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1.
Summary. The square-root energy ratios and pulse shapes are presented for P, SV and SH waves transmitted through a layer of orthorhombic olivine between two isotropic half-spaces. Off incident planes of symmetry, incident P waves generate two small amplitude SH waves (one from each interface), whose amplitudes decrease slowly with increasing period. Incident SV (or SH ) waves can generate large amplitude SH (or SV ) waves which decrease rapidly with increasing period. For incident S waves, many pulses not present in isotropic models are generated, often of large relative amplitude, with many of the transmitted S pulses showing evidence of double arrivals, either in the form of S-wave splitting, or a modification of the shape of the input waveform. 相似文献
2.
Seismic body waves in anisotropic media: synthetic seismograms 总被引：5，自引：0，他引：5
Summary. Synthetic seismograms and particle motion diagrams are computed for simple, layered Earth models containing an anisotropic layer. The presence of anisotropy couples the P, SV and SH wave motion so that P waves incident on the anisotropic layer from below produce P, SV and small-amplitude SH waves at the surface both the P velocity and the amplitudes of the converted phases vary with azimuth. Significant SH amplitudes may be generated even when the wavelength of the P wave is much greater than the thickness of the anisotropic layer. Incident SV or SH waves may each generate large amplitudes of both SV and SH motion. This strong coupling is largely independent of the degree of velocity anisotropy of the medium. The arrivals from short-period S waves exhibit S-wave splitting, but arrivals from longer period S waves superpose into a modified waveform. This strong coupling does not allow the arrival of separate phases with pure SV and SH polarization except along directions of symmetry where the motion decouples. 相似文献
3.
We study properties of the energy-flux vector and other related energy quantities of homogeneous and inhomogeneous time-harmonic P and S plane waves, propagating in unbounded viscoelastic anisotropic media, both analytically and numerically. We propose an algorithm for the computation of the energy-flux vector, which can be used for media of unrestricted anisotropy and viscoelasticity, and for arbitrary homogeneous or inhomogeneous plane waves. Basic part of the algorithm is determination of the slowness vector of a homogeneous or inhomogeneous wave, which satisfies certain constraints following from the equation of motion. Approaches for determination of a slowness vector commonly used in viscoelastic isotropic media are usually difficult to use in viscoelastic anisotropic media. Sometimes they may even lead to non-physical solutions. To avoid these problems, we use the so-called mixed specification of the slowness vector, which requires, in a general case, solution of a complex-valued algebraic equation of the sixth degree. For simpler cases, as for SH waves propagating in symmetry planes, the algorithm yields simple analytic solutions. Once the slowness vector is known, determination of energy flux and of other energy quantities is easy. We present numerical examples illustrating the behaviour of the energy-flux vector and other energy quantities, for homogeneous and inhomogeneous plane P , SV and SH waves. 相似文献
4.
P-SH conversion is commonly observed in teleseismic P waves, and is often attributed to dipping interfaces beneath the receiver. Our modelling suggests an alternative explanation in terms of flat-layered anisotropy. We use reflectivity techniques to compute three-component synthetic seismograms in a 1-D anisotropic layered medium. For each layer of the medium, we prescribe values of seismic velocities and hexagonally symmetric anisotropy about a common symmetry axis of arbitrary orientation. A compressional wave in an anisotropic velocity structure suffers conversion to both SV -and SH -polarized shear waves, unless the axis of symmetry is everywhere vertical or the wave travels parallel to all symmetry axes. The P-SV conversion forms the basis of the widely used 'receiver function' technique. The P-SH conversion occurs at interfaces where one or both layers are anisotropic. A tilted axis of symmetry and a dipping interface in isotropic media produce similar amplitudes of both direct ( P ) and converted ( Ps ) phases, leaving the backazimuth variation of the P-Ps delay as the main discriminant. Seismic anisotropy with a tilted symmetry axis leads to complex synthetic seismograms in velocity models composed of just a few flat homogeneous layers. It is possible therefore to model observations of P coda with prominent transverse components with relatively simple 1-D velocity structures. Successful retrieval of salient model characteristics appears possible using multiple realizations of a genetic-algorithm (GA) inversion of P coda from several backazimuths. Using GA inversion, we determine that six P coda recorded at station ARU in central Russia are consistent with models that possess strong (> 10 per cent) anisotropy in the top 5 km and between 30 and 43 km depth. The symmetry axes are tilted, and appear aligned with the seismic anisotropy orientation in the mantle under ARU suggested by SKS splitting. 相似文献
5.
