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1.
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 This paper reviews recent work, much of it unpublished, on the effects of anisotropy on seismic waves, and lays the theoretical background for some of the other papers in this number of the Geophysical Journal .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   

2.
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   

3.
Seismic body waves in anisotropic media: propagation through a layer   总被引：3，自引：0，他引：3  
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   

4.
Summary. A formulation is derived for calculating the energy division among waves generated by plane waves incident on a boundary between generally anisotropic media. A comprehensive account is presented for P, SV and SH waves incident from an isotropic half-space on an orthorhombic olivine half-space, where the interface is parallel to a plane of elastic symmetry. For comparison, a less anisotropic medium having transverse isotropy with a horizontal axis of symmetry is also considered. The particle motion polarizations of waves in anisotropic medium differ greatly from the polarizations in isotropic media, and are an important diagnostic of the presence of anisotropy. Incident P and SV waves generate quasi- SH waves, and incident SH waves generate quasi- P and quasi- SV waves, often of considerable relative magnitude. The direction of energy transport diverges from the propagation direction.  相似文献   

5.
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   

6.
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   

7.
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   

8.
The particle motion of regional arrivals is frequently treated in automatic phase-recognition schemes as that appropriate to simple P or S waves incident on an elastic, laterally homogeneous half-space. This model implies that the motion in ' P -type' phases can be described in terms of a single, generalized signal process and ' S -type' phases in terms of two independent processes ( SV and SH ) and thus, all regional arrivals could be fully characterized by three components of motion. In this paper, we present anlyses of the particle-motion patterns of various regional arrivals recorded at the ARCESS array from closely spaced events in the Kola Peninsula. We have found that only Pn -particle motion, described in terms of two independent signal processes, can be reliably characterized by three-component recordings. On the other hand, the various regional arrivals following Pn , such as Pg and Sn and Lg , can only be poorly characterized on the basis of three-component recordings alone. The reason is that these arrivals must be described in terms of more than two independent generalized signal processes, at least three for Pg and Sn , and possibly up to five for Lg . Recognition of these phases will thus require the use of more sensors than signal processes in the observing sensor configuration, such as three-component sensors combined with a small tripartite array. We have investigated the feasibility of adaptive, automatic recognition of regional arrivials by a wavefield extrapolation scheme utilizing such a mini-array. The process, which appear to be promising, adaptively learns the particle-motion patterns of individual arrivals, including complex site-response functions, from examples of closely located regional events.  相似文献   

9.
b
Long-period data of the Global Digital Seismograph Network (GDSN) recorded over the three-year period from 1984 to 1986 were studied for the occurrence of S-P and P-S conversions from the upper mantle transition zone that appear as precursors to teleseismic S arrivals. Conversions of this type were identified on a large number of single-station records. Simple stacking of many records enhanced the appearance of converted phases and demonstrated that no major lateral variations in the nature of the transition zone exist between various tectonic regions. S-P and P-S conversions from the 400 km discontinuity were best observed at distances between 70 and 85 while conversions from the 670 km discontinuity showed up best at distances beyond 87. The analysis of published source mechanisms and comparison with synthetic seismograms suggests that the appearance of converted phases is primarily governed by the earthquake radiation pattern. Phases that have undergone S-P conversions beneath the receiver are best observed from dip-slip events that radiate strong SV - and weak P -waves towards the station. P-S conversions beneath the source area, on the other hand, are frequently observed from events that radiate strong P and little SV energy towards the station, and also from some strike-slip events. Comparison of observed with synthetic seismograms suggests that the PREM model of Dziewonski & Anderson (1981) explains most of the observations. Observed S-P and P-S conversions from the 670 km discontinuity, however, often have larger amplitudes than in the synthetics. Constructive interference of converted waves with the P -wave coda, source radiation effects and a velocity contrast across the 670 km discontinuity which is higher than in PREM may all contribute to the discrepancy.  相似文献   

