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1.
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   

2.
Summary Isotropic earth models are unable to provide uniform fits to the gross Earth normal mode data set or, in many cases, to regional Love-and Rayleigh-wave data. Anisotropic inversion provides a good fit to the data and indicates that the upper 200km of the mantle is anisotropic. The nature and magnitude of the required anisotropy, moreover, is similar to that found in body wave studies and in studies of ultramafic samples from the upper mantle. Pronounced upper mantle low-velocity zones are characteristic of models resulting from isotropic inversion of global or regional data sets. Anisotropic models have more nearly constant velocities in the upper mantle.
Normal mode partial (Frediét) derivatives are calculated for a transversely isotropic earth model with a radial axis of symmetry. For this type of anisotropy there are five elastic constant. The two shear-type moduli can be determined from the toroidal modes. Spheroidal and Rayleigh modes are sensitive to all five elastic constants but are mainly controlled by the two compressional-type moduli, one of the shear-type moduli and the remaining, mixed-mode, modulus. The lack of sensitivity of Rayleigh waves to compressional wave velocities is a characteristic only of the isotropic case. The partial derivatives of the horizontal and vertical components of the compressional velocity are nearly equal and opposite in the region of the mantle where the shear velocity sensitivity is the greatest. The net compressional wave partial derivative, at depth, is therefore very small for isotropic perturbations. Compressional wave anisotropy, however, has a significant effect on Rayleigh-wave dispersion. Once it has been established that transverse anisotropy is important it is necessary to invert for all five elastic constants. If the azimuthal effect has not been averaged out a more general anisotropy may have to be allowed for.  相似文献   

3.
Large scale seismic anisotropy in the Earth's mantle is likely dynamically supported by the mantle's deformation; therefore, tomographic imaging of 3-D anisotropic mantle seismic velocity structure is an important tool to understand the dynamics of the mantle. While many previous studies have focused on special cases of symmetry of the elastic properties, it would be desirable for evaluation of dynamic models to allow more general axis orientation. In this study, we derive 3-D finite-frequency surface wave sensitivity kernels based on the Born approximation using a general expression for a hexagonal medium with an arbitrarily oriented symmetry axis. This results in kernels for two isotropic elastic coefficients, three coefficients that define the strength of anisotropy, and two angles that define the symmetry axis. The particular parametrization is chosen to allow for a physically meaningful method for reducing the number of parameters considered in an inversion, while allowing for straightforward integration with existing approaches for modelling body wave splitting intensity measurements. Example kernels calculated with this method reveal physical interpretations of how surface waveforms are affected by 3-D velocity perturbations, while also demonstrating the non-linearity of the problem as a function of symmetry axis orientation. The expressions are numerically validated using the spectral element method. While challenges remain in determining the best inversion scheme to appropriately handle the non-linearity, the approach derived here has great promise in allowing large scale models with resolution of both the strength and orientation of anisotropy.  相似文献   

4.
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   

5.
Summary. Various factors can make it difficult to explain observations of Love- and Rayleigh-wave dispersion with the same relatively simple isotropic model. These factors include systematic errors which might occur in determinations of observed group and phase velocities, lateral variations in structure along the path of travel, and the attempt to explain observations with a model comprised of only a small number of thick layers. The last of these factors is illustrated by an inversion of dispersion data in the central United States where shear-wave anisotropy had previously been invoked as one way to explain incompatible Love- and Rayleigh-wave velocities. It is shown that the data can be satisfied equally well by an isotropic model consisting of several thin layers.
In cases where the incompatibility of Love- and Rayleigh-wave data might be produced by intrinsic anisotropy, it is necessary to invert those data using an anisotropic theory rather than by separate isotropic inversions of Love and Rayleigh waves. Inversions of fundamental-mode data for a region of the Pacific, assuming anisotropic media in which the layers are transversely isotropic with a vertical axis of symmetry, lead to models which are highly non-unique. Even if the inversions solve only for shear velocities in the litho-sphere and asthenosphere it is not possible, without supplementary information, to ascertain the depth interval over which anisotropy occurs or to determine the thickness of the lithosphere or asthenosphere with much precision.  相似文献   

