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1.
We propose approximate equations for P -wave ray theory Green's function for smooth inhomogeneous weakly anisotropic media. Equations are based on perturbation theory, in which deviations of anisotropy from isotropy are considered to be the first-order quantities. For evaluation of the approximate Green's function, earlier derived first-order ray tracing equations and in this paper derived first-order dynamic ray tracing equations are used.
The first-order ray theory P -wave Green's function for inhomogeneous, weakly anisotropic media of arbitrary symmetry depends, at most, on 15 weak-anisotropy parameters. For anisotropic media of higher-symmetry than monoclinic, all equations involved differ only slightly from the corresponding equations for isotropic media. For vanishing anisotropy, the equations reduce to equations for computation of standard ray theory Green's function for isotropic media. These properties make the proposed approximate Green's function an easy and natural substitute of traditional Green's function for isotropic media.
Numerical tests for configuration and models used in seismic prospecting indicate negligible dependence of accuracy of the approximate Green's function on inhomogeneity of the medium. Accuracy depends more strongly on strength of anisotropy in general and on angular variation of phase velocity due to anisotropy in particular. For example, for anisotropy of about 8 per cent, considered in the examples presented, the relative errors of the geometrical spreading are usually under 1 per cent; for anisotropy of about 20 per cent, however, they may locally reach as much as 20 per cent. 相似文献
The first-order ray theory P -wave Green's function for inhomogeneous, weakly anisotropic media of arbitrary symmetry depends, at most, on 15 weak-anisotropy parameters. For anisotropic media of higher-symmetry than monoclinic, all equations involved differ only slightly from the corresponding equations for isotropic media. For vanishing anisotropy, the equations reduce to equations for computation of standard ray theory Green's function for isotropic media. These properties make the proposed approximate Green's function an easy and natural substitute of traditional Green's function for isotropic media.
Numerical tests for configuration and models used in seismic prospecting indicate negligible dependence of accuracy of the approximate Green's function on inhomogeneity of the medium. Accuracy depends more strongly on strength of anisotropy in general and on angular variation of phase velocity due to anisotropy in particular. For example, for anisotropy of about 8 per cent, considered in the examples presented, the relative errors of the geometrical spreading are usually under 1 per cent; for anisotropy of about 20 per cent, however, they may locally reach as much as 20 per cent. 相似文献
2.
Anne Sieminski Qinya Liu Jeannot Trampert Jeroen Tromp 《Geophysical Journal International》2007,171(1):368-389
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
3.
S. D. Kogan 《Geophysical Journal International》1984,76(1):201-207
Summary. Results of earlier studies of P -wave travel-time anisotropy are compared with the P -wave velocity-anisotropy obtained by other authors for different regions of the Earth. The azimuthal relationship of P -wave travel times from surface sources on the Siberian platform is investigated. It is found that the direction of the minimal travel time of P -waves for the Siberian platform, as well as that for European regions, is close to north–south. 相似文献
4.
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
5.
Summary. Four types of crustal and upper-mantle rocks have been used for the investigation of seismic P -wave velocities in three mutually perpendicular directions. Hydrostatic pressure, up to 6 kbar and temperatures up to 500°C were applied to the samples. Measurements of the ultrasonic P -wave travel times and velocities were carried out along two geotherms. All rock types show an anisotropic behaviour which is caused by the orientation of certain minerals. The anisotropy is not dependent on temperature and pressure. Gneiss and peridotite have 5–6 per cent anisotropy whereas granite and a metagabbro show values of only 2–3 per cent. The smallest velocity is always in the z direction, perpendicular to a schistocity or foliation. It is shown that the data agree with those of field observation. We conclude that anisotropy caused by preferred orientation of minerals must be expected in the whole lithosphere. Additional effects of layering, of cracks, and of nonhydrostatic stresses are estimated. 相似文献
6.
Summary. A layer of constant thickness over a half-space is assumed, and the propagation of head waves is considered for the following two cases: (1) the P -wave velocity varies in the layer in the horizontal direction, and is constant in the half-space: (2) the P -wave velocity varies in the half-space in the horizontal direction, and is constant in the layer. In each case the horizontal velocity gradient is assumed to remain constant. The wave propagation is investigated in the direction of the gradient (direct profile), and opposite to it (reverse profile). Formulae for the travel times and the amplitudes are obtained on the basis of ray-theoretical considerations. Conditions are discussed for the discrimination in a field experiment between the case of a sloping boundary separating the homogeneous media, and the case of an intrinsic horizontal velocity gradient. 相似文献
7.
