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1.
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   

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.
Summary. Seismic anisotropy within the upper mantle originates from the preferred orientation of highly anisotropic single crystals. The symmetry and magnitude of anisotropy depend upon: (1) the volume percentages of the minerals constituting the upper mantle, (2) the degree and symmetry of preferred orientation of each mineral and (3) the alignment of the minerals' crystallographic axes relative to one another. The nature of upper mantle anisotropy can be examined by studying mineral orientations within ultramafic rocks which were once part of the mantle. Petrofabric data for olivine and pyroxene have been used to obtain velocity anisotropy patterns over large regions of ultramafic rocks from the Samail ophiolite, Oman, the Troodos ophiolite, Cyprus, the Bay of Islands ophiolife, Newfoundland, the Twin Sisters ultramafic, Washington, USA, the Dun Mountain ophiolite, New Zealand, the Red Hills ophiolite, New Zealand and the Red Mountain ophiolite, New Zealand. The compressional wave anisotropy calculated for these massifs ranges from 3 to 8 per cent, in excellent agreement with observed seismic anisotropy in the upper continental and oceanic mantle. The symmetry varies from orthorhombic to axial, with the axial symmetry axis corresponding to the olivine a-axes maxima and subparallel to spreading directions in oceanic upper mantle. Pyroxene a -, b - and c -axes maxima generally parallel olivine b -, c - and a -axes, respectively, and anisotropy decreases with increasing pyroxene content. Shear-wave splitting is predicted for all propagation directions within the upper mantle. Symmetry is also orthorhombic or axial, with the minimum difference in velocity between the two shear-waves parallel to the maximum compressional wave velocity.  相似文献   

4.
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   

5.
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   

6.
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   

7.
Summary. Seismic anisotropy has been previously studied at depths usually not exceeding 100 or 150 km. In this paper we present a method of analysis of seismic records which is very sensitive to azimuthal anisotropy and is applicable at almost any depth range. The idea of the method is to detect and analyse the SH -component of the waves, converted from P to S in the mantle. The procedure of record processing includes frequency filtering, axis rotation, transformation of the record to a standard form, stacking the standardized SH -component records of many seismic events, and the harmonic analysis of amplitude as a function of the direction of wave propagation. When applied to the long-period records of NORSAR the procedure detected a converted wave with the properties implying the possibility of its propagation in a transversely isotropic medium with a horizontal axis of symmetry . Our preferred model postulates anisotropy of ∼ 1 per cent in a layer 50 km thick at the base of the upper mantle.  相似文献   

8.
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   

9.
Summary. The general problem of inverting Love-wave dispersion and amplitude data to obtain a velocity and Qs structure is considered. A formulation is used which incorporates attenuation into the Haskell-Thompson matrix method in an exact manner and thus retains the inherent non-linearity in the anelasticity. The resulting exact inversion kernels allow simultaneous inversion for velocity and intrinsic attenuation parameters. The method is applied to synthetic data which allows a comparison to be made with inexact kernels. The results indicate that the use of inexact kernels may introduce spurious oscillations into the Qs structure and that a simultaneous inversion can be more stable than inverting for velocity alone.  相似文献   

10.
Rayleigh wave phase velocity maps in southern Africa are obtained at periods from 6 to 40 s using seismic ambient noise tomography applied to data from the Southern Africa Seismic Experiment (SASE) deployed between 1997 and 1999. These phase velocity maps are combined with those from 45 to 143 s period which were determined previously using a two-plane-wave method by Li & Burke. In the period range of overlap (25–40 s), the ambient noise and two-plane-wave methods yield similar phase velocity maps. Dispersion curves from 6 to 143 s period were used to estimate the 3-D shear wave structure of the crust and uppermost mantle on an 1°× 1° grid beneath southern Africa to a depth of about 100 km. Average shear wave velocity in the crust is found to vary from 3.6 km s–1 at 0–10 km depths to 3.86 km s–1 from 20 to 40 km, and velocity anomalies in these layers correlate with known tectonic features. Shear wave velocity in the lower crust is on average low in the Kaapvaal and Zimbabwe cratons and higher in the surrounding Proterozoic terranes, such as the Limpopo and the Namaqua-Natal belts, which suggests that the lower crust underlying the Archean cratons is probably less mafic than beneath the Proterozoic terranes. Crustal thickness estimates agree well with a previous receiver function study of Nair et al. . Archean crust is relatively thin and light and underlain by a fast uppermost mantle, whereas the Proterozoic crust is thick and dense with a slower underlying mantle. These observations are consistent with the southern African Archean cratons having been formed by the accretion of island arcs with the convective removal of the dense lower crust, if the foundering process became less vigorous in arc environments during the Proterozoic.  相似文献   

