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Elastic wave propagation in layered anisotropic media
J. geophys. Res, 1961
A hstrad. This is :-m aJia.ly.�iH of l.l1c dispersive propf)rties of trnnsvcr. �cly isot.ropie media.. This kind of anisotropy is exhibited by hexagonal crystals, sediments, planar igneous bodies, ice sheets, and rolled metal sheets where the unique axis is perpendicular to the direction of surface wave propagation and the other axes are distributed randomly in the plane of the layers. Period equat ions are derived for waves of Rayleigh, Stoneley, and Love types, and comparisons are made, in certain cases, with ray theoretical and plane stress solutions. Anisotropy can have a pronounced effect on both the range of existence and the shape of the dispersion curves and can lead to an apparent discrepancy between Love and Rayleigh wave data. Attention is focused in this initial paper on a single solid layer in vacuo (i.e. a free plate) and a solid layer in contact with a fluid half space. The single layer solutions are generalized ton-layer media by the use of Haskell matrices. l. Introduction. Elastic wave problems are
ON FREE WAVE PROPAGATION IN ANISOTROPIC LAYERED MEDIA
ACTA MECHANICA SOLIDA SINICA, 2008
The method of reverberation-ray matrix (MRRM) is extended and modified for the analysis of free wave propagation in anisotropic layered elastic media. A general, numerically stable formulation is established within the state space framework. The compatibility of physical variables in local dual coordinates gives the phase relation, from which exponentially growing functions are excluded. The interface and boundary conditions lead to the scattering relation, which avoids matrix inversion operation. Numerical examples are given to show the high accuracy of the present MRRM.
Bulletin of the Seismological Society of America, 2008
We investigate the effect of seismic anisotropy on P-wave receiver functions, calculating synthetic seismograms for P-wave incidence on multilayered anisotropic structure with hexagonal symmetry. The main characteristics of the receiver functions affected by the anisotropy are summarized as (1) appearance of seismic energy on radial and transverse receiver functions, (2) systematic change of P-to-S (Ps) converted waveforms on receiver functions as ray back-azimuth increases, and (3) reversal of the Ps-phase polarity on the radial receiver function in a range of the back azimuth. Another important influence is shear-wave splitting of the Ps-converted waves and other later phases reverberated as S wave. By numerical experiments using synthetic receiver functions, we demonstrate that the waveform cross-correlation analysis is applicable to splitting Ps phases on receiver functions to estimate the seismic anisotropy of layer structure. Advantages to utilizing the Ps phases are (1) they appear more clearly on receiver functions than on seismograms and (2) they inform us about what place along the seismic ray path is anisotropic. Real analysis of shear-wave splitting is executed to the Moho-generated Ps phases that are identified on receiver functions at six seismic stations in the Chugoku district, southwest Japan. The time lags between the two arrivals of the split Ps phases are estimated at 0.2-0.7 sec, and the polarization directions of the fast arrival components are from north-south to northeast-southwest. This result is consistent with recent results of shear-wave splitting measurements and the trend of linear epicenter distributions of crustal earthquakes and active fault strikes in the Chugoku district.
High-frequency radiation from earthquake sources in laterally varying layered structures
Geophysical Journal International, 1987
Downloaded from https://academic.oup.com/gji/article/88/1/43/568854 by guest on 26 April 2021 V. terverr.$ et a]. and, perhaps, even faster than the isochrone method. Numerical examples are presented, in which the Gaussian beam synthetic ground-velocity seismograms, evaluated for a rather complex faulting model, are compared with those calculated by the isochrone method and by the finite-element/discrete wavenumber method, based on the complete Green tensor. The comparisons indicate that the Gaussian beam method yields sufficiently accurate results.
A spectral scheme for wave propagation simulation in 3-D elastic-anisotropic media
Geophysics, 1992
This work presents a new scheme for wave propagation simulation in three-dimensional (3-D) elasticanisotropic media. The algorithm is based on the rapid expansion method (REM) as a time integration algorithm, and the Fourier pseudospectral method for computation of the spatial derivatives. The REM expands the evolution operator of the second-order wave equation in terms of Chebychev polynomials, constituting an optimal series expansion with exponential convergence. The modeling allows arbitrary elastic coefficients and density in lateral and vertical directions.
