analysis

    Hoang, Khac Chi; Bordas, Stephane P A


    In this paper, we extend the reduced-basis methods developed earlier for wave equations to goal-oriented wave equations with affine parameter dependence. The essential new ingredient is the dual (or adjoint) problem and the use of its solution in a sampling procedure to pick up "goal-orientedly" parameter samples. First, we introduce the reduced-basis recipe --- Galerkin projection onto a space $Y_N$ spanned by the reduced basis functions which are constructed from the solutions of the governing partial differential equation at several selected points in parameter space. Second, we propose a new "goal-oriented" Proper Orthogonal Decomposition (POD)--Greedy sampling procedure to construct these associated basis functions. Third, based on the assumption of affine parameter dependence, we use the offline-online computational procedures developed earlier to split the computational procedure into offline and online stages. We verify the proposed computational procedure by applying it to a three-dimensional simulat...

  19. Modeling and inversion of PS-wave moveout asymmetry for tilted TI media: Part 2: Dipping TTI layer

    Dewangan, P.; Tsvankin, I.

    for the parameters H20849aH20850 H9280 and H20849bH20850 VP0 obtained from PP- and SS-waves in the symmetry-axis plane by scanning over the tilt H9263. All model parameters except for the tilt H20849H9263 = 5?, 25?, and 60?H20850 are the same as those in Figure 1 H...20849H9280 = 0.25, VP0 =4km/sH20850. D126 DewanganandTsvankin It is important for practical applications to study the inverse prob- lem for the common case when only 2D data in the symmetry-axis plane are available.The pure-mode data vector in this case...

  20. Estimation of Elastic Constants from Surface Acoustic Wave Velocity by Inverse Analysis using the Downhill Simplex Method

    Sato, Harumichi; Nishino, Hideo; Cho, Hideo; Ogiso, Hisato; Yamanaka, Kazushi


    The measurement of surface acoustic wave (SAW) velocity is used to estimate the surface properties because the velocity depends on the elastic properties near the surface.To estimate the elastic constants, we developed a new inverse method combining the Monte Carlo method and the downhill simplex method.The initial values are determined using many random numbers, instead of an arbitrarily chosen several sets of values, in order to reduce the risk of trapping by the local pseudo minima.We confirm that the estimated elastic constants agree well with the reported elastic constants of Si and the experimental SAW velocity is quite well reproduced.We estimate the elastic constants of quartz for application purposes.

  1. Estimation of liquid properties by inverse problem analysis based on shear horizontal surface acoustic wave sensor responses

    Ueda, Kento; Kondoh, Jun


    A shear horizontal surface acoustic wave (SH-SAW) sensor can detect liquid properties, such as viscosity, density, permittivity, and conductivity. The advantage of using the SH-SAW sensors is the simultaneous detection of the mechanical and electrical properties of liquids. In this paper, we proposed a method of estimating the density and viscosity of liquids based on the inverse problem analysis. Glycerol or ethanol aqueous solutions were measured. The estimated and literature values were compared. For glycerol aqueous solutions, when the concentration is low, those values agree well. However, when the concentration is high, those values did not agree because the bulk modulus of glycerin solutions cannot be assumed as constant. On the other hand, as the bulk modulus of ethanol aqueous solutions can be assumed to be the same as that of water, the deviations between those values were small. Therefore, the proposed method is effective when the bulk modulus is assumed as constant.

  2. Potential-vorticity inversion and the wave-turbulence jigsaw: some recent clarifications

    McIntyre, M. E.


    Two key ideas stand out as crucial to understanding atmosphere-ocean dynamics, and the dynamics of other planets including the gas giants. The first key idea is the invertibility principle for potential vorticity (PV). Without it, one can hardly give a coherent account of even so important and elementary a process as Rossby-wave propagation, going beyond the simplest textbook cases. Still less can one fully understand nonlinear processes like the self-sharpening or narrowing of jets the once-mysterious "negative viscosity" phenomenon. The second key idea, also crucial to understanding jets, might be summarized in the phrase "there is no such thing as turbulence without waves", meaning Rossby waves especially. Without this idea one cannot begin to make sense of, for instance, momentum budgets and eddy momentum transports in complex large-scale flows. Like the invertibility principle the idea has long been recognized, or at least adumbrated. However, it is worth articulating explicitly if only because it can be forgotten when, in the usual way, we speak of "turbulence" and "turbulence theory" as if they were autonomous concepts. In many cases of interest, such as the well-studied terrestrial stratosphere, reality is more accurately described as a highly inhomogeneous "wave-turbulence jigsaw puzzle" in which wavelike and turbulent regions fit together and crucially affect each other's evolution. This modifies, for instance, formulae for the Rhines scale interpreted as indicating the comparable importance of wavelike and turbulent dynamics. Also, weakly inhomogeneous turbulence theory is altogether inapplicable. For instance there is no scale separation. Eddy scales are not much smaller than the sizes of the individual turbulent regions in the jigsaw. Here I review some recent progress in clarifying these ideas and their implications.

  3. Potential-vorticity inversion and the wave-turbulence jigsaw: some recent clarifications

    M. E. McIntyre


    Full Text Available Two key ideas stand out as crucial to understanding atmosphere-ocean dynamics, and the dynamics of other planets including the gas giants. The first key idea is the invertibility principle for potential vorticity (PV. Without it, one can hardly give a coherent account of even so important and elementary a process as Rossby-wave propagation, going beyond the simplest textbook cases. Still less can one fully understand nonlinear processes like the self-sharpening or narrowing of jets – the once-mysterious "negative viscosity" phenomenon. The second key idea, also crucial to understanding jets, might be summarized in the phrase "there is no such thing as turbulence without waves", meaning Rossby waves especially. Without this idea one cannot begin to make sense of, for instance, momentum budgets and eddy momentum transports in complex large-scale flows. Like the invertibility principle the idea has long been recognized, or at least adumbrated. However, it is worth articulating explicitly if only because it can be forgotten when, in the usual way, we speak of "turbulence" and "turbulence theory" as if they were autonomous concepts. In many cases of interest, such as the well-studied terrestrial stratosphere, reality is more accurately described as a highly inhomogeneous "wave-turbulence jigsaw puzzle" in which wavelike and turbulent regions fit together and crucially affect each other's evolution. This modifies, for instance, formulae for the Rhines scale interpreted as indicating the comparable importance of wavelike and turbulent dynamics. Also, weakly inhomogeneous turbulence theory is altogether inapplicable. For instance there is no scale separation. Eddy scales are not much smaller than the sizes of the individual turbulent regions in the jigsaw. Here I review some recent progress in clarifying these ideas and their implications.

  4. Ray-tracing traveltime tomography versus wave-equation traveltime inversion for near-surface seismic land data

    Fu, Lei


    Full-waveform inversion of land seismic data tends to get stuck in a local minimum associated with the waveform misfit function. This problem can be partly mitigated by using an initial velocity model that is close to the true velocity model. This initial starting model can be obtained by inverting traveltimes with ray-tracing traveltime tomography (RT) or wave-equation traveltime (WT) inversion. We have found that WT can provide a more accurate tomogram than RT by inverting the first-arrival traveltimes, and empirical tests suggest that RT is more sensitive to the additive noise in the input data than WT. We present two examples of applying WT and RT to land seismic data acquired in western Saudi Arabia. One of the seismic experiments investigated the water-table depth, and the other one attempted to detect the location of a buried fault. The seismic land data were inverted by WT and RT to generate the P-velocity tomograms, from which we can clearly identify the water table depth along the seismic survey line in the first example and the fault location in the second example.

  5. Two-dimensional probabilistic inversion of plane-wave electromagnetic data: Methodology, model constraints and joint inversion with electrical resistivity data

    Rosas-Carbajal, M.; Linde, N.; Kalscheuer, T.; Vrugt, J.A.


    Probabilistic inversion methods based on Markov chain Monte Carlo (MCMC) simulation are well suited to quantify parameter and model uncertainty of nonlinear inverse problems. Yet, application of such methods to CPU-intensive forward models can be a daunting task, particularly if the parameter space

  6. Finite-fault source inversion using teleseismic P waves: Simple parameterization and rapid analysis

    Mendoza, C.; Hartzell, S.


    We examine the ability of teleseismic P waves to provide a timely image of the rupture history for large earthquakes using a simple, 2D finite‐fault source parameterization. We analyze the broadband displacement waveforms recorded for the 2010 Mw∼7 Darfield (New Zealand) and El Mayor‐Cucapah (Baja California) earthquakes using a single planar fault with a fixed rake. Both of these earthquakes were observed to have complicated fault geometries following detailed source studies conducted by other investigators using various data types. Our kinematic, finite‐fault analysis of the events yields rupture models that similarly identify the principal areas of large coseismic slip along the fault. The results also indicate that the amount of stabilization required to spatially smooth the slip across the fault and minimize the seismic moment is related to the amplitudes of the observed P waveforms and can be estimated from the absolute values of the elements of the coefficient matrix. This empirical relationship persists for earthquakes of different magnitudes and is consistent with the stabilization constraint obtained from the L‐curve in Tikhonov regularization. We use the relation to estimate the smoothing parameters for the 2011 Mw 7.1 East Turkey, 2012 Mw 8.6 Northern Sumatra, and 2011 Mw 9.0 Tohoku, Japan, earthquakes and invert the teleseismic P waves in a single step to recover timely, preliminary slip models that identify the principal source features observed in finite‐fault solutions obtained by the U.S. Geological Survey National Earthquake Information Center (USGS/NEIC) from the analysis of body‐ and surface‐wave data. These results indicate that smoothing constraints can be estimated a priori to derive a preliminary, first‐order image of the coseismic slip using teleseismic records.

  7. integral equation methods for the inverse problem with discontinuous wave speed

    Aktosun, T.; Klaus, M.; vanderMee, C.


    The recovery of the coefficient H(x) in the one-dimensional generalized Schrodinger equation d(2) psi dx(2)+k(2)H(x)(2) psi=Q(x)psi, where H(x) is a positive, piecewise continuous function with positive limits H-+/- as x-->+(+/-infinity), is studied. The large-k asymptotics of the wave functions and the scattering coefficients are analyzed. A factorization formula is given expressing the total scattering matrix as a product of simpler scattering matrices. Using this factorization an algorithm...

  8. Inversion method for defects in depth evaluation and thermal wave imaging

    吕跃凯; 张淑仪; 周庆标


    A hybrid Newton-like iterative method and a regularization method are employed to perform the numerical simulations of the defects in depth evaluation and the thermal wave imaging for defects-included solid sample by analysis of the surface photo-thermal signals. A simple and effective data processing method is suggested to improve the reconstructed data. The results of the numerical calculation demonstrate that the algorithm presented in this paper is very effective, and can be used for qualitative and quantitative analyses of homogeneous materials with defects in depth included. It is also proved that the algorithm is stable even with noise disturbance.

  9. Full-wave Moment Tensor and Tomographic Inversions Based on 3D Strain Green Tensor


    at the eastern Himalayan syntaxis (event 03.230 in Figure 4). The GCMT solution shows a strike-slip event at 33 km depth, while our FDSGT solution...2007. Olsen, K.B., Simulation of three-dimensional wave propagation in the Salt Lake Basin, Ph.D. Thesis, University of Utah, Salt Lake City, Utah...agreement. One notable exception is the August 18, 2003 earthquake at the eastern Himalayan syntaxis. The GCMT solution shows a strike-slip event at 33

  10. Ultrafast traveling wave dominates the electric organ discharge of Apteronotus leptorhynchus: an inverse modelling study.

    Shifman, Aaron R; Longtin, André; Lewis, John E


    Identifying and understanding the current sources that give rise to bioelectric fields is a fundamental problem in the biological sciences. It is very difficult, for example, to attribute the time-varying features of an electroencephalogram recorded from the head surface to the neural activity of specific brain areas; model systems can provide important insight into such problems. Some species of fish actively generate an oscillating (c. 1000 Hz) quasi-dipole electric field to communicate and sense their environment in the dark. A specialized electric organ comprises neuron-like cells whose collective signal underlies this electric field. As a step towards understanding the detailed biophysics of signal generation in these fish, we use an anatomically-detailed finite-element modelling approach to reverse-engineer the electric organ signal over one oscillation cycle. We find that the spatiotemporal profile of current along the electric organ constitutes a travelling wave that is well-described by two spatial Fourier components varying in time. The conduction velocity of this wave is faster than action potential conduction in any known neuronal axon (>200 m/s), suggesting that the spatiotemporal features of high-frequency electric organ discharges are not constrained by the conduction velocities of spinal neuron pathways.

  11. An inverse problem for the wave equation with one measurement and the pseudorandom noise

    Helin, Tapio; Oksanen, Lauri


    We consider the wave equation $(\\p_t^2-\\Delta_g)u(t,x)=f(t,x)$, in $\\R^n$, $u|_{\\R_-\\times \\R^n}=0$, where the metric $g=(g_{jk}(x))_{j,k=1}^n$ is known outside an open and bounded set $M\\subset \\R^n$ with smooth boundary $\\p M$. We define a deterministic source $f(t,x)$ called the pseudorandom noise as a sum of point sources, $f(t,x)=\\sum_{j=1}^\\infty a_j\\delta_{x_j}(x)\\delta(t)$, where the points $x_j,\\ j\\in\\Z_+$, form a dense set on $\\p M$. We show that when the weights $a_j$ are chosen appropriately, $u|_{\\R\\times \\p M}$ determines the scattering relation on $\\p M$, that is, it determines for all geodesics which pass through $M$ the travel times together with the entering and exit points and directions. The wave $u(t,x)$ contains the singularities produced by all point sources, but when $a_j=\\lambda^{-\\lambda^{j}}$ for some $\\lambda>1$, we can trace back the point source that produced a given singularity in the data. This gives us the distance in $(\\R^n, g)$ between a source point $x_j$ and an arbitrary p...

  12. P-wave attenuation anisotropy in TI media and its application in fracture parameters inversion

    He, Yi-Yuan; Hu, Tian-Yue; He, Chuan; Tan, Yu-Yang


    The existence of aligned fractures in fluid-saturated rocks leads to obvious attenuation anisotropy and velocity anisotropy. Attenuation anisotropy analysis can be applied to estimate fracture density and scale, which provide important information for reservoir identification. This paper derives P-wave attenuation anisotropy in the ATI media where the symmetry axis is in the arbitrary direction theoretically and modifies the spectral ratio method to measure attenuation anisotropy in the ATI media, thus avoiding a large measurement error when applied to wide azimuth or full azimuth data. Fracture dip and azimuth can be estimated through attenuation anisotropy analysis. For small-scale fractures, fracture scale and fracture density can be determined with enhanced convergence if velocity and attenuation information are both used. We also apply the modified spectralratio method to microseismic field data from an oilfield in East China and extract the fracture dip through attenuation anisotropy analysis. The result agrees with the microseismic monitoring.

  13. Modulational instability arising from collective Rayleigh scattering.

    Robb, G R M; McNeil, B W J


    It is shown that under certain conditions a collection of dielectric Rayleigh particles suspended in a viscous medium and enclosed in a bidirectional ring cavity pumped by a strong laser field can produce a new modulational instability transverse to the wave-propagation direction. The source of the instability is collective Rayleigh scattering i.e., the spontaneous formation of periodic longitudinal particle-density modulations and a backscattered optical field. Using a linear stability analysis a dispersion relation is derived which determines the region of parameter space in which modulational instability of the backscattered field and the particle distribution occurs. In the linear regime the pump is modulationally stable. A numerical analysis is carried out to observe the dynamics of the interaction in the nonlinear regime. In the nonlinear regime the pump field also becomes modulationally unstable and strong pump depletion occurs.

  14. Thermoelectric properties of inverse opals

    Mahan, G. D.; Poilvert, N.; Crespi, V. H.


    Rayleigh's method [Philos. Mag. Ser. 5 34, 481 (1892)] is used to solve for the classical thermoelectric equations in inverse opals. His theory predicts that in an inverse opal, with periodic holes, the Seebeck coefficient and the figure of merit are identical to that of the bulk material. We also provide a major revision to Rayleigh's method, in using the electrochemical potential as an important variable, instead of the electrostatic potential. We also show that in some cases, the thermal boundary resistance is important in the effective thermal conductivity.