Split S waves observed at Hockley, Texas from events in the Tonga–Fiji region of the southwest Pacific show predominantly vertically polarized shear-wave ( SV ) energy arriving earlier than horizontally polarized ( SH ) energy for rays propagating horizontally through D" . After corrections are made for the effects of upper-mantle anisotropy beneath Hockley, a time lag of 1.5 to 2.0 s remains for the furthest events (93.9°–100.6° ), while the time lags of the nearer observations (90.5°–92.9° ) nearly disappear. At closer distances, the S waves from these same events do not penetrate as deeply into the lower mantle, and are not split. These observations suggest that a patch of D" beneath the central Pacific is anisotropic, while the mantle immediately above the patch is isotropic. The thickness of the anisotropic zone appears to be of the order of 100–200 km.
Observations of shear-wave splitting have previously been made for paths that traverse D" under the Caribbean and under Alaska. SH leads SV , the reverse of the Hockley observations, but in these areas the fact that SV leads SH in the HKT data shown here suggests a different sort of anisotropy under the central Pacific from that under Alaska and the Caribbean. The case of SH travelling faster than SV is consistent with transverse isotropy with a vertical axis of symmetry (VTI) and does not require variations with azimuth. The case of SV leading SH is consistent with transverse isotropy with a horizontal axis of symmetry (HTI), an azimuthally anisotropic medium, and with a VTI medium formed by a hexagonal crystal. Given that (Mg,Fe)SiO3 perovskite appears unlikely to form anisotropic fabrics on a large scale, the presence of anisotropy may point to chemical heterogeneity in the lowermost mantle, possibly due to mantle–core interactions. 相似文献
Observations of shear-wave splitting have previously been made for paths that traverse D" under the Caribbean and under Alaska. SH leads SV , the reverse of the Hockley observations, but in these areas the fact that SV leads SH in the HKT data shown here suggests a different sort of anisotropy under the central Pacific from that under Alaska and the Caribbean. The case of SH travelling faster than SV is consistent with transverse isotropy with a vertical axis of symmetry (VTI) and does not require variations with azimuth. The case of SV leading SH is consistent with transverse isotropy with a horizontal axis of symmetry (HTI), an azimuthally anisotropic medium, and with a VTI medium formed by a hexagonal crystal. Given that (Mg,Fe)SiO
6.
Václav Vavry&#;uk 《Geophysical Journal International》1997,130(3):786-800
An explicit analytical formula for the complete elastodynamic Green tensor for homogeneous unbounded weak transversely isotropic media is presented. The formula was derived by analytical calculations of higher-order approximations of the ray series. The ray series is finite and consists of seven non-zero terms. The formula for the Green tensor is complete and correct for the whole frequency range, thus it describes correctly the wavefield at all distances and at all directions including the shear-wave singularity direction. The Green tensor consists of P, SV and SH far-field waves and four coupling waves. Three of them couple P and SV waves, and the fourth wave couples the SV and SH waves. The P-SV coupling waves behave similarly to the near-field waves in isotropy. However, the SV-SH coupling wave, which is called 'shear-wave coupling', behaves exceptionally and it has no analogy in the Green tensor for isotropy. The formula for the elastostatic Green tensor is also derived. 相似文献
7.
Summary. Seismic investigations using shear-wave and converted wave techniques show that very often reflected PS - and SS -waves have anomalous polarizations ( accessory components ). This phenomenon cannot be explained in terms of isotropic models with dipping boundaries. Computations of synthetic seismograms of reflected PS - and SS -waves were made for different models of transversely isotropic media with dipping anisotropic symmetry axes not normal to the boundaries. Synthetic seismograms were computed by ray techniques using an optimization algorithm to construct all rays arriving at a given receiver. These computations indicate that accessory components arise when the medium above the boundary is anisotropic, where they are caused by the constructive interference of qSV - and qSH -waves. If a low-velocity layer is present, displacement vectors of both waves have horizontal projections which are approximately orthogonal. The algorithm for wave separation is presented and some results of its use are given. 相似文献
8.