11.
To quantify the seismic properties of lower crustal rocks and to better constrain the origin of the lower crustal seismic reflectivity, we determined the complete 3-D seismic properties of a lower crustal section. Eight representative samples of the main lithologic and structural units outcropping in the Val Sesia (Ivrea zone) were studied in detail. The seismic velocities were calculated using the single crystal stiffness coefficients and the lattice preferred orientation (LPO) of each mineral in all samples. The 21 stiffness coefficients characterizing the elastic behaviour of each rock are determined. Mafic and ultramafic rocks such as pyroxenite and pyroxene-bearing gabbros display complex shear wave properties. These rocks are weakly birefringent (maximum 0.1 kms−1) and it is difficult to find consistent relationships between the seismic properties and the rock structure. On the other hand, seismic properties of deformed felsic rocks are essentially controlled by mica. They display strong S -wave birefringence (0.3 km s−1) and relatively high V p anisotropy (7.6 per cent). Amphibole also strongly influences the rock birefringence patterns. For both kind of rocks, the foliation is highly birefringent and the fast polarized shear wave is systematically oriented parallel to the foliation. We show that the number of mineral phases in the rock strongly controls the anisotropy. The seismic anisotropy has a complex role in the P -wave reflectivity. Compared to the isotropic case, anisotropy enhances the reflection coefficient for about 60 per cent of the possible lithological interfaces. For 40 per cent of the interfaces, the reflection coefficient is much lower when one considers the medium as anisotropic.  相似文献   

12.
A self-adaptive automated parametrization approach is suggested for the sequential inversion of controlled-source seismic tomography and gravity data. The velocities and interfaces are parametrized by their Haar wavelet expansion coefficients. Only those coefficients that are well constrained by the data, as measured by the number of rays that cross the corresponding wavelet function support area and their angular coverage, are inverted for, others are set to zero. This approach results in a reasonable distribution of resolution throughout the model even in cases of irregular ray coverage and does overcome the trade-off between different types of model parameters. A modified sequential inversion approach is suggested to join the traveltimes and gravity anomalies inversion. An algorithm is developed that inverts for smooth velocity and density variations inside the seismic layer, the position of its bottom interface as well as for optimal values of the velocity-to-density regression coefficients. The algorithm makes use of direct (diving), reflected and head (critically refracted) wave traveltimes. The algorithm workflow is demonstrated on a synthetic data example.  相似文献   

13.
Ray tracing has recently been expressed for anisotropy specified in a local Cartesian coordinate system, which may vary continuously in a model specified by elastic parameters. It takes advantage of the fact that anisotropy is often of a simpler nature locally (and is thus specified by a smaller number of elastic parameters) and that the orientation of its symmetry elements may vary. Here we extend this approach by replacing the local Cartesian coordinate system with a curvilinear coordinate system of global extent and by applying the new approach to ray tracing and inhomogeneous dynamic ray tracing. The curvilinear coordinate system is orthogonal and is constructed so that the coordinate axes are consistent with the considered anisotropy of the medium. Our formulation allows for computation of ray attributes (e.g. ray velocity vector and paraxial ray attributes) in the curvilinear coordinate system, while rays are computed in global Cartesian coordinates. Compared to the classic formulation in terms of 21 elastic moduli in global Cartesian coordinates, the main advantages are improved efficiency, lower computer-memory requirements, and conservation of anisotropic symmetry throughout the model.  相似文献   