  15. A simple analytic approximation to the Rayleigh-Bénard stability threshold

    Prosperetti, Andrea


    The Rayleigh-Bénard linear stability problem is solved by means of a Fourier series expansion. It is found that truncating the series to just the first term gives an excellent explicit approximation to the marginal stability relation between the Rayleigh number and the wave number of the perturbatio

  16. Inverse least-squares modeling of vapor descriptors using polymer-coated surface acoustic wave sensor array responses.

    Grate, J W; Patrash, S J; Kaganovet, S N; Abraham, M H; Wise, B M; Gallagher, N B


    In previous work, it was shown that, in principle, vapor descriptors could be derived from the responses of an array of polymer-coated acoustic wave devices. This new chemometric classification approach was based on polymer/vapor interactions following the well-established linear solvation energy relationships (LSERs) and the surface acoustic wave (SAW) transducers being mass sensitive. Mathematical derivations were included and were supported by simulations. In this work, an experimental data set of polymer-coated SAW vapor sensors is investigated. The data set includes 20 diverse polymers tested against 18 diverse organic vapors. It is shown that interfacial adsorption can influence the response behavior of sensors with nonpolar polymers in response to hydrogen-bonding vapors; however, in general, most sensor responses are related to vapor interactions with the polymers. It is also shown that polymer-coated SAW sensor responses can be empirically modeled with LSERs, deriving an LSER for each individual sensor based on its responses to the 18 vapors. Inverse least-squares methods are used to develop models that correlate and predict vapor descriptors from sensor array responses. Successful correlations can be developed by multiple linear regression (MLR), principal components regression (PCR), and partial least-squares (PLS) regression. MLR yields the best fits to the training data, however cross-validation shows that prediction of vapor descriptors for vapors not in the training set is significantly more successful using PCR or PLS. In addition, the optimal dimension of the PCR and PLS models supports the dimensionality of the LSER formulation and SAW response models.

  17. The Body Wave Velocity Structure in the Upper Crust of Fujian Estimated by Noise Records

    Li Jun; Jin Xing; Bao Ting; Lin Shu; Wei Yongxiang; Zhang Hongcai


    In this paper, the dispersion curves of the Rayleigh wave and Love wave were extracted from the seismic noise records of 25 broadband stations of the Fujian Seismic Network, and inverted for the lithosphere velocity structure. Furthermore, the velocity model was verified by the seismic explosion observations. Our results indicate that the resolution of the lithosphere velocity structure obtained by this method is good in the shallow part, but in the deep part, inversion accuracy for the wave velocity structure is low, which is caused mainly by the small inter-station distance chosen in the paper. Thus the wave dispersion curves have high accuracy in the short-period part, but the warp of the wave dispersion curve in long-period part is large. Considering the results from both the noise inversion and the traditional inversion, we finally present a new velocity model, and the theoretical travel time calculated with the new model matches the explosion travel time very well.

  18. Theoretical investigation of high velocity, temperature compensated Rayleigh waves along AlN/SiC substrates for high sensitivity mass sensors

    Caliendo, Cinzia


    The operation of electroacoustic devices based on surface acoustic waves (SAW) propagation along β-SiC/AlN and amorphous-SiC/AlN substrates is theoretically studied with respect to the AlN film thickness, the SAW propagation direction, temperature and electric boundary conditions. GHz-range, enhanced electroacoustic coupling coefficient, temperature compensated around 20 °C electroacoustic devices are the advantages of SiC/AlN composite structures. These structures are also suitable for the implementation of sensors with improved performances with respect to SAW devices based on bulk single crystal piezoelectric substrates. The structures feasibility was confirmed by structural investigation and quantitative analysis of sputtered amorphous-SiC and AlN films on Si substrates.

  19. Advanced detection technology of Rayleigh wave for detection of abnormal geological structure in excavation face%瑞利波技术超前探测掘进工作面构造异常

    李胜; 祁晓鑫; 李军文


    In the front of excavation face, there exist abnormal geological structures such as fault, karst cave, col-lapsed pillars and aquifer, which usually bring about hazards like “pervious to water” and “roof fall” etc. How to accurately and effectively detect the geological structure in the front of excavation face has became a problem ur-gently needed to solve during production in coal mine. TYR (D) Rayleigh wave detector was adopted in advanced detection in driving face 7603 of Wuyang mine. The collected data were processed and analyzed, the conclusion is basically consistent with the engineering verification, thus obtaining good application effect.%掘进工作面前方存在断层、溶洞、陷落柱、含水层等地质构造,常常导致透水、冒顶等灾害性事故。采用YTR(D)瑞利波探测仪对山西潞安集团五阳煤矿7603掘进工作面进行超前探测,并对现场采集的数据进行处理和分析。结果显示,2个测点共发现9处异常区,通过后期工程验证,有7处探测异常区与实际揭露的结果基本一致,探测与实际揭露异常区域位置误差均在4m以内。

  20. Comparison of the bedrock depth from array measurements of Rayleigh waves associated with microtremor and seismic profile obtained the Seismic Reflection Data, Eskisehir Basin, Turkey

    Tün, Muammer; Karabulut, Savaş; Özel, Oğuz


    Ground motion estimation for future earthquakes is one of the most challenging problems in seismology and earthquake engineering. The bedrock depth has a considerable seismic risk for the urban area of Eskişehir. In this study, multiple station microtremor measurement methods which are more practical, non-distructive, fast and economical compared to seismic reflection method were implemented. These method using microtremor recordings have become a very useful data for microzonation studies because of their simple acquisition and analysis. Extensive ambient noise measurements were performed in the basin of Eskisehir from June 2010 to spring 2012. We use data recorded by a broadband seismometer and digitizer CMG-6TD, Guralp seismometer. Some of the measurement locations, the CMG-6TD sensor was located into 30 cm-deep holes in the ground to avoid strongly wind-generated, long-period noise. Dominant frequency (f), bed-rock depth (h) and shear-wave velocity (Vs) were determined from Spatial Autocorrelation (SPAC) methods. With the SPAC Method, it is possible to constrain the velocity structure underlying the site using microtremor array measurements. The results obtained were compared to the 96-channel seismic reflection data with explosive energy source. Several seismic reflection surveys with P-Gun seismic source have been performed on the same place with array measurements. We used two types of seismic sources: 36 cartridge Gun. Shot interval was 10 meters, group interval (one geophone per group, 48 geophones in total) was 10 meters, near offset was 10 meters, far offset was 480 meters, CDP interval was 5 meters. We adapted the 'Off-End Spread' technique while using the Gun. Reflection images within the sedimentary section correlate well with the velocity structure obtained from SPAC.

  1. Identification of surface wave higher modes using a methodology based on seismic noise and coda waves

    Rivet, Diane; Campillo, Michel; Sanchez-Sesma, Francisco; Shapiro, Nikolaï M.; Singh, Shri Krishna


    Dispersion analysis of Rayleigh waves is performed to assess the velocity of complex structures such as sedimentary basins. At short periods several modes of the Rayleigh waves are often exited. To perform a reliable inversion of the velocity structure an identification of these modes is thus required. We propose a novel method to identify the modes of surface waves. We use the spectral ratio of the ground velocity for the horizontal components over the vertical component (H/V) measured on seismic coda. We then compare the observed values with the theoretical H/V ratio for velocity models deduced from surface wave dispersion when assuming a particular mode. We first invert the Rayleigh wave measurements retrieved from ambient noise cross-correlation with the assumptions that (1) the fundamental mode and (2) the first overtone are excited. Then we use these different velocity models to predict theoretical spectral ratios of the ground velocity for the horizontal components over the vertical component (H/V). These H/V ratios are computed under the hypothesis of equipartition of a diffuse field in a layered medium. Finally we discriminate between fundamental and higher modes by comparing the theoretical H/V ratio with the H/V ratio measured on seismic coda. In an application, we reconstruct Rayleigh waves from cross-correlations of ambient seismic noise recorded at seven broad-band stations in the Valley of Mexico. For paths within the soft quaternary sediments basin, the maximum energy is observed at velocities higher than expected for the fundamental mode. We identify that the dominant mode is the first higher mode, which suggests the importance of higher modes as the main vectors of energy in such complex structures.

  2. A New Inverse Method of Elastic Constants for a Fibre-Reinforced Composite Plate from Laser-Based Ultrasonic Lamb Waves

    杨京; 程建春


    A new inverse method based on the wavelet transform and artificial neural networks (ANN) is presented to recover elastic constants of a fibre-reinforced composite plate from laser-based ultrasonic Lamb waves. The transient waveforms obtained by numerical simulations under different elastic constants are taken as the input of the ANN for training and learning. The wavelet transform is employed for extracting the eigenvectors from the raw Lamb wave signals so as to simplify the structure of the ANN. Then these eigenvectors are input to a multi-layer internally recurrent neural network with a back-propagation algorithm. Finally, the experimental waveforms are used as the input in the whole system to inverse elastic constants of the experimental material.

  3. a Global Shear Velocity Model of the Upper Mantle from New Fundamental and Higher Rayleigh Mode Measurements

    Debayle, E.; Ricard, Y. R.


    We present a global SV-wave tomographic model of the upper mantle, built from a new dataset of fundamental and higher mode Rayleigh waveforms. We use an extension of the automated waveform inversion approach of Debayle (1999) designed to improve the extraction of fundamental and higher mode information from a single surface wave seismogram. The improvement is shown to be significant in the transition zone structure which is constrained by the higher modes. The new approach is fully automated and can be run on a Beowulf computer to process massive surface wave dataset. It has been used to match successfully over 350 000 fundamental and higher mode Rayleigh waveforms, corresponding to about 20 millions of new measurements extracted from the seismograms. For each seismogram, we obtain a path average shear velocity and quality factor model, and a set of fundamental and higher mode dispersion and attenuation curves compatible with the recorded waveform. The set of dispersion curves provides a global database for future finite frequency inversion. Our new 3D SV-wave tomographic model takes into account the effect of azimuthal anisotropy and is constrained with a lateral resolution of several hundred kilometers and a vertical resolution of a few tens of kilometers. In the uppermost 200 km, our model shows a very strong correlation with surface tectonics. The slow velocity signature of mid-oceanic ridges extend down to ~100 km depth while the high velocity signature of cratons vanishes below 200 km depth. At depth greater than 400 km, the pattern of seismic velocities appear relatively homogeneous at large scale, except for high velocity slabs which produce broad high velocity regions within the transition zone. Although resolution is still good, the region between 200 and 400 km is associated with a complex pattern of seismic heterogeneities showing no simple correlation with the shallower or deeper structure.

  4. Joint Inversion of Geoid Anomaly and Teleseismic P-Wave Delay Times: Modeling Density and Velocity Perturbations Beneath the Parana Magmatic Province

    Chaves, C. A. M.; Ussami, N.; Ritsema, J.


    The Parana Magmatic Province (PMP) is one of the largest continental igneous provinces (LIP) on Earth. It is well dated at 133 Ma preceding the opening of the South Atlantic Ocean, but the causative geodynamic processes are still poorly understood. Although a low-velocity anomaly has been imaged by seismic tomography in the northeast region of the PMP and interpreted as a fossil conduct of a mantle plume that is related to the flood basalt eruptions, geochemical data indicate that such magmatism is caused by the melting of a heterogeneous and enriched lithospheric mantle with no deep plume participation. Models of density perturbations in the upper mantle estimated from joint inversion of geoid anomalies and P-wave delay times will offer important constraints on mantle dynamics. A new generation of accurate global geopotential models derived from satellite-missions (e.g. GRACE, GOCE) allows us to estimate density distribution within the Earth from geoid inversion. In order to obtain the residual geoid anomaly related to the density structure of the mantle, we use the EGM2008 model removing estimated geoid perturbations owing to variations in crustal structure (i.e., topographical masses, Moho depth, thickness of sediments and basalts). Using a spherical-Earth approximation, the density model space is represented by a set of tesseroids and the velocity model is parameterized in nodes of a spherical grid where cubic B-splines are utilized as an interpolation function. To constrain the density inversion, we add more than 10,000 manually picked teleseismic P-wave delay times. During the inversion procedure, density and P-wave velocity are linked through the optimization of a constant linear factor correlating density and velocity perturbation. Such optimization will be performed using a probability density function (PDF) [Tarantola, 2005]. We will present the preliminary results of this joint inversion scheme and hypothesize on the geodynamic processes responsible for

  5. Suppression of Rayleigh-Taylor instability by gyroviscosity and sheared axial flow in imploding plasma pinches

    HUANG Lin; JIAN Guang-de; QIU Xiao-ming


    The synergistic stabilizing effect of gyroviscosity and sheared axial flow on the Rayleigh-Taylor instability in Z-pinch implosions is studied by means of the incompressible viscid magneto-hydrodynamic equations. The gyroviscosity (or finite Larmor radius) effects are introduced in the momentum equation through an anisotropic ion stress tensor. Dispersion relation with the effect of a density discontinuity is derived. The results indicate that the short-wavelength modes of the Rayleigh-Taylor instability are easily stabilized by the gyroviscosity effects. The long wavelength modes are stabilized by the sufficient sheared axial flow. However, the synergistic effects of the finite Larmor radius and sheared axial flow can heavily mitigate the Rayleigh-Taylor instability. This synergistic effect can compress the Rayleigh-Taylor instability to a narrow wave number region. Even with a sufficient gyroviscosity and large enough flow velocity, the synergistic effect can completely suppressed the Rayleigh-Taylor instability in whole wave number region.

  6. A combined full wave equation tomography - full waveform inversion and its application to 12 km long streamer data from offshore western Sumatra

    Wang, H.; Singh, S. C.; Ghosal, D.


    Seismic full waveform inversion is an emerging technique to determine fine-scale subsurface velocity structure. However, it requires a good starting velocity model, which is generally obtained using travel time tomography, to converge to a global minimum. Furthermore, the computing cost of full waveform inversion could be very high. In order to converge to a global solution, we have developed a combined full wave equation tomography (WET) and full waveform inversion (FWI) where the large and medium scale velocity is determined using full wave equation tomography first and then the fine-scale elastic parameters are inverted using full waveform inversion. WET and FWI both utilize full wavefield modeling, but differ on the definition of objective functions: WET aims to minimize L2-norm of cross-correlation synthetic and observed data, which is mainly sensitive to travel times, while FWI aims to optimize the L2-norm full waveform misfit, which is sensitive to both amplitudes and travel times of arrivals. Adjoint method is used to calculate the gradient for both methods efficiently. To compensate the energy loss due to wave propagation in the adjoint calculation and geometric limitation of survey, we apply an approximate Hessian preconditioning to the gradient. Further more, to stabilize WET, we precondition the time delay measures observed from cross-relation with maximum cross-correlation coefficients and perform tomographic model regularization to avoid local minimum. By exploring the band-limited feature of seismic wavefield, WET can provide better resolution than ray-based travel time tomography, and hence better suited for the FWI to converge to the true model, which provides very fine detail P and S-wave velocity. Both WET and WFI are based on the solution of full elastic wave equation and hence can model all types of wave present data. In order to reduce the computation cost and to invert seismic refraction arrivals first, we downward continue the streamer data

  7. Graphene-coated rayleigh SAW resonators for NO2 detection

    Thomas, Stephen M.; Cole, Marina; De Luca, A; Torrisi, F.; Ferrari, A. C.; Udrea, Florin; Gardner, J. W.


    This paper describes the development of a novel low-cost Rayleigh Surface Acoustic Wave Resonator (SAWR) device coated with a graphene layer that is capable of detecting PPM levels of NO2 in air. The sensor comprises two 262 MHz ST-cut quartz based Rayleigh SAWRs arranged in a dual oscillator configuration; where one resonator is coated with gas-sensitive graphene, and the other left uncoated to act as a reference. An array of NMP-dispersed exfoliated reduced graphene oxide dots was deposited...