Mathematical modeling of seismic wave propagation in layered media
An analytically based computer model for transient pulse propagation in a layered elastic half-space is developed. The model involves an explicit integral representation derived in terms of an elastodynamic Green's matrix for the half-space. The model is intended to simulate waves from a distant impulsive source. Certain resonance phenomena associated with the specific structure of the dispersion curves for the layered medium are discussed. These results may be helpful for seismic protection and earthquake resistant construction.
Earthquake wave propagation in layered media by boundary integral methods
Soil Dynamics and Earthquake Engineering, 1991
The authors have previously presented work on the use of boundary methods to solve steadystate wave scattering problems in two-dimensional homogeneous systems and on the use of these solutions with Fourier transforms to solve problems of transient input waves. This paper extends that work to nonhomogeneous systems. The methodology is now applicable to profiles with various material parameters in media bounded by irregularly shaped interfaces subjected to transient or periodic incident waves of any form. The profiles which can be solved are layers of finite extent, layers of infinite extent, cavities, inclusions of different materials, lenses, cases of three media and three interfaces meeting at a single point, and any combination thereof. The paper presents the basic equations of wave propagation in a single medium, the extension of these equations to multiple media, and the methodology of correcting for the truncation of the numerical portions of a problem. Using these techniques, several simple geometries are solved and the solutions are compared to closed-form solutions when available. The comparisons are good and the value of correcting for the truncation is verified. The methodology is then applied to a test case of real data taken from real earthquake records, to wit: the response of the Santa Felicia earth dam to the San Fernando (1971) earthquake. The comparison is good in the time domain but in the frequency domain shows some inaccuracy at the higher frequencies. This loss of quality is attributed to the fact that a linear elastic system is not a good model for soil response. The final section is an initial attempt to examine the effects of some simple damping schemes. Great improvement is shown in the attempt to reproduce numerically the response of the Santa Felicia earth dam.
Studia Geophysica et Geodaetica, 2004
Anisotropic material properties are usually neglected during inversions for source parameters of earthquakes. In general anisotropic media, however, moment tensors for pure-shear sources can exhibit significant non-double-couple components. Such effects may be erroneously interpreted as an indication for volumetric changes at the source. Here we investigate effects of anisotropy on seismic moment tensors and radiation patterns for pure-shear and tensile-type sources. Anisotropy can significantly influence the interpretation of the source mechanisms. For example, the orientation of the slip within the fault plane may affect the total seismic moment. Also, moment tensors due to pureshear and tensile faulting can have similar characteristics depending on the orientation of the elastic tensor. Furthermore, the tensile nature of an earthquake can be obscured by near-source anisotropic properties. As an application, we consider effects of inhomogeneous anisotropic properties on the seismic moment tensor and the radiation patterns of a selected type of micro-earthquakes observed in W-Bohemia. The combined effects of near-source and along-path anisotropy cause characteristic amplitude distortions of the P, S1 and S2 waves. However, the modeling suggests that neither homogeneous nor inhomogeneous anisotropic properties alone can explain the observed large non-doublecouple components. The results also indicate that a correct analysis of the source mechanism, in principle, is achievable by application of anisotropic moment tensor inversion.
Reflection and transmission coefficients for seismic waves in ellipsoidally anisotropic media
GEOPHYSICS, 1979
The paper presents a Fourier transform-based signal processing procedure for quantifying the reflection and transmission coefficients and mode conversion of guided waves diffracted by defects in plates made of viscoelastic materials. The case of the S 0 Lamb wave mode incident on a notch in a Perspex plate is considered. The procedure is applied to numerical data produced by a finite element code that simulates the propagation of attenuated guided modes and their diffraction by the notch, including mode conversion. Its validity and precision are checked by the way of the energy balance computation and by comparison with results obtained using an orthogonality relation-based processing method.
Universal Journal of Mechanical Engineering, 2018
A theoretical study of seismic waves propagation in a soil layer with a free surface has a great importance for a prediction in engineering decisions. Wave packets are radiated from an earthquake source and transfer energy. A transformation and a selection of wave packets occur in a process of wave propagating that why waves which arrive in a layer have a length considerably greater than a variation scale of heterogeneity in a medium in a layer near free surface. In the case, when the properties of different layers affect a relatively small degree on a behavior of the waves, an approximation of effective medium gives a fairly good solution. A model of a hypoplastic medium is used for a describing of some effects, which are observed in the time of seismic wave propagation. The model of hypoplastic medium allows describing many effects which are observed in granular soils. We consider a successive application of effective medium and ray methods in order to receive of approximate analytical solutions wishing to describe shear wave propagation in stratified layer, which lies on a half-space.