Kurt Lambeck 《Geophysical Journal International》1981,67(1):91-114
Summary. The response of a stratified elastic medium can be conveniently characterized by the Green's tensor for the medium. For coupled seismic wave propagation ( P—SV or fully anisotropic), the Green's tensor may be constructed directly from two matrices of linearly independent displacement solutions. Rather simple forms for the Green's tensor can be found if each displacement matrix satisfies one of the boundary conditions on the seismic field. This approach relates directly to 'reflection matrix' representations of the seismic field.
For a stratified elastic half space the Green's tensor is used to give a spectral representation for coupled seismic waves. By means of a contour integration a general completeness relation is obtained for the 'body wave' and 'surface wave' parts of the seismic field. This relation is appropriate for SH and P–SV waves in an isotropic medium and also for full anisotropy. 相似文献
For a stratified elastic half space the Green's tensor is used to give a spectral representation for coupled seismic waves. By means of a contour integration a general completeness relation is obtained for the 'body wave' and 'surface wave' parts of the seismic field. This relation is appropriate for SH and P–SV waves in an isotropic medium and also for full anisotropy. 相似文献
9.
M. D. Sharma 《Geophysical Journal International》2008,174(3):971-977
Out of the four waves in an anisotropic poroelastic medium, two are termed as quasi-transverse waves. The prefix 'quasi' refers to their polarizations being nearly, but not exactly, perpendicular to direction of propagation. In this composite medium, unlike perfectly elastic medium, the propagation of a longitudinal wave along a phase direction may not be accompanied by transverse waves. The existence of a transverse wave in anisotropic poroelastic media is ensured by the two equations restricting the choice of elastic coefficients of porous aggregate as well as fluid–solid coupling. Necessary and sufficient conditions for the existence of transverse waves along the coordinate axes and in the coordinate planes for general anisotropy are discussed. The discussion is extended to the case of orthotropic materials and existence for few specific phase directions is also explored. The conditions for the transverse waves decided on the basis of their apparent polarizations, that is, particle motion being perpendicular to ray direction, are also discussed. For a particular numerical model, the existence of these apparent transverse waves is solved numerically for phase directions in coordinate planes. For general directions of phase propagation, the existence of these transverse waves is checked graphically for the chosen numerical model. 相似文献
10.
A review of the effects of anisotropic layering on the propagation of seismic waves 总被引：10，自引：0，他引：10
Stuart Crampin 《Geophysical Journal International》1977,49(1):9-27
Summary. This paper reviews recent work, much of it unpublished, on the effects of anisotropy on seismic waves, and lays the theoretical background for some of the other papers in this number of the Geophysical Journal .
The propagation of both body and surface waves in anisotropic media is fundamentally different from their propagation in isotropic media, although the differences in behaviour may be comparatively subtle and difficult to observe. One of the most diagnostic of these anomalies, which has been observed on some surface-wave trains, and should be evident in body-wave arrivals, is generalized, three-dimensional polarization, where the Rayleigh motion is coupled to the Love, and the P and SV motion is coupled to the SH . This coupling introduces polarization anomalies which may be used to investigate anisotropy within the Earth. 相似文献
The propagation of both body and surface waves in anisotropic media is fundamentally different from their propagation in isotropic media, although the differences in behaviour may be comparatively subtle and difficult to observe. One of the most diagnostic of these anomalies, which has been observed on some surface-wave trains, and should be evident in body-wave arrivals, is generalized, three-dimensional polarization, where the Rayleigh motion is coupled to the Love, and the P and SV motion is coupled to the SH . This coupling introduces polarization anomalies which may be used to investigate anisotropy within the Earth. 相似文献
11.