  8. An automatic differentiation-based gradient method for inversion of the shear wave equation in magnetic resonance elastography: specific application in fibrous soft tissues

    Chatelin, Simon; Charpentier, Isabelle; Corbin, Nadège; Meylheuc, Laurence; Vappou, Jonathan


    Quantitative and accurate measurement of in vivo mechanical properties using dynamic elastography has been the scope of many research efforts over the past two decades. Most of the shear-wave-based inverse approaches for magnetic resonance elastography (MRE) make the assumption of isotropic viscoelasticity. In this paper, we propose a quantitative gradient method for inversion of the shear wave equation in anisotropic media derived from a full waveform description using analytical viscoelastic Green formalism and automatic differentiation. The abilities and performances of the proposed identification method are first evaluated on numerical phantoms calculated in a transversely isotropic medium, and subsequently on experimental MRE data measured on an isotropic hydrogel phantom, on an anisotropic cryogel phantom and on an ex vivo fibrous muscle. The experiments are carried out by coupling circular shear wave profiles generated by acoustic radiation force and MRE acquisition of the wave front. Shear modulus values obtained by our MRE method are compared to those obtained by rheometry in the isotropic hydrogel phantom, and are found to be in good agreement despite non-overlapping frequency ranges. Both the cryogel and the ex vivo muscle are found to be anisotropic. Stiffness values in the longitudinal direction are found to be 1.8 times and 1.9 times higher than those in the transverse direction for the cryogel and the muscle, respectively. The proposed method shows great perspectives and substantial benefits for the in vivo quantitative investigation of complex mechanical properties in fibrous soft tissues.

  9. An automatic differentiation-based gradient method for inversion of the shear wave equation in magnetic resonance elastography: specific application in fibrous soft tissues.

    Chatelin, Simon; Charpentier, Isabelle; Corbin, Nadège; Meylheuc, Laurence; Vappou, Jonathan


    Quantitative and accurate measurement of in vivo mechanical properties using dynamic elastography has been the scope of many research efforts over the past two decades. Most of the shear-wave-based inverse approaches for magnetic resonance elastography (MRE) make the assumption of isotropic viscoelasticity. In this paper, we propose a quantitative gradient method for inversion of the shear wave equation in anisotropic media derived from a full waveform description using analytical viscoelastic Green formalism and automatic differentiation. The abilities and performances of the proposed identification method are first evaluated on numerical phantoms calculated in a transversely isotropic medium, and subsequently on experimental MRE data measured on an isotropic hydrogel phantom, on an anisotropic cryogel phantom and on an ex vivo fibrous muscle. The experiments are carried out by coupling circular shear wave profiles generated by acoustic radiation force and MRE acquisition of the wave front. Shear modulus values obtained by our MRE method are compared to those obtained by rheometry in the isotropic hydrogel phantom, and are found to be in good agreement despite non-overlapping frequency ranges. Both the cryogel and the ex vivo muscle are found to be anisotropic. Stiffness values in the longitudinal direction are found to be 1.8 times and 1.9 times higher than those in the transverse direction for the cryogel and the muscle, respectively. The proposed method shows great perspectives and substantial benefits for the in vivo quantitative investigation of complex mechanical properties in fibrous soft tissues.

  10. Joint body and surface wave tomography applied to the Toba caldera complex (Indonesia)

    Jaxybulatov, Kairly; Koulakov, Ivan; Shapiro, Nikolai


    We developed a new algorithm for a joint body and surface wave tomography. The algorithm is a modification of the existing LOTOS code (Koulakov, 2009) developed for local earthquake tomography. The input data for the new method are travel times of P and S waves and dispersion curves of Rayleigh and Love waves. The main idea is that the two data types have complementary sensitivities. The body-wave data have good resolution at depth, where we have enough crossing rays between sources and receivers, whereas the surface waves have very good near-surface resolution. The surface wave dispersion curves can be retrieved from the correlations of the ambient seismic noise and in this case the sampled path distribution does not depend on the earthquake sources. The contributions of the two data types to the inversion are controlled by the weighting of the respective equations. One of the clearest cases where such approach may be useful are volcanic systems in subduction zones with their complex magmatic feeding systems that have deep roots in the mantle and intermediate magma chambers in the crust. In these areas, the joint inversion of different types of data helps us to build a comprehensive understanding of the entire system. We apply our algorithm to data collected in the region surrounding the Toba caldera complex (north Sumatra, Indonesia) during two temporary seismic experiments (IRIS, PASSCAL, 1995, GFZ, LAKE TOBA, 2008). We invert 6644 P and 5240 S wave arrivals and ~500 group velocity dispersion curves of Rayleigh and Love waves. We present a series of synthetic tests and real data inversions which show that joint inversion approach gives more reliable results than the separate inversion of two data types. Koulakov, I., LOTOS code for local earthquake tomographic inversion. Benchmarks for testing tomographic algorithms, Bull. seism. Soc. Am., 99(1), 194-214, 2009, doi:10.1785/0120080013

  11. Information content in frequency-dependent, multi-offset GPR data for layered media reconstruction using full-wave inversion

    De Coster, Albéric; Phuong Tran, Anh; Lambot, Sébastien


    Water lost through leaks can represent high percentages of the total production in water supply systems and constitutes an important issue. Leak detection can be tackled with various techniques such as the ground-penetrating radar (GPR). Based on this technology, various procedures have been elaborated to characterize a leak and its evolution. In this study, we focus on a new full-wave radar modelling approach for near-field conditions, which takes into account the antenna effects as well as the interactions between the antenna(s) and the medium through frequency-dependent global transmission and reflection coefficients. This approach is applied to layered media for which 3-D Green's functions can be calculated. The model allows for a quantitative estimation of the properties of multilayered media by using full-wave inversion. This method, however, proves to be limited to provide users with an on-demand assessment as it is generally computationally demanding and time consuming, depending on the medium configuration as well as the number of unknown parameters to retrieve. In that respect, we propose two leads in order to enhance the parameter retrieval step. The first one consists in analyzing the impact of the reduction of the number of frequencies on the information content. For both numerical and laboratory experiments, this operation has been achieved by investigating the response surface topography of objective functions arising from the comparison between measured and modelled data. The second one involves the numerical implementation of multistatic antenna configurations with constant and variable offsets in the model. These two kinds of analyses are then combined in numerical experiments to observe the conjugated effect of the number of frequencies and the offset configuration. To perform the numerical analyses, synthetic Green's functions were simulated for different multilayered medium configurations. The results show that an antenna offset increase leads

  12. Inverse problems in cancellous bone: estimation of the ultrasonic properties of fast and slow waves using Bayesian probability theory.

    Anderson, Christian C; Bauer, Adam Q; Holland, Mark R; Pakula, Michal; Laugier, Pascal; Bretthorst, G Larry; Miller, James G


    Quantitative ultrasonic characterization of cancellous bone can be complicated by artifacts introduced by analyzing acquired data consisting of two propagating waves (a fast wave and a slow wave) as if only one wave were present. Recovering the ultrasonic properties of overlapping fast and slow waves could therefore lead to enhancement of bone quality assessment. The current study uses Bayesian probability theory to estimate phase velocity and normalized broadband ultrasonic attenuation (nBUA) parameters in a model of fast and slow wave propagation. Calculations are carried out using Markov chain Monte Carlo with simulated annealing to approximate the marginal posterior probability densities for parameters in the model. The technique is applied to simulated data, to data acquired on two phantoms capable of generating two waves in acquired signals, and to data acquired on a human femur condyle specimen. The models are in good agreement with both the simulated and experimental data, and the values of the estimated ultrasonic parameters fall within expected ranges.

  13. Analysis shear wave velocity structure obtained from surface wave methods in Bornova, Izmir

    Pamuk, Eren, E-mail:; Akgün, Mustafa, E-mail: [Department of Geophysical Engineering, Dokuz Eylul University, Izmir (Turkey); Özdağ, Özkan Cevdet, E-mail: [Dokuz Eylul University Rectorate, Izmir (Turkey)


    Properties of the soil from the bedrock is necessary to describe accurately and reliably for the reduction of earthquake damage. Because seismic waves change their amplitude and frequency content owing to acoustic impedance difference between soil and bedrock. Firstly, shear wave velocity and depth information of layers on bedrock is needed to detect this changing. Shear wave velocity can be obtained using inversion of Rayleigh wave dispersion curves obtained from surface wave methods (MASW- the Multichannel Analysis of Surface Waves, ReMi-Refraction Microtremor, SPAC-Spatial Autocorrelation). While research depth is limeted in active source study, a passive source methods are utilized for deep depth which is not reached using active source methods. ReMi method is used to determine layer thickness and velocity up to 100 m using seismic refraction measurement systems.The research carried out up to desired depth depending on radius using SPAC which is utilized easily in conditions that district using of seismic studies in the city. Vs profiles which are required to calculate deformations in under static and dynamic loads can be obtained with high resolution using combining rayleigh wave dispersion curve obtained from active and passive source methods. In the this study, Surface waves data were collected using the measurements of MASW, ReMi and SPAC at the İzmir Bornova region. Dispersion curves obtained from surface wave methods were combined in wide frequency band and Vs-depth profiles were obtained using inversion. Reliability of the resulting soil profiles were provided by comparison with theoretical transfer function obtained from soil paremeters and observed soil transfer function from Nakamura technique and by examination of fitting between these functions. Vs values are changed between 200-830 m/s and engineering bedrock (Vs>760 m/s) depth is approximately 150 m.

  14. Estimation of Q and inverse Q filtering for prestack reflected PP-and converted PS-waves%叠前纵波和转换波地震资料Q值提取及反Q滤波

    严红勇; 刘洋


    Multi-component seismic exploration technology, combining reflected PP- and converted PS-waves, is an effective tool for solving complicated oil and gas' exploration problems. The improvement of converted wave resolution is one of the key problems.The main factor affecting converted wave resolution is the absorption of seismic waves in overlying strata. In order to remove the effect of absorption on converted waves, inverse Q filtering is used to improve the resolution. In this paper, we present a method to estimate the S-wave Q values from prestack converted wave gathers. Furthermore, we extend a stable and effective poststack inverse Q filtering method to prestack data which uses wave field continuation along the ray path to compensate for attenuation in prestack common shot PP-and PS-waves. The results of theoretical modeling prove that the method of estimating the S-wave Q values has high precision. The results from synthetic and real data prove that the stable inverse Q filtering method can effectively improve the resolution of prestack PP- and PS-waves.


    袁伟; 周洪生; 刘成东; 李江鹏; 张薇


    Rayleigh wave exploration as a non-destructive in situ detection method has been increasingly used in geotechnical engineering testing and environmental engineering. Extraction of dispersion curves is an important step in the surface wave velocity. This will be short-time Fourier transform and the generalized S transform two linear time - frequency analysis method for Rayleigh wave dispersion curve extraction. According to the analysis of the theoretical model and real seismic data, it is concluded that; ①Short-time Fourier transform only for shallow high-frequency part of the energy of strong Rayleigh wave dispersion curve extraction is better, while the low-frequency energy extraction is the weaker part of the poor.②Generalized S transform X and p by the introduction of two parameters to the signal frequency according to the level of automatic mediation shape and size of the window function, with multi-resolution features, so while the high and low frequency of the Rayleigh wave signal better treatment effect, and thus help to improve the exploration depth of the Rayleigh wave.%瑞雷面波勘探作为一种无损原位检测方法,已越来越多的应用于岩土工程测试与环境工程中,其中频散曲线的提取则是得到面波速度的重要一步.这里将短时傅里叶变换与广义S变换两种线性时~频分析方法用于瑞雷面波的频散曲线提取,并加以对比分析它们的应用效果.通过理论模型与实际地震记录分析得出:①短时傅里叶变换只能对浅部能量较强的高频部份的瑞雷面波的频散曲线提取效果较好,而对低频能量较弱的部份提取效果则不佳;②广义S变换通过λ和ρ两个参数的引入,使其能根据信号频率的高低自动调解窗函数的形态与大小,具有多分辨的特性,使其同时对高频、低频的瑞雷面波信号有更好的处理效果,从而有利于提高瑞雷波的勘探深度.

  16. Statistical distribution of nonlinear random wave height

    HOU; Yijun; GUO; Peifang; SONG; Guiting; SONG; Jinbao; YIN; Baoshu; ZHAO; Xixi


    A statistical model of random wave is developed using Stokes wave theory of water wave dynamics. A new nonlinear probability distribution function of wave height is presented. The results indicate that wave steepness not only could be a parameter of the distribution function of wave height but also could reflect the degree of wave height distribution deviation from the Rayleigh distribution. The new wave height distribution overcomes the problem of Rayleigh distribution that the prediction of big wave is overestimated and the general wave is underestimated. The prediction of small probability wave height value of new distribution is also smaller than that of Rayleigh distribution. Wave height data taken from East China Normal University are used to verify the new distribution. The results indicate that the new distribution fits the measurements much better than the Rayleigh distribution.

  17. Short Rayleigh length free electron lasers

    W. B. Colson


    Full Text Available Conventional free electron laser (FEL oscillators minimize the optical mode volume around the electron beam in the undulator by making the resonator Rayleigh length about one third to one half of the undulator length. This maximizes gain and beam-mode coupling. In compact configurations of high-power infrared FELs or moderate power UV FELs, the resulting optical intensity can damage the resonator mirrors. To increase the spot size and thereby reduce the optical intensity at the mirrors below the damage threshold, a shorter Rayleigh length can be used, but the FEL interaction is significantly altered. We model this interaction using a coordinate system that expands with the rapidly diffracting optical mode from the ends of the undulator to the mirrors. Simulations show that the interaction of the strongly focused optical mode with a narrow electron beam inside the undulator distorts the optical wave front so it is no longer in the fundamental Gaussian mode. The simulations are used to study how mode distortion affects the single-pass gain in weak fields, and the steady-state extraction in strong fields.

  18. A McMC Method for the Inference of Radial and Azimuthal Anisotropy of the Crust and Upper Mantle from Surface-Wave Dispersion Curves

    Ravenna, Matteo; Lebedev, Sergei


    We develop a Markov Chain Monte Carlo method for joint inversion of Rayleigh- and Love-wave dispersion curves that is able to yield robust radially and azimuthally anisotropic shear velocity profiles, with resolution to depths down to the transition zone. The probabilistic feature of the algorithm is a powerful tool that is able to provide error assessment of the shear velocity models, quantify non-uniqueness and address the issue of data noise estimation by treating it as an unknown parameter in the inversion. In a fixed dimensional Bayesian formulation, we choose to set the number of parameters relatively high, with a more dense parametrization in the uppermost mantle in order to have a good resolution of the Litosphere-Astenosphere Boundary region. We apply the MCMC algorithm to the inversion of surface-wave phase velocities accurately determined in broad period ranges in a few test regions. In the Baikal-Mongolia region we invert Rayleigh- and Love- wave dispersion curves for radially anisotropic structure (Vsv,Vsh) of the crust and upper mantle. In the Tuscany region, where we have phase velocity data with good azimuthal coverage, a different implementation of the algorithm is applied that is able to resolve azimuthal anisotropy; the Rayleigh wave dispersion curves measured at different azimuths have been inverted for the Vsv structure and the depth distribution of the 2-psi azimuthal anisotropy of the region, with good resolution down to asthenospheric depths.

  19. Coordinated investigation of midlatitude upper mesospheric temperature inversion layers and the associated gravity wave forcing by Na lidar and Advanced Mesospheric Temperature Mapper in Logan, Utah

    Yuan, Tao; Pautet, P.-D.; Zhao, Y.; Cai, X.; Criddle, N. R.; Taylor, M. J.; Pendleton, W. R.


    Mesospheric inversion layers (MIL) are well studied in the literature but their relationship to the dynamic feature associated with the breaking of atmospheric waves in the mesosphere/lower thermosphere (MLT) region are not well understood. Two strong MIL events (ΔT ~30 K) were observed above 90 km during a 6 day full diurnal cycle Na lidar campaign conducted from 6 August to 13 August Logan, Utah (42°N, 112°W). Colocated Advanced Mesospheric Temperature Mapper observations provided key information on concurrent gravity wave (GW) events and their characteristics during the nighttime observations. The study found both MILs were well correlated with the development and presence of an unstable region ~2 km above the MIL peak altitudes and a highly stable region below, implicating the strengthening of MIL is likely due to the increase of downward heat flux by the enhanced saturation of gravity wave, when it propagates through a highly stable layer. Each MIL event also exhibited distinct features: one showed a downward progression most likely due to tidal-GW interaction, while the peak height of the other event remained constant. During further investigation of atmospheric stability surrounding the MIL structure, lidar measurements indicate a sharp enhancement of the convective stability below the peak altitude of each MIL. We postulate that the sources of these stable layers were different; one was potentially triggered by concurrent large tidal wave activity and the other during the passage of a strong mesospheric bore.