6.
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   

7.
Amplitude measurements of the transverse component of SKS waves, the so-called splitting intensity, can be used to formulate a non-linear inverse problem to image the 3-D variations of upper mantle anisotropy. Assuming transverse isotropy (or hexagonal symmetry), one can parametrize anisotropy by two anisotropic parameters and two angles describing the orientation of the symmetry axis. These can also be written as two collinear pseudo-vectors. The tomographic process consists of retrieving the spatial distribution of these pseudo-vectors, and thus resembles surface wave vectorial tomography. Spatial resolution results from the sensitivity of low-frequency SKS waves to seismic anisotropy off the ray path. The expressions for the 3-D sensitivity kernels for splitting intensity are derived, including the near-field contributions, and validated by comparison with a full wave equation solution based upon the finite element method. These sensitivity kernels are valid for any orientation of the symmetry axis, and thus generalize previous results that were only valid for a horizontal symmetry axis. It is shown that both lateral and vertical subwavelength variations of anisotropy can be retrieved with a dense array of broad-band stations, even in the case of vertically propagating SKS waves.  相似文献   

8.
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   

9.
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   

10.
It is well established that the Earth's uppermost mantle is anisotropic, but there are no clear observations of anisotropy in the deeper parts of the mantle. Surface waves are well suited to observe anisotropy since they carry information about both radial and azimuthal anisotropy. Fundamental mode surface waves, for commonly used periods up to 200 s, are sensitive to structure in the first few hundred kilometres, and therefore, do not provide information on anisotropy below. Higher mode surface waves have sensitivities that extend to and beyond the transition zone, and should thus give insight about azimuthal anisotropy at greater depths. We have measured higher mode Love and Rayleigh phase velocities using a model space search approach, which provides us with consistent relative uncertainties from measurement to measurement and from mode to mode. From these phase velocity measurements, we constructed global anisotropic phase velocity maps. Prior to inversion, we determine the optimum relative weighting for anisotropy. We present global azimuthal phase velocity maps for higher mode Rayleigh waves (up to the sixth higher mode) and Love waves (up to the fifth higher mode) with corresponding average model uncertainties. The anisotropy we derive is robust within the uncertainties for all modes. Given the ray theoretical sensitivity kernels of Rayleigh and Love wave modes, the source of anisotropy is complex, but mainly located in the asthenosphere and deeper. Our models show a good correspondence with other studies for the fundamental mode, but we have been able to achieve higher resolution.  相似文献   

11.
Shear-wave splitting from local deep earthquakes is investigated to clarify the volume and the location of two anisotropic bodies in the mantle wedge beneath central Honshu, Japan. We observe a spatial variation in splitting parameters depending on the combination of sources and receivers, nearly N–S fast in the northern region, nearly E–W fast in the southern region and small time delays in the eastern region. Using forward modelling, two models with 30 and 10 per cent anisotropy are tested by means of a global search for the locations of anisotropic bodies with various volumes. The optimum model is obtained for 30 per cent anisotropy, which means a 5 per cent velocity difference between fast and slow polarized waves. The northern anisotropic body has a volume of 1.00° (longitude) × 0.5° (latitude) × 75 km (depth), with the orientation of the symmetry axis being N20°E. The southern anisotropic body has a volume of 1.25° × 1.25° × 100 km with the symmetry axis along N95°E. Our results show that the anisotropic bodies are located in low-velocity and low- Q regions of the mantle. This, together with petrological data and the location of volcanoes in the arc, suggests that the possible cause of the anisotropy is the preferred alignment of cracks filled with melt.  相似文献   