14.
In this study, we test the adequacy of 2-D sensitivity kernels for fundamental-mode Rayleigh waves based on the single-scattering (Born) approximation to account for the effects of heterogeneous structure on the wavefield in a regional surface wave study. The calculated phase and amplitude data using the 2-D sensitivity kernels are compared to phase and amplitude data obtained from seismic waveforms synthesized by the pseudo-spectral method for plane Rayleigh waves propagating through heterogeneous structure. We find that the kernels can accurately predict the perturbation of the wavefield even when the size of anomaly is larger than one wavelength. The only exception is a systematic bias in the amplitude within the anomaly itself due to a site response.
An inversion method of surface wave tomography based on the sensitivity kernels is developed and applied to synthesized data obtained from a numerical simulation modelling Rayleigh wave propagation over checkerboard structure. By comparing recovered images to input structure, we illustrate that the method can almost completely recover anomalies within an array of stations when the size of the anomalies is larger than or close to one wavelength of the surface waves. Surface wave amplitude contains important information about Earth structure and should be inverted together with phase data in surface wave tomography.  相似文献   

15.
Summary. Phase velocity variations obtained in the previous paper are inverted by the Backus–Gilbert method for the velocity structure of the upper mantle. Spheroidal modes and toroidal modes in the period range of 125–260 s are used in the inversion. The data cannot constrain all six parameters in a transversely isotropic medium and we chose to perturb only two parameters, SH and SV velocities. SV velocities are resolved between the depths of about 200 and 400 km and SH velocities between 0 and 200 km. Resolution kernels have half-peak widths of about 200–300 km in depth, becoming broader for deeper target depths. SV velocity kernels show secondary peaks near the surface of the Earth, with widths varying from 50 to 100 km. The deeper the target depths, the wider the secondary peaks near the surface. SH velocity kernels do not possess such secondary peaks. The trade-off between SV and SH velocities is small. SV velocity is essentially determined by spheroidal modes and SH velocity by toroidal modes. Because of the broad width of the resolution kernels, the structure in the resolved region is difficult to detect from our data set; for example the differences in SV velocity structure between 250 and 350 km or the differences in SH velocity between 100 and 200 km are difficult to distinguish. Considering the horizontal resolution of about 2000 km, obtained in the previous paper, averaging kernels for 3-D structure are quite elongated in the horizontal dimension.  相似文献   

16.
Summary. Numerical modelling is one of the most efficient methods for an investigation of the relationship between structural features and peculiarities of observed wavefields. It is practically the only method for 2-D and 3-D inhomogeneous media.
An algorithm based on ray theory has been developed for calculations of travel times and amplitudes of seismic waves in 3-D inhomogeneous media with curved interfaces. It was applied for numerical modelling of kinematic and dynamic characteristics of seismic waves propagating in laterally inhomogeneous media.
Travel-time and amplitude patterns were studied in the 2-D and 3-D models of a geosyncline, in which velocity distribution was given by an analytical function of the coordinates. For a more complicated model representing a subducting high-velocity lithospheric plate in a transition zone between oceanic and continental upper mantle, the velocity distribution was given by discrete values on a 2-D non-rectangular grid. It was shown that when a source was placed above the lithospheric plate, a shadow zone appeared along a strike of the structure, i.e. in the direction which is perpendicular to a strong lateral velocity gradient. Travel-time residuals were calculated along the seismological profile for a 3-D velocity distribution in the upper mantle beneath Central Asia, obtained as a result of inversion of travel times by the Backus-Gilbert method. They were found to be in a good agreement with the observed data.  相似文献   