  20. Bi-directional four wave mixing in semiconductor amplifiers for mid-span spectral inversion: theory and experiment

    Bischoff, Svend; Buxens, Alvaro A.; Poulsen, Henrik Nørskov


    Summary form only given. We have developed a large signal model to theoretically assess the performance of a mid span spectral inversion (MSSI) transmission system. The large signal model has previously been used to successfully model the fast gain dynamics of semiconductor optical amplifiers....

  1. Remarks on the Rayleigh-Benard Convection on Spherical Shells

    Wang, Shouhong


    The main objective of this article is to study the effect of spherical geometry on dynamic transitions and pattern formation for the Rayleigh-Benard convection. The study is mainly motivated by the importance of spherical geometry and convection in geophysical flows. It is shown in particular that the system always undergoes a continuous (Type-I) transition to a $2l_c$-dimensional sphere $S^{2lc}$, where lc is the critical wave length corresponding to the critical Rayleigh number. Furthermore, it has shown in [12] that it is critical to add nonisotropic turbulent friction terms in the momentum equation to capture the large-scale atmospheric and oceanic circulation patterns. We show in particular that the system with turbulent friction terms added undergoes the same type of dynamic transition, and obtain an explicit formula linking the critical wave number (pattern selection), the aspect ratio, and the ratio between the horizontal and vertical turbulent friction coefficients.

  2. Intensity-only imaging with waves, restarted inverse Born series, and analysis of coarsening in polycrystalline materials

    Bardsley, Patrick

    We first study the inverse problem of recovering a complex Schrodinger potential from a discrete set of measurements of the solution to the Schrodinger equation using different source terms. We solve this problem by generalizing the inverse Born series method to nonlinear mappings between Banach spaces. In this general setting, we show convergence and stability of inverse Born series follow from a single problem-specific bound. We show this bound for the inverse Schrodinger problem, and study numerically an application of this inverse problem to transient hydraulic tomography. Additionally, we develop a family of iterative methods based on truncated inverse Born series that are akin to iterative methods based on truncated Taylor series. Next, we study the inverse problem of imaging scatterers in a homogeneous medium when only intensities of wavefields can be measured. Classic imaging methods, such as Kirchhoff migration, rely on phase information contained in full waveform data and thus cannot be used directly with intensity-only data. In situations where scattered wavefields are small compared to the incident wavefields, we can form and solve a linear least squares problem to recover a projection (on a known subspace) of full waveform data from intensity data. We show that for sufficiently high frequencies, this projection gives a Kirchhoff image asymptotically equivalent to the Kirchhoff image obtained from full waveform data. We also generalize this imaging method to using stochastic incident fields with autocorrelation measurements. Finally, we study a mathematical model of grain growth in polycrystalline materials. We review a simplified 1D grain growth model and an entropy-based theory for the evolution of an important statistic harvested from this model, the GBCD. The theory suggests the GBCD evolves according to a Fokker-Planck equation, which we validate numerically. We derive methods to estimate times from the GBCD, thus fitting it to Fokker-Planck time

  3. Dynamical inverse problems

    Gladwell, Graham ML


    The papers in this volume present an overview of the general aspects and practical applications of dynamic inverse methods, through the interaction of several topics, ranging from classical and advanced inverse problems in vibration, isospectral systems, dynamic methods for structural identification, active vibration control and damage detection, imaging shear stiffness in biological tissues, wave propagation, to computational and experimental aspects relevant for engineering problems.

  4. Blue Skies, Coffee Creamer, and Rayleigh Scattering

    Liebl, Michael


    The first physical explanation of Earths blue sky was fashioned in 1871 by Lord Rayleigh. Many discussions of Rayleigh scattering and approaches to studying it both in and out of the classroom are available. Rayleigh scattering accounts for the blue color of the sky and the orange/red color of the Sun near sunset and sunrise, and a number of…

  5. Blue Skies, Coffee Creamer, and Rayleigh Scattering

    Liebl, Michael


    The first physical explanation of Earths blue sky was fashioned in 1871 by Lord Rayleigh. Many discussions of Rayleigh scattering and approaches to studying it both in and out of the classroom are available. Rayleigh scattering accounts for the blue color of the sky and the orange/red color of the Sun near sunset and sunrise, and a number of…

  6. Beating Rayleigh's Curse by Imaging Using Phase Information

    Tham, Weng Kian; Steinberg, Aephraim M


    Any imaging device such as a microscope or telescope has a resolution limit, a minimum separation it can resolve between two objects or sources; this limit is typically defined by "Rayleigh's criterion", although in recent years there have been a number of high-profile techniques demonstrating that Rayleigh's limit can be surpassed under particular sets of conditions. Quantum information and quantum metrology have given us new ways to approach measurement ; a new proposal inspired by these ideas has now re-examined the problem of trying to estimate the separation between two poorly resolved point sources. The "Fisher information" provides the inverse of the Cramer-Rao bound, the lowest variance achievable for an unbiased estimator. For a given imaging system and a fixed number of collected photons, Nair and Tsang observed that the Fisher information carried by the intensity of the light in the image-plane (the only information available to traditional techniques, including previous super-resolution approaches...

  7. The effect of small-scale heterogeneity on the propagation of waves : with applications to forward modeling and inversion in global surface wave tomography

    Spetzler, J.


    Small-scale heterogeneity alters the arrival time of waves in a way that cannot be explained by ray theory. It is because ray theory is a high-frequency approximation that does not take the finite-frequency of wavefields into account. A theory based on the first Rytov approximation is develope

  8. Rayleigh-type Surface Quasimodes in General Linear Elasticity

    Hansen, Sönke


    Rayleigh-type surface waves correspond to the characteristic variety, in the elliptic boundary region, of the displacement-to-traction map. In this paper, surface quasimodes are constructed for the reduced elastic wave equation, anisotropic in general, with traction-free boundary. Assuming a global variant of a condition of Barnett and Lothe, the construction is reduced to an eigenvalue problem for a selfadjoint scalar first order pseudo-differential operator on the boundary. The principal and the subprincipal symbol of this operator are computed. The formula for the subprincipal symbol seems to be new even in the isotropic case.

  9. Rotating Rayleigh-Taylor turbulence

    Boffetta, G.; Mazzino, A.; Musacchio, S.


    The turbulent Rayleigh-Taylor system in a rotating reference frame is investigated by direct numerical simulations within the Oberbeck-Boussinesq approximation. On the basis of theoretical arguments, supported by our simulations, we show that the Rossby number decreases in time, and therefore the Coriolis force becomes more important as the system evolves and produces many effects on Rayleigh-Taylor turbulence. We find that rotation reduces the intensity of turbulent velocity fluctuations and therefore the growth rate of the temperature mixing layer. Moreover, in the presence of rotation the conversion of potential energy into turbulent kinetic energy is found to be less effective, and the efficiency of the heat transfer is reduced. Finally, during the evolution of the mixing layer we observe the development of a cyclone-anticyclone asymmetry.

  10. Modeling and inversion of PS-wave moveout asymmetry for tilted TI media: Part 1 - Horizontal TTI layer

    Dewangan, P.; Tsvankin, I.

    rays H20849re- corded at points xH208493H20850 and xH208494H20850H20850 with the same reflection point as the PP reflection xH208491H20850RxH208492H20850.Then the traveltime of the SS-wave is determined from H9270SSH20849xH208493H20850,xH208494H20850H..., the slownesses are computed under the convention that the x3-axis points up and both legs of the PS ray represent upgoing waves H20849i.e., the corresponding group-velocity vectors point toward the earth?s surfaceH20850. Here, we study a horizontal layer in which...

  11. Causative Mechanisms of Tropical (10°N-15°N) Mesospheric Inversion Layers

    Ramesh, Karanam; Sundararajan, Sridharan; Vijaya Bhaskara Rao, S.


    The inversion of temperature gradient from negative to positive superimposed upon the characteristically decreasing mesospheric thermal structure is known as Mesospheric Inversion Layer (MIL). Gravity wave breaking, planetary wave critical level interaction and the chemical heating have been suggested as potential causative mechanisms for the occurrence of the MILs. Although the morphological characteristics of MIL have been studied in detail at different sites using various instrumental techniques, their causative mechanisms are still unknown. In the present study, nearly all these major causative mechanisms have been addressed through a few case studies observed from Rayleigh lidar and TIMED-SABER (Thermosphere Ionosphere Mesosphere Energetics and Dynamics - Sounding of Atmosphere by Broadband Emission Radiometry) nightly temperatures over a tropical site, Gadanki (13.5°N,79.2°E). A few large MILs are observed above ˜80 km with amplitude and thickness of ˜50 K and ˜5 km respectively in 2007 and 2011 which are found to be predominantly due to gravity wave breaking and large chemical heating rate (˜15 K/day) by the exothermic reaction, H+O _{3}->OH+O _{2} respectively. It is also found that the SABER shows larger ozone (O _{3}) mixing ratios at the inversion heights (˜80-85 km) during the MIL events in 2011. In another special case study, a triple layered MIL event with three inversion layers at ˜70 km (˜11 K), 80 km (˜44 K), 90 km (˜109 K) has been observed in September 2011 over Gadanki region. It is found that these three inversion layers are respectively due to planetary wave breaking, gravity wave tidal interaction and chemical heating by the reaction, O+O+M->O _{2}+M.

  12. Joint inversion of teleseismic body-waves and geodetic data for the Mw6.8 aftershock of the Balochistan earthquake with refined epicenter location

    Wei, S.; Wang, T.; Jonsson, S.; Avouac, J. P.; Helmberger, D. V.


    Aftershocks of the 2013 Balochistan earthquake are mainly concentrated along the northeastern end of the mainshock rupture despite of much larger coseismic slip to the southwest. The largest event among them is an Mw6.8 earthquake which occurred three days after the mainshock. A kinematic slip model of the mainshock was obtained by joint inversion of the teleseismic body-waves and horizontal static deformation field derived from remote sensing optical and SAR data, which is composed of seven fault segments with gradually changing strikes and dips [Avouac et al., 2014]. The remote sensing data provide well constraints on the fault geometry and spatial distribution of slip but no timing information. Meanwhile, the initiation of the teleseismic waveform is very sensitive to fault geometry of the epicenter segment (strike and dip) and spatial slip distribution but much less sensitive to the absolute location of the epicenter. The combination of the two data sets allows a much better determination of the absolute epicenter location, which is about 25km to the southwest of the NEIC epicenter location. The well located mainshock epicenter is used to establish path calibrations for teleseismic P-waves, which are essential for relocating the Mw6.8 aftershock. Our grid search shows that the refined epicenter is located right at the northeastern end of the mainshock rupture. This is confirmed by the SAR offsets calculated from images acquired after the mainshock. The azimuth and range offsets display a discontinuity across the rupture trace of the mainshock. Teleseismic only and static only, as well as joint inversions all indicate that the aftershock ruptured an asperity with 25km along strike and range from 8km to 20km in depth. The earthquake was originated in a positive Coulomb stress change regime due to the mainshock and has complementary slip distribution to the mainshock rupture at the northeastern end, suggesting that the entire seismic generic zone in the crust was

  13. High-resolution monitoring of root water uptake dynamics in laboratory conditions using full-wave inversion of near-field radar

    Mourmeaux, Nicolas; Meunier, Félicien; Tran, Phuong Anh; Draye, Xavier; Lambot, Sébastien


    Root water uptake dynamics at local scale can be studied in laboratory conditions by growing plants in rhizotron containing sand and by imaging the water content evolution of the medium using light transmission. This technique allows to retrieve the water content with high resolution but cannot be applied in opaque media such as leaf-mold or clay, which is a major limitation for more realistic applications. Recently, ground-penetrating radar (GPR) has proven to be one of the most promising techniques for high-resolution digital soil mapping at the field scale. Particularly, by using full-wave inverse modeling of near-field GPR data with a high frequency antenna, the electrical properties of soil and their correlated water content can be reconstructed with a high spatiotemporal resolution. In this study, we applied the approach by using an ultra-wideband frequency-domain radar with a transmitting and receiving horn antenna operating in the frequency range 3-6 GHz for imaging, in near-field conditions, a rhizotron containing sand subject to different water content conditions. Synthetic radar data were also generated to examine the well-posedness of the full-waveform inverse problem at high frequencies. Finally, we compared the water content obtained by GPR and light transmission measurements. The results have shown that the near-field modeled and measured GPR data match very well in the frequency and time domains for both dry and wet sands. In the case of the dry sand, the estimated water content based on GPR and light transmission data was retrieved with small differences. This research shows the potential of the GPR system and near-field full-wave antenna-medium model to accurately estimate the water content of soils with a high spatial resolution. Future studies will focus on the use of GPR to monitor root water uptake dynamics of plants in field conditions. This abstract is of interest for COST Action TU1208.

  14. A one-dimensional seismic model for Uturuncu volcano, Bolivia, and its impact on full moment tensor inversions

    Shen, Weisen


    Using receiver functions, Rayleigh wave phase velocity dispersion determined from ambient noise and teleseismic earthquakes, and Rayleigh wave horizontal to vertical ground motion amplitude ratios from earthquakes observed across the PLUTONS seismic array, we construct a one-dimensional (1-D) S-wave velocity (Vs) seismic model with uncertainties for Uturuncu volcano, Bolivia, located in the central Andes and overlying the eastward-subducting Nazca plate. We find a fast upper crustal lid placed upon a low-velocity zone (LVZ) in the mid-crust. By incorporating all three types of measurements with complimentary sensitivity, we also explore the average density and Vp/Vs (ratio of P-wave to S-wave velocity) structures beneath the young silicic volcanic field. We observe slightly higher Vp/Vs and a decrease in density near the LVZ, which implies a dacitic source of the partially molten magma body. We exploit the impact of the 1-D model on full moment tensor inversion for the two largest local earthquakes recorded (both magnitude ∼3), demonstrating that the 1-D model influences the waveform fits and the estimated source type for the full moment tensor. Our 1-D model can serve as a robust starting point for future efforts to determine a three-dimensional velocity model for Uturuncu volcano.

  15. Kinetic Simulations of Rayleigh-Taylor Instabilities

    Sagert, Irina; Colbry, Dirk; Howell, Jim; Staber, Alec; Strother, Terrance


    We report on an ongoing project to develop a large scale Direct Simulation Monte Carlo code. The code is primarily aimed towards applications in astrophysics such as simulations of core-collapse supernovae. It has been tested on shock wave phenomena in the continuum limit and for matter out of equilibrium. In the current work we focus on the study of fluid instabilities. Like shock waves these are routinely used as test-cases for hydrodynamic codes and are discussed to play an important role in the explosion mechanism of core-collapse supernovae. As a first test we study the evolution of a single-mode Rayleigh-Taylor instability at the interface of a light and a heavy fluid in the presence of a gravitational acceleration. To suppress small-wavelength instabilities caused by the irregularity in the separation layer we use a large particle mean free path. The latter leads to the development of a diffusion layer as particles propagate from one fluid into the other. For small amplitudes, when the instability is i...

  16. Instantaneous Rayleigh scattering from excitons localized in monolayer islands

    Langbein, Wolfgang; Leosson, Kristjan; Jensen, Jacob Riis;


    We show that the initial dynamics of Rayleigh scattering from excitons in quantum wells can be either instantaneous or delayed, depending on the exciton ensemble studied. For excitation of the entire exciton resonance, a finite rise time given by the inverse inhomogeneous broadening: of the exciton...... resonance is observed. Instead, when exciting only a subsystem of the exciton resonance, in our case excitons localized in quantum well regions of a specific monolayer thickness, the rise has an instantaneous component. This is due to the spatial nonuniformity of the initially excited exciton polarization...

  17. Direct Numerical Simulation of the Rayleigh-Taylor Instability with the Spectral Element Method

    ZHANG Xu; TAN Duo-Wang


    A novel method is proposed to simulate Rayleigh-Taylor instabilities using a specially-developed unsteady threedimensional high-order spectral element method code.The numerical model used consists of Navier-Stokes equations and a transport-diffusive equation.The code is first validated with the results of linear stability perturbation theory.Then several characteristics of the Rayleigh-Taylor instabjJjties are studied using this three-dimensional unsteady code,inducling instantaneous turbulent structures and statistical turbulent mixing heights under different initial wave numbers.These results indicate that turbulent structures ofRayleigh-Taylor instabilities are strongly dependent on the initial conditions.The results also suggest that a high-order numerical method should provide the capability of sir.ulating small scale fluctuations of Rayleigh-Taylor instabilities of turbulent flows.