Evidence for anisotropy in the upper mantle beneath Eurasia from the polarization of higher mode seismic surface waves 总被引：1，自引：0，他引：1
Summary. Analysis of NORSAR records and a number of Soviet microfilms reveals second-mode surface Caves propagating along paths covering a large part of Eurasia. These second modes in the 6–15-s period band are frequently disturbed by other surface-wave modes and by body-wave arrivals. However, in all cases, where the modes appear to be undisturbed and show normal dispersion, the Second Rayleigh modes have a slowly varying phase difference with the Second Love modes. This coupling has the particle motion of Inclined Rayleigh waves characteristic of surface-wave propagation in anisotropic media, where the anisotropy possesses a horizontal plane of symmetry. Numerical examination of surface wave propagating in Earth models, with an anisotropic layer in the upper mantle, demonstrate that comparatively small thicknesses of material with weak velocity anisotropy can produce large deviations in the polarizations of Inclined Rayleigh Second modes. In many structures, these inclinations are very sensitive to small changes in anisotropic orientation and to small changes in the surrounding isotropic structure. It is suggested that examination of second mode inclination anomalies of second mode surface waves may be a powerful technique for examining the detailed anisotropic structure of the upper mantle. 相似文献
12.
Matthias Zillmer Boris Kashtan & Dirk Gajewski 《Geophysical Journal International》1998,132(3):643-653
Wave propagation in weakly anisotropic inhomogeneous media is studied by the quasi-isotropic approximation of ray theory. The approach is based on the ray-tracing and dynamic ray-tracing differential equations for an isotropic background medium. In addition, it requires the integration of a system of two complex coupled differential equations along the isotropic ray.
The interference of the qS waves is described by traveltime and polarization corrections of interacting isotropic S waves. For qP waves the approach leads to a correction of the traveltime of the P wave in the isotropic background medium.
Seismograms and particle-motion diagrams obtained from numerical computations are presented for models with different strengths of anisotropy.
The equivalence of the quasi-isotropic approximation and the quasi-shear-wave coupling theory is demonstrated. The quasi-isotropic approximation allows for a consideration of the limit from weak anisotropy to isotropy, especially in the case of qS waves, where the usual ray theory for anisotropic media fails. 相似文献
The interference of the qS waves is described by traveltime and polarization corrections of interacting isotropic S waves. For qP waves the approach leads to a correction of the traveltime of the P wave in the isotropic background medium.
Seismograms and particle-motion diagrams obtained from numerical computations are presented for models with different strengths of anisotropy.
The equivalence of the quasi-isotropic approximation and the quasi-shear-wave coupling theory is demonstrated. The quasi-isotropic approximation allows for a consideration of the limit from weak anisotropy to isotropy, especially in the case of qS waves, where the usual ray theory for anisotropic media fails. 相似文献
13.
Summary. We present polarization diagrams of the particle motions at the free surface of an isotropic half-space generated by incident shear waves from a local buried point source. The reflectivity technique is used to calculate synthetic seismograms from which the particle motions are plotted. The particle motions are examined over a range of epicentral distances in a uniform isotropic half-space for different source frequencies and polarization angles, and for different Poisson's ratios. The particle motions due to a curved wavefront possess different characteristics from those generated by plane wavefronts at corresponding incidence angles. A curved wavefront generates a local SP -phase: a P -headwave which propagates along the free surface, and arrives shortly before the direct S -wave. These two arrivals give rise to cruciform particle motions in the sagittal and horizontal planes, which could be misinterpreted as anisotropy-induced shear-wave splitting. An examination of the particle motion in the transverse plane, mutually orthogonal to the sagittal and horizontal planes, can be used to discriminate between isotropic and anisotropic interpretations. The amplitude of the SP -phase is enhanced when it propagates in a low-velocity surface layer overlying the source layer, and may then become the dominant phase on radial-component seismograms. The presence of even a single surface layer may introduce considerable complexity into the seismogram, and we examine the effects of layer thickness, velocity contrast, and source depth on the corresponding polarization diagrams. Reliable information on the source and propagation path characteristics of shear waves from a buried local point source can only be obtained from free-surface records if they are recorded within a very limited epicentral distance range. 相似文献
14.
Summary. Polarization anomalies in seismic shear wavetrains, diagnostic of propagation through anisotropic media, have now been observed in dilatancy zones in seismic regions. Stress-induced dilatancy will open cracks with preferred orientations, which will be effectively anisotropic to short-period seismic waves. The polarization anomalies are due to the shear waves splitting, in propagation through anisotropic media, into components with different polarizations and different velocities. This writes characteristic signatures into the shear wavetrains. The paper examines ways in which the differential shear-wave anisotropy (the delay between the split shear-waves) varies with direction by plotting stereograms of the relative delays, and their polarizations, for possible dilatancy symmetry-systems. It seems likely, that if sufficient observations of these anomalies can be obtained at each stage of the dilatancy episode, it will be possible to estimate the symmetry directions of the dilatancy and the geometry of the stress-induced crack-system, as well as monitoring the progress of the dilatancy episode. 相似文献
15.