10.
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   

11.
Shear-wave polarization anisotropy in the Pacific Basin   总被引：1，自引：0，他引：1  
Summary. Inversion of 295. Love- and Rayleigh-wave phase travel times across the Pacific Basin has yielded a structure which has a channel that is anisotropic with respect to the polarization of shear waves. The velocity of SH waves is approximately 4.24 km/s, and the velocity of SV waves is approximately 4.10 km/s in the low-velocity channel. The lid to the channel is isotropic with respect to the polarization of S waves and the velocity is approximately 4.60 km/s. The lid to the low-velocity channel increases in thickness with lithospheric age at the expense of the channel, and its thickness is apparently still increasing at a sea-floor age of 150 Myr.
These results can be explained in terms of a model with both randomly-and preferentially-oriented, liquid-filled cracks in the channel. In the model, it is assumed that the liquid-filled cracks are due to partial melting in the channel, and that any preferred orientation is caused by a shear-flow gradient resulting from differential motion between the lid and the deeper parts of the mantle.  相似文献   

12.
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   

13.
Summary. Approximate methods are applied to problems of internal reflection in a continuous medium when the changes of properties in a wave-length are small. It is found that total internal reflection gives a phase shift of 1/2π in harmonic waves and hence a blunting of a pulse and the introduction of some oscillation.
In the absence of a free surface P and SV movements are substantially independent even if total reflection takes place. SH and SV can travel in an internal layer of low velocity, but will not produce much motion at a free surface unless the total variation of properties is small. P waves in such a channel will suffer attenuation by conversion to SV at the free surface.  相似文献   

14.
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   

15.
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   

16.
This paper investigates the ability of P -wave receiver functions to constrain both the velocity and density contrasts across the Moho. Expressions for receiver function amplitudes corresponding to a layer over a half-space are extended to media with depth-dependent properties by explicitly accounting for free-surface reflection coefficients. Forward numerical computations show that receiver function amplitudes become frequency-dependent for depth-dependent structures and that, for a given frequency, wavelengths associated to Ps converted phases are larger than wavelengths associated to multiply reverberated phases. When consistent measurements of the amplitudes of Ps phase and multiples can be obtained, the extended expressions suffice to account for the observed amplitudes. Receiver function amplitudes are sensitive to both velocity and density contrasts across the Moho, and a two-step grid-search procedure is proposed to recover the contrasts from their measurement. The near-surface velocity is recovered in the first step from the amplitude of the direct P wave and then used in the second step to work out the relative density and S -wave velocity contrast from the amplitude of the secondary phases. Examples from central Spain (PAB) and the Indian Shield (HYB) are discussed and demonstrate that receiver function amplitudes can constrain contrasts across the Moho accurately enough to be utilized in geological interpretation.  相似文献   

17.
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18.
We investigate large-amplitude phases arriving in the P -wave coda of broad-band seismograms from teleseisms recorded by the Gräfenberg array, the German Regional Seismic Network and the Global Seismic Network. The data set consists of all events m b≤ 5.6 from the Aleutian arc between 1977 and 1992. Earthquakes with large-amplitude coda waves correlate with the presence of oceanic crust in the source region. The amplitudes sometimes approach those of the P wave, much larger than predicted by theory. Modelling indicates that phases in the P -wave coda cannot be P -wave multiples beneath the source and receiver, or underside reflections, which precede PP , from upper-mantle discontinuities. Among the events, seismograms are very similar, where the arrival times of the unusual phases agree approximately with the predicted times of S -to- P conversions from the upper-mantle discontinuities under the source. Because the large-amplitude phases in the P -wave coda have little, if any, dependence on event depth and have predominantly an SV -wave radiation pattern towards the receiver, we suggest that they originate as SV and/or Rayleigh waves and are enhanced by lateral heterogeneity and multipathing from the subducting Aleutian slab.  相似文献   

19.
Summary. Peculiarities of propagation in the upper mantle of western Europe are documented by profiles of stations recording body waves generated by explosions. Azimuthal variations of travel times and amplitudes of P waves and possible birefringence of S waves may be associated with an anisotropic layer at depths where the lithosphere-asthenosphere transition is supposed to be.  相似文献   

20.
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   

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