  18. Toward analytic theory of the Rayleigh-Taylor instability: lessons from a toy model

    Mailybaev, Alexei A


    In this work we suggest that a turbulent phase of the Rayleigh-Taylor instability can be explained as a universal stochastic wave traveling with constant speed in a properly renormalized system. This wave, originating from ordinary deterministic chaos in a renormalized time, has two constant limiting states at both sides. These states are related to the initial discontinuity at large scales and to stationary turbulence at small scales. The theoretical analysis is confirmed with extensive numerical simulations made for a new shell model, which features all basic properties of the phenomenological theory for the Rayleigh-Taylor instability.

  19. Precursor arrivals in the Yellow Sea, their distinction from first-order head waves, and their geoacoustic inversion.

    Dahl, Peter H; Choi, Jee Woong


    Measurements made as part of the 1996 Yellow Sea experiment at location 37 degrees N, 124 degrees E, undertaken by China and the U.S. are analyzed. Signals generated by explosive sources were received by a 60-m-length vertical line array deployed in waters 75 m deep. Evidence is presented that precursor arrivals measured at ranges less than 1 km are refracted waves that are zeroth order in their ray series classification, and this directly points to the existence of a gradient in sediment sound speed. In contrast, first-order head waves, which are much weaker in amplitude, would exist only if this gradient were absent. It is found that the energy spectrum of precursor arrivals agrees well with a zeroth-order model, i.e., it is proportional to the source amplitude spectrum, S(f), where f is frequency, rather than a first-order model, which would have it proportional to S(f)/f. From travel time analysis the sediment sound speed just below the water-sediment interface is estimated to be 1573 m/s with a gradient of 1.1 s(-1), and from analysis of the energy spectrum of the precursor arrivals the sediment attenuation is estimated to be 0.08 dB/m/kHz over the frequency range 150-420 Hz. The results apply to a nominal sediment depth of 100 m.

  20. Observations of the UTLS: An analysis of the double tropopause and its relationship to Rossby waves and the tropopause inversion layer

    Peevey, Tanya

    The upper troposphere lower stratosphere (UTLS) is a region of minimum temperatures that contains the tropopause. As a transition region between the troposphere and the stratosphere, the UTLS contains various processes that facilitate stratosphere-troposphere exchange (STE) which can redistribute radiatively important species such as water vapor or ozone. One potential marker for STE is the double tropopause (DT). Therefore this study seeks to further understand how DTs form and how they could enhance the current understanding of some STE processes in the UTLS. Using data from the High Resolution Dynamic Limb Sounder (HIRDLS), a data set with high vertical and horizontal resolution, newly discovered DT structures are found over the Pacific and Atlantic oceans that suggest a relationship between the DT and both storm tracks and Rossby waves. The association between DTs and storm tracks is examined by further analyzing the recently discovered and unexpected relationship between the DT and the tropopause inversion layer (TIL) in a developing baroclinic disturbance. Results show an increase in the number of DTs when the lapse rate of the extratropical TIL is less than -2°C/km, i.e. when the TIL is stronger and the local stability is higher. Composites of ERA-Interim DT profiles for three different TIL strengths shows that the vertical motion and relative vorticity both decrease as the TIL increases, which suggests the warm conveyor belt as a mechanism. This is investigated further with a case study analysis of a developing extratropical cyclone in the Pacific Ocean. Additionally, an analysis of DTs in relation to the large scale flow responsible for storm development shows a strong correlation between monthly Rossby wave activity, ozone laminae and DT variability. Further examination shows that if these waves break a DT will be found with a wave breaking event about 30% of the time in the eastern Pacific and eastern Atlantic oceans, both regions of poleward wave

  1. Inverse approach to estimating larval dispersal reveals limited population connectivity along 700 km of wave-swept open coast.

    Hameed, Sarah O; White, J Wilson; Miller, Seth H; Nickols, Kerry J; Morgan, Steven G


    Demographic connectivity is fundamental to the persistence and resilience of metapopulations, but our understanding of the link between reproduction and recruitment is notoriously poor in open-coast marine populations. We provide the first evidence of high local retention and limited connectivity among populations spanning 700 km along an open coast in an upwelling system. Using extensive field measurements of fecundity, population size and settlement in concert with a Bayesian inverse modelling approach, we estimated that, on average, Petrolisthes cinctipes larvae disperse only 6.9 km (±25.0 km s.d.) from natal populations, despite spending approximately six weeks in an open-coast system that was once assumed to be broadly dispersive. This estimate differed substantially from our prior dispersal estimate (153.9 km) based on currents and larval duration and behaviour, revealing the importance of employing demographic data in larval dispersal estimates. Based on this estimate, we predict that demographic connectivity occurs predominantly among neighbouring populations less than 30 km apart. Comprehensive studies of larval production, settlement and connectivity are needed to advance an understanding of the ecology and evolution of life in the sea as well as to conserve ecosystems. Our novel approach provides a tractable framework for addressing these questions for species occurring in discrete coastal populations.

  2. Measured comparison of the inversion periods for polarimetric and conventional thermal long-wave IR (LWIR) imagery

    Felton, M.; Gurton, K. P.; Roth, L. E.; Pezzaniti, J. L.; Chenault, D. B.


    We report the results of a multi-day diurnal study in which radiometrically calibrated polarimetric and conventional thermal imagery is recorded in the LWIR to identify/compare the respective time periods in which minimum target contrast is achieved, e.g., thermal inversion periods are typically experienced during dusk and dawn. Imagery is recorded with a polarimetric IR sensor employing a 324x256 microbolometer array using a spinning achromatic retarder to perform the polarimetric filtering. The images used in this study include the S0, normalized S1, and normalized S2 Stokes images and the degree of linear polarization (DOLP) images of a scene containing military vehicles and the natural background. In addition, relevant meteorological parameters measured during the test period include air temperature, ambient loading in the LWIR, relative humidity, and cloud cover, height and density. The data shows that the chief factors affecting polarimetric contrast are the amount of thermal emission from the objects in the scene and the abundance of LWIR sources in the optical background. In addition, we found that contrast between targets and background within polarimetric images often remains relatively high during periods of low thermal contrast.

  3. Lithosphere-asthenosphere interaction beneath the western United States from the joint inversion of body-wave traveltimes and surface-wave phase velocities

    Obrebski, M.; Allen, R.M.; Pollitz, F.; Hung, S.-H.


    The relation between the complex geological history of the western margin of the North American plate and the processes in the mantle is still not fully documented and understood. Several pre-USArray local seismic studies showed how the characteristics of key geological features such as the Colorado Plateau and the Yellowstone Snake River Plains are linked to their deep mantle structure. Recent body-wave models based on the deployment of the high density, large aperture USArray have provided far more details on the mantle structure while surface-wave tomography (ballistic waves and noise correlations) informs us on the shallow structure. Here we combine constraints from these two data sets to image and study the link between the geology of the western United States, the shallow structure of the Earth and the convective processes in mantle. Our multiphase DNA10-S model provides new constraints on the extent of the Archean lithosphere imaged as a large, deeply rooted fast body that encompasses the stable Great Plains and a large portion of the Northern and Central Rocky Mountains. Widespread slow anomalies are found in the lower crust and upper mantle, suggesting that low-density rocks isostatically sustain part of the high topography of the western United States. The Yellowstone anomaly is imaged as a large slow body rising from the lower mantle, intruding the overlying lithosphere and controlling locally the seismicity and the topography. The large E-W extent of the USArray used in this study allows imaging the 'slab graveyard', a sequence of Farallon fragments aligned with the currently subducting Juan de Fuca Slab, north of the Mendocino Triple Junction. The lithospheric root of the Colorado Plateau has apparently been weakened and partly removed through dripping. The distribution of the slower regions around the Colorado Plateau and other rigid blocks follows closely the trend of Cenozoic volcanic fields and ancient lithospheric sutures, suggesting that the

  4. Inversion of H/V ratio in layered systems

    Pina Flores, J.; García-Jerez, A.; Luzon, F.; Perton, M.; Sanchez-Sesma, F. J.


    Both coda of earthquakes and microtremors are assumed to be diffuse fields resulting from multiple scattering. From the diffuse field theory, the average of the autocorrelation of displacement components at a given receiver measures the directional energy densities that are proportional to the imaginary parts of the Green's function for source and receiver at the same point. The directional energies have been recently related to the calculation of microtremor H/V spectral ratio (MHVSR). These ratios are widely used in the assessment of the dominant frequency of soil sites and their measurements are relatively simple as only one station is required. The H/V spectral ratios have also been interpreted as representing either directly the S wave amplification or the Rayleigh wave ellipticity. Moreover, the H/V ratios can be also used for a finer characterization of the site assuming horizontally layered media without lateral heterogeneities. In that case and for an appropriate noise normalization the experimental spectral ratios H2/V2 should correspond to their theoretical counterpart: the ratio 2 ImG11 / ImG33, where ImG11 and ImG33 are the imaginary parts of Green functions at the load point for horizontal and vertical components, respectively and for horizontally layered media. In order to guarantee a viable inversion, the imaginary part of the theoretical Green's functions must be efficiently computed using both an integral in the complex k plane (in terms of homogeneous plane waves) and the pole contributions due to Rayleigh and Love normal modes, which result from the (application of the) Cauchy residue theorem. ACKNOWLEDGEMENTS. This research has been partially supported by DGAPA-UNAM under Project IN104712 and the AXA Research Fund.

  5. The uniqueness in the inverse problem for transmission eigenvalues for the spherically symmetric variable-speed wave equation

    Aktosun, Tuncay; Gintides, Drossos; Papanicolaou, Vassilis G.


    The recovery of a spherically symmetric wave speed v is considered in a bounded spherical region of radius b from the set of the corresponding transmission eigenvalues for which the corresponding eigenfunctions are also spherically symmetric. If the integral of 1/v on the interval [0, b] is less than b, assuming that there exists at least one v corresponding to the data, it is shown that v is uniquely determined by the data consisting of such transmission eigenvalues and their ‘multiplicities’, where the ‘multiplicity’ is defined as the multiplicity of the transmission eigenvalue as a zero of a key quantity. When that integral is equal to b, the unique recovery is obtained when the data contain one additional piece of information. Some similar results are presented for the unique determination of the potential from the transmission eigenvalues with ‘multiplicities’ for a related Schrödinger equation.

  6. Magmatic arc structure around Mount Rainier, WA, from the joint inversion of receiver functions and surface wave dispersion

    Obrebski, Mathias; Abers, Geoffrey A.; Foster, Anna


    The deep magmatic processes in volcanic arcs are often poorly understood. We analyze the shear wave velocity (VS) distribution in the crust and uppermost mantle below Mount Rainier, in the Cascades arc, resolving the main velocity contrasts based on converted phases within P coda via source normalization or receiver function (RF) analysis. To alleviate the trade-off between depth and velocity, we use long period phase velocities (25-100 s) obtained from earthquake surface waves, and at shorter period (7-21 s) we use seismic noise cross correlograms. We use a transdimensional Bayesian scheme to explore the model space (VS in each layer, number of interfaces and their respective depths, level of noise on data). We apply this tool to 15 broadband stations from permanent and Earthscope temporary stations. Most results fall into two groups with distinctive properties. Stations east of the arc (Group I) have comparatively slower middle-to-lower crust (VS = 3.4-3.8 km/s at 25 km depth), a sharp Moho and faster uppermost mantle (VS = 4.2-4.4 km/s). Stations in the arc (Group II) have a faster lower crust (VS = 3.7-4 km/s) overlying a slower uppermost mantle (VS = 4.0-4.3 km/s), yielding a weak Moho. Lower crustal velocities east of the arc (Group I) most likely represent ancient subduction mélanges mapped nearby. The lower crust for Group II ranges from intermediate to felsic. We propose that intermediate-felsic to felsic rocks represent the prearc basement, while intermediate composition indicates the mushy andesitic crustal magmatic system plus solidified intrusion along the volcanic conduits. We interpret the slow upper mantle as partial melt.

  7. Fracture channel waves

    Nihei, Kurt T.; Yi, Weidong; Myer, Larry R.; Cook, Neville G. W.; Schoenberg, Michael


    The properties of guided waves which propagate between two parallel fractures are examined. Plane wave analysis is used to obtain a dispersion equation for the velocities of fracture channel waves. Analysis of this equation demonstrates that parallel fractures form an elastic waveguide that supports two symmetric and two antisymmetric dispersive Rayleigh channel waves, each with particle motions and velocities that are sensitive to the normal and tangential stiffnesses of the fractures. These fracture channel waves degenerate to shear waves when the fracture stiffnesses are large, to Rayleigh waves and Rayleigh-Lamb plate waves when the fracture stiffnesses are low, and to fracture interface waves when the fractures are either very closely spaced or widely separated. For intermediate fracture stiffnesses typical of fractured rock masses, fracture channel waves are dispersive and exhibit moderate to strong localization of guided wave energy between the fractures. The existence of these waves is examined using laboratory acoustic measurements on a fractured marble plate. This experiment confirms the distinct particle motion of the fundamental antisymmetric fracture channel wave (A0 mode) and demonstrates the ease with which a fracture channel wave can be generated and detected.

  8. Diuresis and inversion therapy to improve clearance of lower caliceal stones after shock wave lithotripsy: A prospective, randomized, controlled, clinical study

    Abul-fotouh Ahmed


    Full Text Available Objective: To improve the clearance of lower caliceal stones (LCSs after shock wave lithotripsy (SWL using a combination of intra-operative forced diuresis and inversion therapy. Materials and Methods: One hundred and fifty-seven consecutive patients with symptomatic, single LCSs of 5-20 mm size were prospectively randomized into two groups. The first (study group, SG underwent SWL at the time of the maximum diuresis with the patient in the Trendelenburg position with an angle of 30 degree, while the second group (control group, CG underwent standard SWL. After the last SWL session, patients were followed-up regularly using plain abdominal X-ray and renal ultrasound. The primary endpoint of the study was the stone-free rate (SFR at 12 weeks. Results: A total of 141 patients completed the study treatment protocol and follow-up: 69 patients in SG and 72 patients in CG. Both groups were comparable in baseline data. SG showed significantly higher SFR at all follow-up time points. At week 12, 78.3% of SG were rendered stone free, whereas only 61.1% were stone free in CG (P = 0.030. Also, there was a significantly higher SFR for larger stones (>10 mm and stones with higher attenuation value (>500 Hounsfield units in SG than CG. Mild non-significant complications were reported in both groups. Conclusion: SWL with intraoperative forced diuresis and inversion seems to be an effective measure with minimal extra cost to improve LCS clearance post-SWL.

  9. Rayleigh imaging in spectral mammography

    Berggren, Karl; Danielsson, Mats; Fredenberg, Erik


    Spectral imaging is the acquisition of multiple images of an object at different energy spectra. In mammography, dual-energy imaging (spectral imaging with two energy levels) has been investigated for several applications, in particular material decomposition, which allows for quantitative analysis of breast composition and quantitative contrast-enhanced imaging. Material decomposition with dual-energy imaging is based on the assumption that there are two dominant photon interaction effects that determine linear attenuation: the photoelectric effect and Compton scattering. This assumption limits the number of basis materials, i.e. the number of materials that are possible to differentiate between, to two. However, Rayleigh scattering may account for more than 10% of the linear attenuation in the mammography energy range. In this work, we show that a modified version of a scanning multi-slit spectral photon-counting mammography system is able to acquire three images at different spectra and can be used for triple-energy imaging. We further show that triple-energy imaging in combination with the efficient scatter rejection of the system enables measurement of Rayleigh scattering, which adds an additional energy dependency to the linear attenuation and enables material decomposition with three basis materials. Three available basis materials have the potential to improve virtually all applications of spectral imaging.