17.
Summary. The Backus-Gilbert method has been extended to the estimation of the seismic wave velocity distribution in 2-D or 3-D inhomogeneous media from a finite set of travel-time data. The method may be applied to the inversion of body wave as well as surface wave data. The problem of determining a local average of the unknown velocity corrections may be reduced to a choice of a suitable δ-ness criterion for the averaging kernel. For 2-D and 3-D inhomogeneous media the simplest criterion is to minimize a sum of 'spreads' over all the coordinates. The use of this criterion requires the solution (the averaged velocity corrections) to be represented as a sum of functions, each of which depends only on one coordinate. This is a basic restriction of the method. In practice it is possible to achieve good agreement between the solution and a real velocity distribution by a reasonable choice of the coordinate system.
Numerical tests demonstrate the efficiency of the method. Some examples of the application of the method to the inversion of real seismological data for body and surface waves are given.  相似文献   

18.
P-wave velocity anisotropy in crystalline rocks   总被引：1，自引：0，他引：1  
Summary. Compressional wave velocities and anisotropy coefficients determined at high hydrostatic pressures are compiled from the data published for the main types of crystalline rocks. The crack-free elastic anisotropy of igneous crustal rocks is generally very low, between 1 and 3 per cent on average. The anisotropy of metamorphic rocks is higher (up to 22 per cent), but very variable. The average anisotropy coefficients in schists and amphibolites are about 10 per cent, in gneisses between 3 and 7 per cent, and in granulites less than 3 per cent. The average anisotropy of olivine ultramafites is between 7 and 12 per cent, whereas in pyroxenites and eclogites it is usually less than 4 per cent. A comparison of ranges of average velocities and average anisotropies for the individual rock groups suggests that, whereas in the crust the lateral velocity variations are mainly due to compositional changes, in the olivine of the uppermost mantle the velocity variations due to anisotropic structures could be of the same magnitude as the variations due to inhomogeneities.  相似文献   

19.
Collocated magnetotelluric (MT) and seismic profiling is emerging as a necessary combined approach for deep and near-surface imaging but the resulting experimental data are typically interpreted separately since no production programs exist for multidimensional joint inversion of MT and seismic data. We present a joint 2-D inversion approach for imaging collocated MT and seismic refraction data with cross-gradient structural constraints. We describe the main features of the algorithm and first apply it to synthetic data generated for a hypothetical complex geological model. For the synthetic data, we find that the scheme leads to models with remarkable structural resemblance and improved estimates of electrical resistivity and seismic velocity. We apply the scheme to near-surface field data to test the consistency of a previously suggested resistivity–velocity interrelationship and its potential use for subsurface lithofacies discrimination or structural classification. The MT-seismic relationship is found to be in excellent accord with that derived previously for DC resistivity and seismic data set at the test site. Our results suggest that joint MT-seismic cross-gradient imaging leads to improved characterization of heterogeneous geological targets at near-surface to mantle depths.  相似文献   

20.
It is now widely accepted that elastic properties of the continental lithosphere and the underlying sublithospheric mantle are both anisotropic and laterally heterogeneous at a range of scales. To fully exploit modern three-component broad-band array data sets requires the use of comprehensive modelling tools. In this work, we investigate the use of a wide-angle, one-way wave equation to model variations in teleseismic 3-D waveforms due to 2-D elastic heterogeneity and anisotropy. The one-way operators are derived based on a high-frequency approximation of the square-root operator and include the effects of wave propagation as well as multiple scattering. Computational cost is reduced through a number of physically motivated approximations. We present synthetic results from simple 1-D (layer over a half-space) and 2-D (subduction zone) models that are compared with reference solutions. The algorithm is then used to model data from an array of broad-band seismograph stations deployed in northwestern Canada as part of the IRIS-PASSCAL/LITHOPROBE CANOE experiment. In this region radial-component receiver functions show a clear continental Moho and the presence of crustal material dipping into the mantle at the suture of two Palaeo-Proterozoic terranes. The geometry of the suture is better defined on the transverse component where subduction is associated with a ∼10 km thick layer exhibiting strong elastic anisotropy. The modelling reproduces the main features of the receiver functions, including the effects of anisotropy, heterogeneity and finite-frequency scattering.  相似文献   

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