12.
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   

13.
We present a complete ray theory for the calculation of surface-wave observables from anisotropic phase-velocity maps. Starting with the surface-wave dispersion relation in an anisotropic earth model, we derive practical dynamical ray-tracing equations. These equations allow calculation of the observables phase, arrival-angle and amplitude in a ray theoretical framework. Using perturbation theory, we also obtain approximate expressions for these observables. We assess the accuracy of the first-order approximations by using both theories to make predictions on a sample anisotropic phase-velocity map. A comparison of the two methods illustrates the size and type of errors which are introduced by perturbation theory. Perturbation theory phase and arrival-angle predictions agree well with the exact calculation, but amplitude predictions are poor. Many previous studies have modelled surface-wave propagation using only isotropic structure, not allowing for anisotropy. We present hypothetical examples to simulate isotropic modelling of surface waves which pass through anisotropic material. Synthetic data sets of phase and arrival angle are produced by ray tracing with exact ray theory on anisotropic phase-velocity maps. The isotropic models obtained by inverting synthetic anisotropic phase data sets produce deceptively high variance reductions because the effects of anisotropy are mapped into short-wavelength isotropic structure. Inversion of synthetic arrival-angle data sets for isotropic models results in poor variance reductions and poor recovery of the isotropic part of the anisotropic input map. Therefore, successful anisotropic phase-velocity inversions of real data require the inclusion of both phase and arrival-angle measurements.  相似文献   

14.
A general tomographic technique is designed in order (i) to operate in anisotropic media; (ii) to account for the uneven seismic sampling and (iii) to handle massive data sets in a reasonable computing time. One modus operandi to compute a 3-D body wave velocity model relies on surface wave phase velocity measurements. An intermediate step, shared by other approaches, consists in translating, for each period of a given mode branch, the phase velocities integrated along ray paths into local velocity perturbations. To this end, we develop a method, which accounts for the azimuthal anisotropy in its comprehensive form. The weakly non-linear forward problem allows to use a conjugate gradient optimization. The Earth's surface is regularly discretized and the partial derivatives are assigned to the individual grid points. Possible lack of lateral resolution, due to the inescapable uneven ray path coverage, is taken into account through the a priori covariances on parameters with laterally variable correlation lengths. This method allows to efficiently separate the 2ψ and the 4ψ anisotropic effects from the isotropic perturbations. Fundamental mode and overtone phase velocity maps, derived with real Rayleigh wave data sets, are presented and compared with previous maps. The isotropic models concur well with the results of Trampert & Woodhouse. Large 4ψ heterogeneities are located in the tectonically active regions and over the continental lithospheres such as North America, Antarctica or Australia. At various periods, a significant 4ψ signature is correlated with the Hawaii hotspot track. Finally, concurring with the conclusions of Trampert & Woodhouse, our phase velocity maps show that Rayleigh wave data sets do need both 2ψ and 4ψ anisotropic terms.  相似文献   

15.
In this article the interaction of plane waves with a weak-contrast interface between two weakly anisotropic half-spaces is investigated. The anisotropy dealt with is of a general type. The stress–displacement vectors of the plane waves are calculated by perturbation theory. By assuming that the jump in elastic parameters and density across the interface is small, one can derive a simple expression for the R qPqP coefficient. In cases in which the wave motion is restricted to a symmetry plane of an anisotropic medium, simple expressions for the R qSVqSV and R SHSH coefficients are also derived.  相似文献   