  10. Series Solutions and a Perturbation Formula for the Extended Rayleigh Problem of Hydrodynamic Stability

    V Ganesh; M Subbiah


    We generalize Tollmien’s solutions of the Rayleigh problem of hydrodynamic stability to the case of arbitrary channel cross sections, known as the extended Rayleigh problem. We prove the existence of a neutrally stable eigensolution with wave number $k_s>0$; it is also shown that instability is possible only for $0 < k < k_s$ and not for $k>k_s$. Then we generalize the Tollmien–Lin perturbation formula for the behavior of $c_i$, the imaginary part of the phase velocity as the wave number $k→ k_s$ − to the extended Rayleigh problem and subsequently, we use this formula to demonstrate the instability of a particular shear flow.

  11. Multiphase Rayleigh-Bénard convection

    Oresta, P.; Fornarelli, F.; Prosperetti, Andrea


    Numerical simulations of two-phase Rayleigh-Bénard convection in a cylindrical cell with particles or vapor bubbles suspended in the fluid are described. The particles or bubbles are modeled as points, the Rayleigh number is 2×106 and the fluids considered are air, for the particle case, and

  12. Importance sampling the Rayleigh phase function

    Frisvad, Jeppe Revall


    Rayleigh scattering is used frequently in Monte Carlo simulation of multiple scattering. The Rayleigh phase function is quite simple, and one might expect that it should be simple to importance sample it efficiently. However, there seems to be no one good way of sampling it in the literature. Thi....... This paper provides the details of several different techniques for importance sampling the Rayleigh phase function, and it includes a comparison of their performance as well as hints toward efficient implementation.......Rayleigh scattering is used frequently in Monte Carlo simulation of multiple scattering. The Rayleigh phase function is quite simple, and one might expect that it should be simple to importance sample it efficiently. However, there seems to be no one good way of sampling it in the literature...

  13. Three-parameter shear wave inversion in MR elastography of incompressible transverse isotropic media: Application to in vivo lower leg muscles.

    Guo, Jing; Hirsch, Sebastian; Scheel, Michael; Braun, Jürgen; Sack, Ingolf


    To develop and demonstrate MR elastography (MRE) for the measurement of three independent viscoelastic constants of skeletal muscle according to the theory of linear elasticity of incompressible materials with transverse isotropy (TI). Three-dimensional multifrequency MRE was applied to soleus, gastrocnemius, and tibialis anterior muscles in 10 healthy volunteers. The rotational wave fields were solved for complex-valued viscoelastic parameters μ12, μ13, and E3 corresponding to two shear moduli (within the planes of isotropy and symmetry of TI materials) and Young's modulus (along the principal fiber axis). Anisotropy was represented by the inequality μ12  muscles, whereas storage shear moduli of tibialis were indistinguishable. Storage moduli were: 1.06 ± 0.12, 1.33 ± 0.10, 6.92 ± 0.95 kPa (soleus); 0.90 ± 0.11, 1.30 ± 0.15, 8.22 ± 1.37 kPa (gastrocnemius); 1.26 ± 0.16, 1.27 ± 0.11, 9.29 ± 1.42 kPa (tibialis), for μ12, μ13, and E3, respectively. The muscles were different in their μ12 and E3 values, whereas μ13 was less sensitive to the muscle type. Leg differences were observed in the soleus and gastrocnemius muscles. Recovery of the full elasticity tensor in incompressible TI materials is feasible by three-dimensional inversion of the time-harmonic shear wave equation. The method is potentially useful for the clinical evaluation of skeletal muscle anisotropy. © 2015 Wiley Periodicals, Inc.

  14. Dynamic stabilization of Rayleigh-Taylor instability in ablation fronts

    Piriz A.R.


    Full Text Available Dynamic stabilization of Rayleigh-Taylor instability in an ablation front is studied by considering the simplest possible modulations in the acceleration. Explicit analytical expressions for the instability growth rate and for the boundaries of the stability region are obtained by considering a sequence of Dirac deltas. Besides, general square waves allow for studying the effect of the driving asymmetries on the stability region as well as the optimization process. The essential role of compressibility is phenomenologically addressed in order to find the constraints it imposes on the stability region.

  15. Potential Misidentification of Love-Wave Phase Velocity Based on Three-Component Ambient Seismic Noise

    Xu, Zongbo; Xia, Jianghai; Luo, Yinhe; Cheng, Feng; Pan, Yudi


    People have calculated Rayleigh-wave phase velocities from vertical component of ambient seismic noise for several years. Recently, researchers started to extract Love waves from transverse component recordings of ambient noise, where "transverse" is defined as the direction perpendicular to a great-circle path or a line in small scale through observation sensors. Most researches assumed Rayleigh waves could be negligible, but Rayleigh waves can exist in the transverse component when Rayleigh waves propagate in other directions besides radial direction. In study of data acquired in western Junggar Basin near Karamay city, China, after processing the transverse component recordings of ambient noise, we obtain two energy trends, which are distinguished with Rayleigh-wave and Love-wave phase velocities, in the frequency-velocity domain using multichannel analysis of surface waves (MASW). Rayleigh waves could be also extracted from the transverse component data. Because Rayleigh-wave and Love-wave phase velocities are close in high frequencies (>0.1 Hz), two kinds of surface waves might be merged in the frequency-velocity domain. Rayleigh-wave phase velocities may be misidentified as Love-wave phase velocities. To get accurate surface-wave phase velocities from the transverse component data using seismic interferometry in investigating the shallow geology, our results suggest using MASW to calculate real Love-wave phase velocities.

  16. A proper methodology aimed at surface wave tomography

    J. Badal


    Full Text Available When applying a methodology for obtaining the 3D shear-wave velocity structure of a medium from surface wave dispersion data, the problem must be considered with caution since one inverts path-averaged velocities and the use of any inversion method entails some drawbacks such as lack of uniqueness, unwarranted stability and constraints affecting the data. In order to avoid the application of consecutive inversions and to overcome these drawbacks, we propose alternative mapping methods, for example spatial prediction methods, or else the use of an algorithm that, from a mathematical viewpoint, can be understood through the application of the orthogonal projection theorem onto convex sets (POCS. Among the first ones, we try inverse weighted distance interpolation. The POCS algorithm we have used discretises a second order differential equation for the velocity field with boundary conditions. All these imaging techniques aimed at volumetric modelling and the visualisation of data are discussed, and finally we show some results based on ray path velocities obtained previously by inversion of phase and group velocities of Rayleigh waves propagating across the Iberian peninsula.

  17. Analysis of the multi-component pseudo-pure-mode qP-wave inversion in vertical transverse isotropic (VTI) media

    Djebbi, Ramzi


    Multi-parameter inversion in anisotropic media suffers from the inherent trade-off between the anisotropic parameters, even under the acoustic assumption. Multi-component data, often acquired nowadays in ocean bottom acquisition and land data, provide additional information capable of resolving anisotropic parameters under the acoustic approximation assumption. Based on Born scattering approximation, we develop formulas capable of characterizing the radiation patterns for the acoustic pseudo-pure mode P-waves. Though commonly reserved for the elastic fields, we use displacement fields to constrain the acoustic vertical transverse isotropic (VTI) representation of the medium. Using the asymptotic Green\\'s functions and a horizontal reflector we derive the radiation patterns for perturbations in the anisotropic media. The radiation pattern for the anellipticity parameter η is identically zero for the horizontal displacement. This allows us to dedicate this component to invert for velocity and δ. Computing the traveltime sensitivity kernels based on the unwrapped phase confirms the radiation patterns observations, and provide the model wavenumber behavior of the update.

  18. Strong lateral variations of S-wave velocity in the upper mantle across the western Alps

    Lyu, Chao; Pedersen, Helle; Paul, Anne; Zhao, Liang


    Absolute S-wave velocity gives more insight into temperature and mineralogy than relative P-wave velocity variations (ΔV p/ V p) imaged by teleseismic traveltime tomography. Moreover, teleseismic P-wave tomography has poor vertical but good horizontal resolution. By contrast, the inversion of surface waves dispersion data gives absolute S-wave velocity with a good vertical but relatively poor horizontal resolution. However, the horizontal resolution of surface wave imaging can be improved by using closely spaced stations in mini-arrays. In this work, we use Rayleigh wave phase velocity dispersion data to measure absolute S-wave velocities beneath the CIFALPS profile across the French-Italian western Alps. We apply the array processing technique proposed by Pedersen et al. (2003) to derive Rayleigh wave phase dispersion curves between 20 s and 100 s period in 15 mini-arrays along the CIFALPS line. We estimate a 1-D S-wave velocity model at depth 50-150 km beneath each mini-array by inverting the dispersion curves jointly with receiver functions. The joint inversion helps separating the crustal and mantle contributions in the inversion of dispersion curves. Distinct lithospheric structures and marked lateral variations are revealed beneath the study region, correlating well with regional geological and tectonic features. The average S-wave velocity from 50 to 150 km depth beneath the CIFALPS area is ˜4.48km/s, almost the same as in model AK135, indicating a normal upper mantle structure in average. Lateral variations are dominated by relatively low velocities (˜4.4km/s) in the mantle of the European plate, very low velocities (4.0km/s, i.e. approximately 12% lower than AK135) beneath the Dora Maira internal crystalline massif and high velocities (˜ 5.0km/s, i.e. 12% higher than AK135) beneath the Po plain. The lateral variations of S-wave velocity perturbation show the same features as the P wave tomography (Zhao et al., submitted), but with different amplitudes

  19. Surface waves in fibre-reinforced anisotropic elastic media

    P R Sengupta; Sisir Nath


    The aim of this paper is to investigate surface waves in anisotropic fibre-reinforced solid elastic media. First, the theory of general surface waves has been derived and applied to study the particular cases of surface wavesRayleigh, Love and Stoneley types. The wave velocity equations are found to be in agreement with the corresponding classical result when the anisotropic elastic parameters tends to zero. It is important to note that the Rayleigh type of wave velocity in the fibre-reinforced elastic medium increases to a considerable amount in comparison with the Rayleigh wave velocity in isotropic materials.

  20. Direct Waveform Inversion by Iterative Inverse Propagation

    Schlottmann, R B


    Seismic waves are the most sensitive probe of the Earth's interior we have. With the dense data sets available in exploration, images of subsurface structures can be obtained through processes such as migration. Unfortunately, relating these surface recordings to actual Earth properties is non-trivial. Tomographic techniques use only a small amount of the information contained in the full seismogram and result in relatively low resolution images. Other methods use a larger amount of the seismogram but are based on either linearization of the problem, an expensive statistical search over a limited range of models, or both. We present the development of a new approach to full waveform inversion, i.e., inversion which uses the complete seismogram. This new method, which falls under the general category of inverse scattering, is based on a highly non-linear Fredholm integral equation relating the Earth structure to itself and to the recorded seismograms. An iterative solution to this equation is proposed. The res...

  1. Spectra and probability distributions of thermal flux in turbulent Rayleigh-B\\'{e}nard convection

    Pharasi, Hirdesh K; Kumar, Krishna; Bhattacharjee, Jayanta K


    The spectra of turbulent heat flux $\\mathrm{H}(k)$ in Rayleigh-B\\'{e}nard convection with and without uniform rotation are presented. The spectrum $\\mathrm{H}(k)$ scales with wave number $k$ as $\\sim k^{-2}$. The scaling exponent is almost independent of the Taylor number $\\mathrm{Ta}$ and Prandtl number $\\mathrm{Pr}$ for higher values of the reduced Rayleigh number $r$ ($ > 10^3$). The exponent, however, depends on $\\mathrm{Ta}$ and $\\mathrm{Pr}$ for smaller values of $r$ ($<10^3$). The probability distribution functions of the local heat fluxes are non-Gaussian and have exponential tails.

  2. Rayleigh-Taylor instability of viscous fluids with phase change

    Kim, Byoung Jae; Kim, Kyung Doo


    Film boiling on a horizontal surface is a typical example of the Rayleigh-Taylor instability. During the film boiling, phase changes take place at the interface, and thus heat and mass transfer must be taken into consideration in the stability analysis. Moreover, since the vapor layer is not quite thick, a viscous flow must be analyzed. Existing studies assumed equal kinematic viscosities of two fluids, and/or considered thin viscous fluids. The purpose of this study is to derive the analytical dispersion relation of the Rayleigh-Taylor instability for more general conditions. The two fluids have different properties. The thickness of the vapor layer is finite, but the liquid layer is thick enough to be nearly semi-infinite in view of perturbation. Initially, the vapor is in equilibrium with the liquid at the interface, and the direction of heat transfer is from the vapor side to the liquid side. In this case, the phase change has a stabilizing effect on the growth rate of the interface. When the vapor layer is thin, there is a coupled effect of the vapor viscosity, phase change, and vapor thickness on the critical wave number. For the other limit of a thick vapor, both the liquid and vapor viscosities influence the critical wave number. Finally, the most unstable wavelength is investigated. When the vapor layer is thin, the most unstable wavelength is not affected by phase change. When the vapor layer is thick, however, it increases with the increasing rate of phase change.

  3. High Prandtl number effect on Rayleigh-Bénard convection heat transfer at high Rayleigh number

    Ma, Li; Li, Jing; Ji, Shui; Chang, Huajian


    This paper represents results of the Rayleigh-Bénard convection heat transfer in silicon oil confined by two horizontal plates, heated from below, and cooled from above. The Prandtl numbers considered as 100-10,000 corresponding to three types of silicon oil. The experiments covered a range of Rayleigh numbers from 2.14·109 to 2.27·1013. The data points that the Nusselt number dependents on the Rayleigh number, which is asymptotic to a 0.248 power. Furthermore, the experiment results can fit the data in low Rayleigh number well.

  4. Overview of Rayleigh-Taylor instability

    Sharp, D.H.


    The aim of this talk is to survey Rayleigh-Taylor instability, describing the phenomenology that occurs at a Taylor unstable interface, and reviewing attempts to understand these phenomena quantitatively.

  5. Solute redistribution and Rayleigh number in the mushy zone during directional solidifi cation of Inconel 718

    Wang Ling


    Full Text Available The interdendritic segregation along the mushy zone of directionally solidifi ed superalloy Inconel 718 has been measured by scanning electron microscope (SEM and energy dispersion analysis spectrometry (EDAXtechniques and the corresponding liquid composition profile was presented. The liquid density and Rayleigh number (Ra profi les along the mushy zone were calculated as well. It was found that the liquid density difference increased from top to bottom in the mushy zone and there was no density inversion due to the segregation of Nb and Mo. However carbide formation in the freezing range and the preferred angle of the orientated dendrite array could prompt the fl uid fl ow in the mushy zone although there was no liquid density inversion. The largest relative Rayleigh number appeared at 1,326 篊 for Inconel 718 where the fl uid fl ow most easily occurred.

  6. Solute redistribution and Rayleigh number in the mushy zone during directional solidification of Inconel 718

    Wang Ling; Dong Jianxin; Liu Lin; Zhang Lei


    The interdendritic segregation along the mushy zone of directionally solidified superalloy Inconel 718has been measured by scanning electron microscope (SEM) and energy dispersion analysis spectrometry (EDAX)techniques and the corresponding liquid composition profile was presented. The liquid density and Rayleigh number (Ra) profiles along the mushy zone were calculated as well. It was found that the liquid density difference increased from top to bottom in the mushy zone and there was no density inversion due to the segregation of Nb and Mo. However carbide formation in the freezing range and the preferred angle of the odentated dendrite array could prompt the fluid flow in the mushy zone although there was no liquid density inversion. The largest relative Rayleigh number appeared at 1,326℃ for Inconel 718 where the fluid flow most easily occurred.

  7. Modeling and Control Of Surface Acoustic Wave Motors

    Feenstra, P.J.