F. Luzón F. J. Sánchez-Sesma J. L. Rodríguez-Zúñiga A. M. Posadas J. M. García J. Martin M. D. Romacho M. Navarro 《Geophysical Journal International》1997,129(3):571-578
The diffraction of P, S and Rayleigh waves by 3-D topographies in an elastic half-space is studied using a simplified indirect boundary element method (IBEM). This technique is based on the integral representation of the diffracted elastic fields in terms of single-layer boundary sources. It can be seen as a numerical realization of Huygens principle because diffracted waves are constructed at the boundaries from where they are radiated by means of boundary sources. A Fredholm integral equation of the second kind for such sources is obtained from the stress-free boundary conditions. A simplified discretization scheme for the numerical and analytical integration of the exact Green's functions, which employs circles of various sizes to cover most of the boundary surface, is used.
The incidence of elastic waves on 3-D topographical profiles is studied. We analyse the displacement amplitudes in the frequency, space and time domains. The results show that the vertical walls of a cylindrical cavity are strong diffractors producing emission of energy in all directions. In the case of a mountain and incident P, SV and SH waves the results show a great variability of the surface ground motion. These spatial variations are due to the interference between locally generated diffracted waves. A polarization analysis of the surface displacement at different locations shows that the diffracted waves are mostly surface and creeping waves. 相似文献
The incidence of elastic waves on 3-D topographical profiles is studied. We analyse the displacement amplitudes in the frequency, space and time domains. The results show that the vertical walls of a cylindrical cavity are strong diffractors producing emission of energy in all directions. In the case of a mountain and incident P, SV and SH waves the results show a great variability of the surface ground motion. These spatial variations are due to the interference between locally generated diffracted waves. A polarization analysis of the surface displacement at different locations shows that the diffracted waves are mostly surface and creeping waves. 相似文献
16.
Implementation of perfectly matched layers in an arbitrary geometrical boundary for elastic wave modelling 总被引：1，自引：0，他引：1
The perfectly matched layer (PML) absorbing boundary condition is incorporated into an irregular-grid elastic-wave modelling scheme, thus resulting in an irregular-grid PML method. We develop the irregular-grid PML method using the local coordinate system based PML splitting equations and integral formulation of the PML equations. The irregular-grid PML method is implemented under a discretization of triangular grid cells, which has the ability to absorb incident waves in arbitrary directions. This allows the PML absorbing layer to be imposed along arbitrary geometrical boundaries. As a result, the computational domain can be constructed with smaller nodes, for instance, to represent the 2-D half-space by a semi-circle rather than a rectangle. By using a smooth artificial boundary, the irregular-grid PML method can also avoid the special treatments to the corners, which lead to complex computer implementations in the conventional PML method. We implement the irregular-grid PML method in both 2-D elastic isotropic and anisotropic media. The numerical simulations of a VTI lamb's problem, wave propagation in an isotropic elastic medium with curved surface and in a TTI medium demonstrate the good behaviour of the irregular-grid PML method. 相似文献
17.
Summary. The paper gives the results of a study of the anisotropy of seismic wave velocities within the Ashkhabad test field in Central Asia. The anisotropy was studied by analysing variations in the values of apparent velocities of first arrivals for epicentral distances ranging from 30 to 130 km and by analysing the delays (Δ ts1 -s2 ) between the arrival times of shear waves with different polarizations.
The velocities of P -waves vary with azimuth from 5.3 to 6.27 km s-1 and the velocities of S -waves vary from 3.15 to 3.5 km s-1 .
The delay times Δ tS1 - S2 depend on the direction of the propagation. The character of the variation of the propagation velocity of the longitudinal wave, the presence of two differently polarized shear waves S 1 and S 2 propagating at different velocities, and the character of the distribution of Δ tS1 - S2 on the stereogram suggest that the symmetry of the anisotropic medium is close to hexagonal with a nearly horizontal symmetry axis coinciding with the direction of maximal velocity. The azimuth of the symmetry axis of the medium is 140° and coincides with the direction of geological faults. 相似文献
The velocities of P -waves vary with azimuth from 5.3 to 6.27 km s
The delay times Δ t
18.