16.
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   

17.
ScS wave splitting of deep earthquakes around Japan   总被引：4，自引：0，他引：4  
ScS wave splitting of five deep earthquakes in subduction zones near Japan is investigated using horizontal seismograms recorded al JMA stations. For each earthquake, we clearly observe uniform ScS wave splitting in all stations over Japan, especially for the events located south of Honshu in 1982, 1984 and 1993. However, the directions of fast-polarized waves of these events differed by a maximum of about 50° from one another. The orientation of fast-polarized waves in the 1982 event was NNW-SSE; those in the two later events WNW-ESE. We also recognize this discrepancy in the results of the analysis of the 1971 Sea of Okhotsk event reported by Fukao (1984). The Sakhalin Islands event in 1990 reveals a linear particle motion without such a change in direction of the second arrivals, implying no anisotropy. These observations are interpreted as indicating an anisotropic region within the slab near the earthquake sources but not beneath the receivers, since the orientations of fast-polarized waves recorded at each station are not common to all the earthquakes. Furthermore, we consider that anisotropy exists non-uniformly within the slab. The event in 1982, which occurred in almost the same area as those in 1984 and 1993, showed a fast direction different from the events in 1984 and 1993. The 1982 event was 179 km deep, but the two later events were at 398 km and 360 km, respectively. The fast direction observed from the 1982 event is parallel to the fossil plate motion, whereas those from the events in 1984 and 1993 are parallel to the compression axis within the subducting slab. The depth of 400 km is a phase boundary, where olivine changes to β spinel. We consider that the most likely cause of the change in anisotropy direction is the re-orientation of crystals associated with the phase change of olivine to β spinel due to subduction of the slab.  相似文献   

18.
Summary. A novel method is proposed for retrieving the 3-D orientation of axes of symmetry of near-source anisotropy by a non-linear inversion of observed radiation patterns of seismic displacement spectra of Rayleigh waves.
If faulting is generated within an anisotropic source region, body force equivalents for the faulting are in general not a double couple but the sum of three orthogonal dipole forces (Kosevich; Kawasaki & Tanimoto). As a result of the third dipole force, radiation patterns of Rayleigh waves are deformed, the deformation amounting to several per cent of those for an isotropic source medium. The non-linear inversion is carried out to find the optimum fault plane solutions giving the minimum square residual between observed and theoretical radiation patterns in some period range. In order to remove effects of heterogeneity along propagation paths, a pair-event scheme is involved in the inversion, which denotes taking spectral amplitude ratios and differential phases of the seismic displacement spectra of the pair-events having close hypocentres and different fault plane solutions. The uniqueness of the fault plane solutions of the non-linear inversion is afforded a proof by the Monte-Carlo experiment.
The non-linear inversion is repeated for some possible types of symmetry of the near-source orthotropic anisotropy due to the preferred orientation of olivine crystals as mantle materials. Square residuals thus obtained are compared with each other to see which orientation gives the minimum.
The method is applied to pair-events which occurred in the anomalous mantle beneath the Mid-Atlantic Ridge. This leads to a discovery that one type of symmetry of the preferred orientations with a -, b - and c-axes aligned vertical, parallel to and perpendicular to the trend (N11E) of the ridge axis, respectively, is most likely existing in the anomalous mantle.  相似文献   

19.
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   

20.
We investigate the sensitivity of finite-frequency body-wave observables to mantle anisotropy based upon kernels calculated by combining adjoint methods and spectral-element modelling of seismic wave propagation. Anisotropy is described by 21 density-normalized elastic parameters naturally involved in asymptotic wave propagation in weakly anisotropic media. In a 1-D reference model, body-wave sensitivity to anisotropy is characterized by 'banana–doughnut' kernels which exhibit large, path-dependent variations and even sign changes. P -wave traveltimes appear much more sensitive to certain azimuthally anisotropic parameters than to the usual isotropic parameters, suggesting that isotropic P -wave tomography could be significantly biased by coherent anisotropic structures, such as slabs. Because of shear-wave splitting, the common cross-correlation traveltime anomaly is not an appropriate observable for S waves propagating in anisotropic media. We propose two new observables for shear waves. The first observable is a generalized cross-correlation traveltime anomaly, and the second a generalized 'splitting intensity'. Like P waves, S waves analysed based upon these observables are generally sensitive to a large number of the 21 anisotropic parameters and show significant path-dependent variations. The specific path-geometry of SKS waves results in favourable properties for imaging based upon the splitting intensity, because it is sensitive to a smaller number of anisotropic parameters, and the region which is sampled is mainly limited to the upper mantle beneath the receiver.  相似文献   

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