    This thesis introduces Rayleigh waves and describes the generation of Rayleigh waves. Furthermore, the principle of operation of a SAW motor is analyzed. The analysis is based on a contact model, which describes the behavior between slider and stator. Due to the contact model, the microscopic and

  8. Importance of a 3D forward modeling tool for surface wave analysis methods

    Pageot, Damien; Le Feuvre, Mathieu; Donatienne, Leparoux; Philippe, Côte; Yann, Capdeville


    Since a few years, seismic surface waves analysis methods (SWM) have been widely developed and tested in the context of subsurface characterization and have demonstrated their effectiveness for sounding and monitoring purposes, e.g., high-resolution tomography of the principal geological units of California or real time monitoring of the Piton de la Fournaise volcano. Historically, these methods are mostly developed under the assumption of semi-infinite 1D layered medium without topography. The forward modeling is generally based on Thomson-Haskell matrix based modeling algorithm and the inversion is driven by Monte-Carlo sampling. Given their efficiency, SWM have been transfered to several scale of which civil engineering structures in order to, e.g., determine the so-called V s30 parameter or assess other critical constructional parameters in pavement engineering. However, at this scale, many structures may often exhibit 3D surface variations which drastically limit the efficiency of SWM application. Indeed, even in the case of an homogeneous structure, 3D geometry can bias the dispersion diagram of Rayleigh waves up to obtain discontinuous phase velocity curves which drastically impact the 1D mean velocity model obtained from dispersion inversion. Taking advantages of high-performance computing center accessibility and wave propagation modeling algorithm development, it is now possible to consider the use of a 3D elastic forward modeling algorithm instead of Thomson-Haskell method in the SWM inversion process. We use a parallelized 3D elastic modeling code based on the spectral element method which allows to obtain accurate synthetic data with very low numerical dispersion and a reasonable numerical cost. In this study, we choose dike embankments as an illustrative example. We first show that their longitudinal geometry may have a significant effect on dispersion diagrams of Rayleigh waves. Then, we demonstrate the necessity of 3D elastic modeling as a forward

  9. Shear-wave velocity profiling according to three alternative approaches: A comparative case study

    Dal Moro, G.; Keller, L.; Al-Arifi, N. S.; Moustafa, S. S. R.


    The paper intends to compare three different methodologies which can be used to analyze surface-wave propagation, thus eventually obtaining the vertical shear-wave velocity (VS) profile. The three presented methods (currently still quite unconventional) are characterized by different field procedures and data processing. The first methodology is a sort of evolution of the classical Multi-channel Analysis of Surface Waves (MASW) here accomplished by jointly considering Rayleigh and Love waves (analyzed according to the Full Velocity Spectrum approach) and the Horizontal-to-Vertical Spectral Ratio (HVSR). The second method is based on the joint analysis of the HVSR curve together with the Rayleigh-wave dispersion determined via Miniature Array Analysis of Microtremors (MAAM), a passive methodology that relies on a small number (4 to 6) of vertical geophones deployed along a small circle (for the common near-surface application the radius usually ranges from 0.6 to 5 m). Finally, the third considered approach is based on the active data acquired by a single 3-component geophone and relies on the joint inversion of the group-velocity spectra of the radial and vertical components of the Rayleigh waves, together with the Radial-to-Vertical Spectral Ratio (RVSR). The results of the analyses performed while considering these approaches (completely different both in terms of field procedures and data analysis) appear extremely consistent thus mutually validating their performances. Pros and cons of each approach are summarized both in terms of computational aspects as well as with respect to practical considerations regarding the specific character of the pertinent field procedures.

  10. Wave

    Ibsen, Lars Bo


    Estimates for the amount of potential wave energy in the world range from 1-10 TW. The World Energy Council estimates that a potential 2TW of energy is available from the world’s oceans, which is the equivalent of twice the world’s electricity production. Whilst the recoverable resource is many t...

  11. Ambient Noise Tomography of central Java, with Transdimensional Bayesian Inversion

    Zulhan, Zulfakriza; Saygin, Erdinc; Cummins, Phil; Widiyantoro, Sri; Nugraha, Andri Dian; Luehr, Birger-G.; Bodin, Thomas


    Delineating the crustal structure of central Java is crucial for understanding its complex tectonic setting. However, seismic imaging of the strong heterogeneity typical of such a tectonically active region can be challenging, particularly in the upper crust where velocity contrasts are strongest and steep body wave ray-paths provide poor resolution. We have applied ambient noise cross correlation of pair stations in central Java, Indonesia by using the MERapi Amphibious EXperiment (MERAMEX) dataset. The data were collected between May to October 2004. We used 120 of 134 temporary seismic stations for about 150 days of observation, which covered central Java. More than 5000 Rayleigh wave Green's function were extracted by cross-correlating the noise simultaneously recorded at available station pairs. We applied a fully nonlinear 2D Bayesian inversion technique to the retrieved travel times. Features in the derived tomographic images correlate well with previous studies, and some shallow structures that were not evident in previous studies are clearly imaged with Ambient Noise Tomography. The Kendeng Basin and several active volcanoes appear with very low group velocities, and anomalies with relatively high velocities can be interpreted in terms of crustal sutures and/or surface geological features.

  12. Rayleigh--Taylor spike evaporation

    Schappert, G. T.; Batha, S. H.; Klare, K. A.; Hollowell, D. E.; Mason, R. J.


    Laser-based experiments have shown that Rayleigh--Taylor (RT) growth in thin, perturbed copper foils leads to a phase dominated by narrow spikes between thin bubbles. These experiments were well modeled and diagnosed until this '' spike'' phase, but not into this spike phase. Experiments were designed, modeled, and performed on the OMEGA laser [T. R. Boehly, D. L. Brown, R. S. Craxton , Opt. Commun. 133, 495 (1997)] to study the late-time spike phase. To simulate the conditions and evolution of late time RT, a copper target was fabricated consisting of a series of thin ridges (spikes in cross section) 150 {mu}m apart on a thin flat copper backing. The target was placed on the side of a scale-1.2 hohlraum with the ridges pointing into the hohlraum, which was heated to 190 eV. Side-on radiography imaged the evolution of the ridges and flat copper backing into the typical RT bubble and spike structure including the '' mushroom-like feet'' on the tips of the spikes. RAGE computer models [R. M. Baltrusaitis, M. L. Gittings, R. P. Weaver, R. F. Benjamin, and J. M. Budzinski, Phys. Fluids 8, 2471 (1996)] show the formation of the '' mushrooms,'' as well as how the backing material converges to lengthen the spike. The computer predictions of evolving spike and bubble lengths match measurements fairly well for the thicker backing targets but not for the thinner backings.

  13. Interface-wave dispersion curves inversion based on nonlinear Bayesian theory%根据非线性贝叶斯理论的界面波频散曲线反演

    李翠琳; Stan E Dosso; Hefeng Dong


    通过时频分析法从海底环境噪声数据中提取界面波频散曲线,进而采用非线性贝叶斯反演方法估算海底沉积物厚度、剪切波速度、压缩波速度和密度等参数及其不确定性.参数的最大后验概率(MAP)估计值和边缘概率分布分别通过自适应单纯形模拟退火法和Metropolis-Hastings采样法在各参数先验区间内搜索获得,采用贝叶斯信息准则(BIC)从不同参数化模型中选择最优模型.界面波频散曲线反演结果表明:满足实测数据的最优海底模型结构为3层均匀分布剪切波速度剖面结构,海底深度的反演精度在800 m以内,比起压缩波速度和密度,剪切波速度的不确定性更小,对界面波频散曲线更敏感.%This paper applies a dataset of ocean ambient noise data to extract interface-wave dispersion curves using time-frequency analysis. The nonlinear Bayesian inversion is applied to estimate seabed sediment parameters such as thickness, shear-wave velocity, compression wave velocity and density, and their uncertainties from interface-wave dispersion curves. The maximum a posterior (MAP) model and marginal probability distributions of parameters are estimated using posterior probability densities computed by adaptive simplex simulated annealing and Metropolis-Hastings sampling methods. The Bayesian information criterion is applied to determine the optimal model that fully explains the observed data by the different parameterizations. The inversion results indicate that 3-uniform-layer model is chosen as the preferred parameterization. The resolution of inversion is up to 800 m-depth. The shear-wave velocity and layer thickness have fewer uncertainties and are more sensitive to the interface wave dispersion than the compression wave velocity and density.

  14. Bayesian seismic AVO inversion

    Buland, Arild


    A new linearized AVO inversion technique is developed in a Bayesian framework. The objective is to obtain posterior distributions for P-wave velocity, S-wave velocity and density. Distributions for other elastic parameters can also be assessed, for example acoustic impedance, shear impedance and P-wave to S-wave velocity ratio. The inversion algorithm is based on the convolutional model and a linearized weak contrast approximation of the Zoeppritz equation. The solution is represented by a Gaussian posterior distribution with explicit expressions for the posterior expectation and covariance, hence exact prediction intervals for the inverted parameters can be computed under the specified model. The explicit analytical form of the posterior distribution provides a computationally fast inversion method. Tests on synthetic data show that all inverted parameters were almost perfectly retrieved when the noise approached zero. With realistic noise levels, acoustic impedance was the best determined parameter, while the inversion provided practically no information about the density. The inversion algorithm has also been tested on a real 3-D dataset from the Sleipner Field. The results show good agreement with well logs but the uncertainty is high. The stochastic model includes uncertainties of both the elastic parameters, the wavelet and the seismic and well log data. The posterior distribution is explored by Markov chain Monte Carlo simulation using the Gibbs sampler algorithm. The inversion algorithm has been tested on a seismic line from the Heidrun Field with two wells located on the line. The uncertainty of the estimated wavelet is low. In the Heidrun examples the effect of including uncertainty of the wavelet and the noise level was marginal with respect to the AVO inversion results. We have developed a 3-D linearized AVO inversion method with spatially coupled model parameters where the objective is to obtain posterior distributions for P-wave velocity, S-wave

  15. Inverse Limits

    Ingram, WT


    Inverse limits provide a powerful tool for constructing complicated spaces from simple ones. They also turn the study of a dynamical system consisting of a space and a self-map into a study of a (likely more complicated) space and a self-homeomorphism. In four chapters along with an appendix containing background material the authors develop the theory of inverse limits. The book begins with an introduction through inverse limits on [0,1] before moving to a general treatment of the subject. Special topics in continuum theory complete the book. Although it is not a book on dynamics, the influen

  16. 高分辨率的频率空间域声波全波形速度反演-理论模型%High resolution acoustic wave full waveform velocity inversion in frequency space domain-theoretical model

    廖建平; 刘和秀; 王华忠; 彭叶辉; 杨天春; 王齐仁


    使用最速下降法进行二维频率空间域声波波动方程全波形速度反演,讨论了如何快速实现高精度的二维频率空间域声波波动方程全波形速度反演.多尺度的思想耦合在反演框架中.把非线性问题化为逐步线性问题是我们关注的焦点,目的是把整个非线性反演的黑匣子转化成为每一步可控的过程,尽可能得到想要的反演解.仅仅使用3个离散的频率,每个频率迭代10次,对广角Marmousi模型进行地面地震声波全波形速度反演,反演得到高分辨率、高精度的速度,为全波形反演实际资料奠定了很好的基础.%We use the steepest descent method based on two-dimensional frequency space domain acoustic wave equation for full waveform velocity inversion, discuss how to quickly realize high precision two-dimensional frequency domain full waveform velocity inversion. Multi-scale criterial is coupling in the inversion framework. The nonlinear problem changes into gradually linear problem is our focus. The purpose is the whole nonlinear inverse black box into every step of controllable process as far as possible, getting an inversion solution we want. Use only three discrete frequencies, each frequency iterative ten times, we make surface seismic acoustic wave full waveform inversion on extended Marmousi and get a high resolution and high precision imaging of velocity. This gives a good foundation for full waveform inversion on real field data.

  17. Seismic Waveform Inversion Using the Finite-Difference Contrast Source Inversion Method

    Bo Han; Qinglong He; Yong Chen; Yixin Dou


    This paper extends the finite-difference contrast source inversion method to reconstruct the mass density for two-dimensional elastic wave inversion in the framework of the full-waveform inversion. The contrast source inversion method is a nonlinear iterative method that alternatively reconstructs contrast sources and contrast function. One of the most outstanding advantages of this inversion method is the highly computational efficiency, since it does not need to simulate a fu...

  18. Chromo-Rayleigh Interactions of Dark Matter

    Bai, Yang


    For a wide range of models, dark matter can interact with QCD gluons via chromo-Rayleigh interactions. We point out that the Large Hadron Collider (LHC), as a gluon machine, provides a superb probe of such interactions. In this paper, we introduce simplified models to UV-complete two effective dark matter chromo-Rayleigh interactions and identify the corresponding collider signatures, including four jets or a pair of di-jet resonances plus missing transverse energy. After performing collider studies for both the 8 TeV and 14 TeV LHC, we find that the LHC can be more sensitive to dark matter chromo-Rayleigh interactions than direct detection experiments and thus provides the best opportunity for future discovery of this class of models.

  19. Optical results with Rayleigh quotient discrimination filters

    Juday, Richard D.; Rollins, John M.; Monroe, Stanley E., Jr.; Morelli, Michael V.


    We report experimental laboratory results using filters that optimize the Rayleigh quotient [Richard D. Juday, 'Generalized Rayleigh quotient approach to filter optimization,' JOSA-A 15(4), 777-790 (April 1998)] for discriminating between two similar objects. That quotient is the ratio of the correlation responses to two differing objects. In distinction from previous optical processing methods it includes the phase of both objects -- not the phase of only the 'accept' object -- in the computation of the filter. In distinction from digital methods it is explicitly constrained to optically realizable filter values throughout the optimization process.

  20. From the Somigliana waves to the evanescent waves

    Pietro Caloi


    Full Text Available The Rayleigh equation has real coefficients; therefore, also the case of complex conjugated roots may be explained physically. The Author proves that the Somigliana waves may be formed for Poisson ratio values until 0.30543; for gradually less rigid media, they are missing altogether and degenerate into evanescent waves.

  1. A Variable-resolution Surface Wave Dispersion Study of Eurasia, North Africa, and Surrounding Regions

    Pasyanos, M E


    This paper presents the results of a large-scale study of surface wave dispersion performed across Eurasia and North Africa. Improvements were made to previous surface wave work by enlarging the study region, increasing path density, improving spatial resolution, and expanding the period range. This study expands the coverage area northwards and eastwards relative to a previous dispersion analysis, which covered only North Africa and the Middle East. We have significantly increased the number of seismograms examined and group velocity measurements made. We have now made good quality dispersion measurements for about 30,000 Rayleigh wave and 20,000 Love wave paths, and have incorporated measurements from several other researchers into the study. A conjugate gradient method was employed for the group velocity tomography, which improved the inversion from the previous study by adopting a variable smoothness. This technique allows us to go to higher resolution where the data allow without producing artifacts. The current results include both Love and Rayleigh wave inversions across the region for periods from 7 to 100 seconds at 1{sup o} resolution. Short period group velocities are sensitive to slow velocities associated with large sedimentary features such as the Caspian Sea, West Siberian Platform, Mediterranean Sea, Bay of Bengal, Tarim Basin, and Persian Gulf. Intermediate periods are sensitive to differences in crustal thickness, such as those between oceanic and continental crust or along orogenic zones and continental plateaus. At longer periods, fast velocities are consistently found beneath cratons while slow upper mantle velocities occur along rift systems, subduction zones, and collision zones such as the Tethys Belt. We have compared the group velocities at various periods with features such as sediment thickness, topographic height, crustal thickness, proximity to plate boundaries, lithospheric age and lithospheric thickness, and find significant

  2. Size Effects on Surface Elastic Waves in a Semi-Infinite Medium with Atomic Defect Generation

    F. Mirzade


    Full Text Available The paper investigates small-scale effects on the Rayleigh-type surface wave propagation in an isotopic elastic half-space upon laser irradiation. Based on Eringen’s theory of nonlocal continuum mechanics, the basic equations of wave motion and laser-induced atomic defect dynamics are derived. Dispersion equation that governs the Rayleigh surface waves in the considered medium is derived and analyzed. Explicit expressions for phase velocity and attenuation (amplification coefficients which characterize surface waves are obtained. It is shown that if the generation rate is above the critical value, due to concentration-elastic instability, nanometer sized ordered concentration-strain structures on the surface or volume of solids arise. The spatial scale of these structures is proportional to the characteristic length of defect-atom interaction and increases with the increase of the temperature of the medium. The critical value of the pump parameter is directly proportional to recombination rate and inversely proportional to deformational potentials of defects.

  3. Upper-Mantle Shear Velocities beneath Southern California Determined from Long-Period Surface Waves

    Polet, J.; Kanamori, H.


    We used long-period surface waves from teleseismic earthquakes recorded by the TERRAscope network to determine phase velocity dispersion of Rayleigh waves up to periods of about 170 sec and of Love waves up to about 150 sec. This enabled us to investigate the upper-mantle velocity structure beneath southern California to a depth of about 250 km. Ten and five earthquakes were used for Rayleigh and Love waves, respectively. The observed surface-wave dispersion shows a clear Love/Rayleigh-wave d...