Summary. The symmetry relations between the reflection and transmission coefficients for plane elastic waves incident upon an arbitrary horizontally stratified medium are derived by a novel approach. Previous results, particularly for a single interface, are obtained as special cases of this treatment.
In addition, for perfectly elastic media, projection operators for travelling and evanescent waves are introduced and used to derive a number of new relationships between the reflection and transmission coefficients. 相似文献
In addition, for perfectly elastic media, projection operators for travelling and evanescent waves are introduced and used to derive a number of new relationships between the reflection and transmission coefficients. 相似文献
19.
Reflection coefficients for weak anisotropic media 总被引：1，自引：0，他引：1
Matthias Zillmer Dirk Gajewski Boris M. Kashtan 《Geophysical Journal International》1997,129(2):389-398
The interaction of plane elastic waves with a plane boundary between two anisotropic elastic half-spaces is investigated. The anisotropy dealt with in this study is of a general type. Explicit expressions for energy-related reflection and transmission coefficients are derived. They represent an approximation which is valid for a small deviation of the elastic parameters from isotropy.
Classical perturbation theory is applied on a 6times6 non-symmetric real eigenvalue problem to calculate first-order corrections for the polarization and stress of the plane waves. The explicit solution of the isotropic problem is used as a reference case. Degenerate perturbation theory is used to consider the splitting of the isotropic S -wave into two anisotropic qS-waves. The boundary conditions for two half-spaces in welded contact lead to a 6times6 system of linear equations. A correction to the isotropic solution is calculated by linearization. The resultant coefficients are functions of horizontal slowness, Lamé parameters and densities of the reference media, and of the perturbation of the elasticity tensors from isotropy. 相似文献
Classical perturbation theory is applied on a 6times6 non-symmetric real eigenvalue problem to calculate first-order corrections for the polarization and stress of the plane waves. The explicit solution of the isotropic problem is used as a reference case. Degenerate perturbation theory is used to consider the splitting of the isotropic S -wave into two anisotropic qS-waves. The boundary conditions for two half-spaces in welded contact lead to a 6times6 system of linear equations. A correction to the isotropic solution is calculated by linearization. The resultant coefficients are functions of horizontal slowness, Lamé parameters and densities of the reference media, and of the perturbation of the elasticity tensors from isotropy. 相似文献
20.
T. J. Clarke 《Geophysical Journal International》1984,78(3):775-793
Summary. We develop a méthod of reconstructing the elastic paraméters as functions of depth, for a horizontally stratified, isotropic elastic half-space. Unlike previous schemes, which have been able to retrieve the shear wave speed and density from SH seismograms slant stacked at two angles, our méthod makes use of P - SV data at a single stacking paraméter to obtain all three elastic constants. The data required are the elements of the full reflection matrix at the surface, corresponding to measurements of two separate components of the response to two independent sources, one explosive, the other generating shear waves.
In developing this inverse scheme fundamental differences emerge between the acoustic or SH problem, and the coupled P - SV case, the most important being in the nature of the interfacial scattering matrix. We show that it is not possible to make use of the downward reflection data for an interface to determine directly the remaining reflection and transmission coefficients, but that the scattering data may be completed by applying a simple iterative procedure at each interface.
We show the result of applying our inverse scheme to seismograms generated for a six-layered model, including a low-velocity layer. We are able to reconstruct both wave speeds and the density as functions of depth, all quantities being in close agreement with the original model. 相似文献
In developing this inverse scheme fundamental differences emerge between the acoustic or SH problem, and the coupled P - SV case, the most important being in the nature of the interfacial scattering matrix. We show that it is not possible to make use of the downward reflection data for an interface to determine directly the remaining reflection and transmission coefficients, but that the scattering data may be completed by applying a simple iterative procedure at each interface.
We show the result of applying our inverse scheme to seismograms generated for a six-layered model, including a low-velocity layer. We are able to reconstruct both wave speeds and the density as functions of depth, all quantities being in close agreement with the original model. 相似文献