  4. Three dimensional shear wave velocity structure of crust and upper mantle in South China Sea and its adjacent regions by surface waveform inversion


    We assembled approximately 328 seismic records. The data set wasfrom 4 digitally recording long-period and broadband stations of CDSN. We carried out the inversion based on the partitioned waveform inversion (PWI). It partitions the large-scale optimization problem into a number of independent small-scale problems. We adopted surface waveform inversion with an equal block (2°′2°) discretization in order to acquire the images of shear velocity structure at different depths (from surface to 430 km) in the crust and upper-mantle. The resolution of all these anomalies has been established with 2check-board2 resolution tests. These results show significant difference in velocity, lithosphere and asthenosphere structure between South China Sea and its adjacent regions.

  5. Making Waves: Seismic Waves Activities and Demonstrations

    Braile, S. J.; Braile, L. W.


    The nature and propagation of seismic waves are fundamental concepts necessary for understanding the exploration of Earth's interior structure and properties, plate tectonics, earthquakes, and seismic hazards. Investigating seismic waves is also an engaging approach to learning basic principles of the physics of waves and wave propagation. Several effective educational activities and demonstrations are available for teaching about seismic waves, including the stretching of a spring to demonstrate elasticity; slinky wave propagation activities for compressional, shear, Rayleigh and Love waves; the human wave activity to demonstrate P- and S- waves in solids and liquids; waves in water in a simple wave tank; seismic wave computer animations; simple shake table demonstrations of model building responses to seismic waves to illustrate earthquake damage to structures; processing and analysis of seismograms using free and easy to use software; and seismic wave simulation software for viewing wave propagation in a spherical Earth. The use of multiple methods for teaching about seismic waves is useful because it provides reinforcement of the fundamental concepts, is adaptable to variable classroom situations and diverse learning styles, and allows one or more methods to be used for authentic assessment. The methods described here have been used effectively with a broad range of audiences, including K-12 students and teachers, undergraduate students in introductory geosciences courses, and geosciences majors.

  6. Crust and upper mantle structure beneath the Pacific Northwest from joint inversions of ambient noise and earthquake data

    Wagner, Lara S.; Fouch, Matthew J.; James, David E.; Hanson-Hedgecock, Sara


    We perform a joint inversion of phase velocities from both earthquake and ambient noise induced Rayleigh waves to determine shear wave velocity structure in the crust and upper mantle beneath the Pacific Northwest. We focus particularly on the areas affected by mid-Miocene to present volcanic activity. The joint inversion, combined with the high density seismic network of the High Lava Plains seismic experiment and data from the EarthScope Transportable Array, provides outstanding resolution for this area. In Oregon, we find that the pattern of low velocities in the crust and uppermost mantle varies between the High Lava Plains physiographic province and the adjacent northwestern Basin and Range. These patterns may be due to the presence of the Brothers Fault Zone which separates the clockwise rotating northwest Basin and Range from the relatively undeformed areas further north. Further to the east, the Owyhee Plateau, Snake River Plain (SRP) and northeastern Basin and Range are characterized by high crustal velocities, though the depth extent of these fast wave speeds varies by province. Of particular interest is the mid-crustal high velocity sill, previously only identified within the SRP. We show this anomaly extends significantly further south into Utah and Nevada. We suggest that one possible explanation is lateral crustal extrusion due to the emplacement of the high density mafic mid-crustal sill structures within the SRP.

  7. A computer code for forward calculation and inversion of the H/V spectral ratio under the diffuse field assumption

    García-Jerez, Antonio; Piña-Flores, José; Sánchez-Sesma, Francisco J.; Luzón, Francisco; Perton, Mathieu


    During a quarter of a century, the main characteristics of the horizontal-to-vertical spectral ratio of ambient noise HVSRN have been extensively used for site effect assessment. In spite of the uncertainties about the optimum theoretical model to describe these observations, over the last decade several schemes for inversion of the full HVSRN curve for near surface surveying have been developed. In this work, a computer code for forward calculation of H/V spectra based on the diffuse field assumption (DFA) is presented and tested. It takes advantage of the recently stated connection between the HVSRN and the elastodynamic Green's function which arises from the ambient noise interferometry theory. The algorithm allows for (1) a natural calculation of the Green's functions imaginary parts by using suitable contour integrals in the complex wavenumber plane, and (2) separate calculation of the contributions of Rayleigh, Love, P-SV and SH waves as well. The stability of the algorithm at high frequencies is preserved by means of an adaptation of the Wang's orthonormalization method to the calculation of dispersion curves, surface-waves medium responses and contributions of body waves. This code has been combined with a variety of inversion methods to make up a powerful tool for passive seismic surveying.

  8. Geophysical Modeling in Eurasia: 2D Crustal P and LG Propagation; Upper- Mantle Shear Wave Propagation and Anisotropy; and 3D, Joint, Simultaneous Inversions


    nonunique properties of inversion methods, we may often find a solution for one data type, but we must acknowledge that, although it can predict behavior...H. K., H. Kanamori, P. C. Jennings, and C. Kissling (Eds.) (2002). International Handbook of Earthquake and Engineering Seismology (CD-ROM

  9. Upper mantle compositional variations and discontinuity topography imaged beneath Australia from Bayesian inversion of surface-wave phase velocities and thermochemical modeling

    Khan, A.; Zunino, Andrea; Deschamps, F.


    models of the thermochemical and anisotropic structure of the mantle to 450 km depth. Dispersion data are linked to thermochemical parameters through a thermodynamic formalism for computing mantle mineral phase equilibria and physical properties. The inverse problem is solved using a probabilistic...

  10. Nonequilibrium fluctuations from a nematic under a thermal gradient and a gravity field*. II. Rayleigh scattering

    Camacho, Jorge F.; Rodríguez, Rosalío F.


    The fluctuating hydrodynamic treatment developed in the previous article for a nematic liquid crystal under the influence of a thermal gradient α and a uniform gravity field g, is used to calculate its Rayleigh light scattering spectrum. We find that the dissipative thermal gradient force enhances the Rayleigh-line intensity which varies as k -4 with the fluctuations of the wave number k. The Rayleigh line consists of three central Lorentzians, two of which are determined by the visco-heat modes coupling the entropy and director fluctuations, which is a pure non-equilibrium effect. The third Lorentzian is due only to director fluctuations. We find that the former peaks contain the Rayleigh wings owing to the orientational fluctuations of the aniosotropic molecules. It is also shown that the obtained spectrum reduces to the known equilibrium spectrum of a nematic and to that of a simple fluid. For the particular case in which the decay rates are diffusive, we calculate and plot the amplitudes of non-equilibrium fluctuations of the dynamic structure factor as a function of | α|2/ k 4, and also, the intermediate function in the equilibrium and non-equilibrium states.

  11. Inverse methods in hydrologic optics

    Howard R. Gordon


    Full Text Available Methods for solving the hydrologic-optics inverse problem, i.e., estimating the inherent optical properties of a water body based solely on measurements of the apparent optical properties, are reviewed in detail. A new method is developed for the inverse problem in water bodies in which fluorescence is important. It is shown that in principle, given profiles of the spectra of up- and downwelling irradiance, estimation of the coefficient of inelastic scattering from any wave band to any other wave band can be effected.

  12. Inverse disjuncties

    Malepaard, J.


    Balansschikkingen (of negatief gebonden of-constructies) zijn volgens de in dit artikel ontwikkelde hypothese inverse disjuncties (id's). Het zijn tweeledige zinnen waarvan het eerste lid een verplichte negatieve of minimaliserende constituent bevat en het tweede lid met of begint. Evenals

  13. 转换波AVO反演速度比各横波反射系数%Converted wave AVO inversion for average velocity ratio and shear wave reflection coefficient

    魏修成; 陈天胜; 季玉新


    Based on the empirical Gardner equation describing the relationship between density and compressional wave velocity, the converted wave reflection coefficient extrema attributes for AVO analysis are proposed and the relations between the extrema position and amplitude, average velocity ratio across the interface, and shear wave reflection coefficient are derived. The extrema position is a monotonically decreasing function of average velocity ratio, and the extrema amplitude is a function of average velocity ratio and shear wave reflection coefficient. For theoretical models, the average velocity ratio and shear wave reflection coefficient are inverted from the extrema position and amplitude obtained from fitting a power function to converted wave AVO curves. Shear wave reflection coefficient sections have clearer physical meaning than conventional converted wave stacked sections and establish the theoretical foundation for geological structural interpretation and event correlation. 'The method of inverting average velocity ratio and shear wave reflection coefficient from the extrema position and amplitude obtained from fitting a power function is applied to real CCP gathers. The inverted average velocity ratios are consistent with those computed from compressional and shear wave well logs.

  14. A global shear velocity model of the mantle from normal modes and surface waves

    durand, S.; Debayle, E.; Ricard, Y. R.; Lambotte, S.


    We present a new global shear wave velocity model of the mantle based on the inversion of all published normal mode splitting functions and the large surface wave dataset measured by Debayle & Ricard (2012). Normal mode splitting functions and surface wave phase velocity maps are sensitive to lateral heterogeneities of elastic parameters (Vs, Vp, xi, phi, eta) and density. We first only consider spheroidal modes and Rayleigh waves and restrict the inversion to Vs, Vp and the density. Although it is well known that Vs is the best resolved parameter, we also investigate whether our dataset allows to extract additional information on density and/or Vp. We check whether the determination of the shear wave velocity is affected by the a priori choice of the crustal model (CRUST2.0 or 3SMAC) or by neglecting/coupling poorly resolved parameters. We include the major discontinuities, at 400 and 670 km. Vertical smoothing is imposed through an a priori gaussian covariance matrix on the model and we discuss the effect of coupling/decoupling the inverted structure above and below the discontinuities. We finally discuss the large scale structure of our model and its geodynamical implications regarding the amount of mass exchange between the upper and lower mantle.

  15. Measurement and simulation of ground-coupled air waves and diffracted infrasound from the Kokoxili Earthquake, 14th Nov. 2001

    Guilbert, J.; Le Pichon, A.; Vallee, M.; Alcoverro, B.; Ulziibat, M.


    On November 14, 2001, a strong earthquake measuring Mm 7.8 occurred in the Qinghai Province (China). Coherent infrasonic waves were detected during more than one hour by the IS34 infrasound station in Mongolia (~1500 km from the epicenter). Using an appropriate acoustic propagation model, the inversion of the infrasonic measurements allows a precise localization of the secondary sources distribution along the Qinghai mountains. The predominant source of infrasound is likely ground-coupled air waves generated by the strong variations of topography due to energy carried out by surface seismic waves that travel from the epicenter region through the Qinghai mountains. To confirm the locations of these distant source regions, the pressure field has been reconstructed at IS34. For each element of the topography, a synthetic seismogram used as an input of the integral relation of Huygens-Rayleigh permits to estimate the pressure variation. The synthetic pressure field fit the recorded data in azimuth and in relative amplitude. These results confirm the hypothesis of a strong coupling between the Rayleigh waves and the atmosphere, as it has already been observed during the Arequipa earthquake of June 23rd 2001. The simulations also permit to validate the infrasonic propagation model. This favorable setting within a region of high mountains makes easier the evaluation of the relative contribution of the different source mechanisms involved in large earthquake.

  16. ALE simulation of Rayleigh-Taylor instability

    Anbarlooei, H.R. [Univ. of Science and Technology, Dept. of Mechanical Engineering, Tehran (Iran, Islamic Republic of); Mazaheri, K. [Univ. of Tarbiyat Modares, Dept. of Mechanical Engineering, Tehran, (Iran, Islamic Republic of)]. E-mail:; Bidabadi, M. [Univ. of Science and Technology, Dept. of Mechanical Engineering, Tehran (Iran, Islamic Republic of)


    This paper investigates the use of an Arbitrary Lagrangian-Eulerian (ALE) technique for the simulation of a single mode Rayleigh-Taylor instability. A compatible Lagrangian algorithm is used on a simply connected quadrilateral grid in Lagrangian Phase. This algorithm includes subzonal pressures, which are used to control spurious grid motion, and an edge centered artificial viscosity. We use Reference Jacobians optimization based rezone algorithm in the rezoning phase of ALE method. Also a second order sign preserving method is used for remapping. To force monotonocity in remapping phase a Repair algorithm is used. Finally, for remapping of nodal variables we used a second order transformer to transfer these data to cell centers. It is shown that the usage of these algorithms for an ALE method can improve the simulation of a single mode Rayleigh-Taylor Instability. (author)

  17. Seismic Response to Sonic Boom-Coupled Rayleigh Waves


    microtremor measurements carried out by Instituto de Ingenieria , UNAM and scientists from Japan (for a total of 181 sites). Using this data and the natural... Ingenieria , LINAM. Using this new data and results from the analysis of previous accelerograms we present spectral ratios at 40 sites in the valley of...Esteves. J. M., 1978, Control of vibration caused by blasting: Laboratorio National De Engenharia Civil , Lisboa, Portugal, Memoria 498. Ewing, W. M

  18. Crustal velocity structure of the Deccan Volcanic Province, Indian Peninsula, from observed surface wave dispersion

    Gaddale Suresh


    Full Text Available Through inversion of fundamental mode group velocities of Love and Rayleigh waves, we study the crustal and subcrustal structure across the central Deccan Volcanic Province (DVP, which is one of the world’s largest terrestrial flood basalts. Our analysis is based on broadband seismograms recorded at seismological station Bhopal (BHPL in the central India from earthquakes located near west coast of India, with an average epicentral distance about 768 km. The recording station and epicentral zone are situated respectively on the northern and southern edges of DVP with wave paths across central DVP. The period of group velocity data ranges from 5 to 60 s for Rayleigh waves and 5 to 45 s for Love waves. Using the genetic algorithm, the observed data have been inverted to obtain the crust and subcrustal velocity structure along the wavepaths. Using this procedure, a similar velocity structure was also obtained earlier for the northwestern DVP, which is in the west of the present study region. Comparison of results show that the crustal thickness decreases westward from central DVP (39.6 km to northwestern DVP (37.8 km along with the decrease of thickness of upper crust; while the thickness of lower crust remains nearly same. From east to west S-wave velocity in the upper crust decreases by 2 to 3 per cent, while P-wave velocity in the whole crust and subcrust decreases by 3 to 6 per cent. The P- and S-wave velocities are positively correlated with crustal thickness and negatively correlated with earth’s heat flow. It appears that the elevated crustal and subcrustal temperature in the western side is the main factor for low velocities on this side.

  19. Linking Rayleigh-Rice theory with near linear shift invariance in light scattering phenomena

    Stover, John C.; Schroeder, Sven; Staats, Chris; Lopushenko, Vladimir; Church, Eugene


    Understanding topographic scatter has been the subject of many publications. For optically smooth surfaces that scatter only from roughness (and not from contamination, films or bulk defects) the Rayleigh-Rice relationship resulting from a rigorous electromagnetic treatment has been successfully used for over three decades and experimentally proven at wavelengths ranging from the X-Ray to the far infrared (even to radar waves). The "holy grail" of roughness-induced scatter would be a relationship that is not limited to just optically smooth surfaces, but could be used for any surface where the material optical constants and the surface power spectral density function (PSD) are known. Just input these quantities and calculate the BRDF associated with any source incident angle, wavelength and polarization. This is an extremely challenging problem, but that has not stopped a number of attempts. An intuitive requirement on such general relationships is that they must reduce to the simple Rayleigh-Rice formula for sufficiently smooth surfaces. Unfortunately that does not always happen. Because most optically smooth surfaces also scatter from non-topographic features, doubt creeps in about the accuracy of Rayleigh-Rice. This paper investigates these issues and explains some of the confusion generated in recent years. The authors believe there are measurement issues, scatter source issues and rough surface derivation issues, but that Rayleigh- Rice is accurate as formulated and should not be "corrected." Moreover, it will be shown that the empirically observed near shift invariance of surface scatter phenomena is a direct consequence of the Rayleigh-Rice theory.

  20. Assembling Stabilization of the Rayleigh-Taylor Instability by the Effects of Finite Larmor Radius and Sheared Axial Flow

    Jian Guangde; Huang Lin; Qiu Xiaoming


    The assembling stabilizing effect of the finite Larmor radius (FLR) and the sheared axial