Summary. We examine the way in which measurements of velocity anisotropy can add to our understanding of upper mantle structure. Measurements of P -wave velocity anisotropy in a single plane contain very little direct information about the anisotropic structure. A promising technique is to fit the observed velocity variation with a mixture of an assumed anisotropic constituent and a proportion of isotropic material. Using this technique, mixtures of orthorhombic and transversely isotropic olivine are obtained, which are in excellent agreement with observed velocity variations in the Pacific. 相似文献
8.
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
9.
Hideki Shimamura 《Geophysical Journal International》1984,76(1):253-260
Summary. A series of long-range explosion seismological experiments has been conducted by the use of specially designed ocean bottom seismographs (OBSs) in the Western Pacific. OBS studies of apparent velocity measurements by the use of natural earthquakes have also been made. The experiments have made clear that large-scale P -wave anisotropy exists in the entire thickness of the oceanic lithosphere. The existence of the large-scale anisotropy in the oceanic lithosphere has been demonstrated for the first time by seismic body-wave studies. Previously, anisotropy had been found only in the uppermost oceanic mantle in the Eastern Pacific.
The azimuth of the maximum velocity, 8.6 km s-1 , is about 155° clock-wise from north. The direction is perpendicular to the magnetic lineation of the region, however, the direction differs from the direction of the present plate motion by about 30°. So it appears that the anisotropy has been 'frozen' at least since the change of the plate motion that occurred 40 Myr ago. The frozen anisotropy should set important constraints on the mechanical properties of the lithosphere such as the viscosity and temperature of the lower lithosphere. 相似文献
The azimuth of the maximum velocity, 8.6 km s
10.
Velocity anisotropy in granodiorite and quartzite due to the distribution of microcracks 总被引：2，自引：0，他引：2
Summary. The spatial anisotropy of P -wave velocities was investigated in spherical samples of granodiorite and quartzite and correlated with the orientation of microcracks and grain boundaries, determined optically by universal stage techniques. The preferred orientation of normals to cleavage cracks of biotite and amphibole in granodiorite correlates well with the direction of maximum velocity increase under hydrostatic pressure, although the minerals form only nine per cent of the volume. Irregular microcracks in an almost monomineral quartzite have only a very small effect on the velocity anisotropy, although they are also preferentially oriented. The nature of the microdiscontinuities is of primary importance for the velocity anisotropy observed at atmospheric and low hydrostatic pressures. 相似文献
11.
Anisotropy in multi-offset deep-crustal seismic experiments 总被引：1，自引：0，他引：1
Modelling of deep-seismic wide-angle data commonly assumes that the Earth is heterogeneous and isotropic. It is important to know the magnitudes of errors that may be introduced by isotropic-based wide-angle models when the Earth is anisotropic. It is equally important to find ways of detecting anisotropy and determining its properties.
This paper explores the errors introduced by interpreting anisotropic seismic data with isotropic models. Errors in P -wave reflector depths are dependent on the magnitude of the velocity anisotropy and the direction of the fast axis. The interpreted, isotropic, model velocity function is found to correspond closely to the horizontal velocity of the anisotropic medium. An additional observed parameter is the time mismatch , which we define to be the difference between the vertical two-way traveltime to a reflector and the time-converted wide-angle position of the reflector. The magnitude of the time mismatch is typically <1.0 s (when the whole crust is anisotropic) and is found to be closely related to the magnitude and sign of the anisotropic anellipticity. The relationships are extendible to more complicated models, including those with vertical velocity gradients, crustal zonation, and lower symmetry orders.
A time mismatch may be symptomatic of the presence of anisotropy. We illustrate the observation of a time mismatch for a real multi-offset seismic data set collected north of Scotland and discuss the implications for crustal anisotropy in that region. 相似文献
This paper explores the errors introduced by interpreting anisotropic seismic data with isotropic models. Errors in P -wave reflector depths are dependent on the magnitude of the velocity anisotropy and the direction of the fast axis. The interpreted, isotropic, model velocity function is found to correspond closely to the horizontal velocity of the anisotropic medium. An additional observed parameter is the time mismatch , which we define to be the difference between the vertical two-way traveltime to a reflector and the time-converted wide-angle position of the reflector. The magnitude of the time mismatch is typically <1.0 s (when the whole crust is anisotropic) and is found to be closely related to the magnitude and sign of the anisotropic anellipticity. The relationships are extendible to more complicated models, including those with vertical velocity gradients, crustal zonation, and lower symmetry orders.
A time mismatch may be symptomatic of the presence of anisotropy. We illustrate the observation of a time mismatch for a real multi-offset seismic data set collected north of Scotland and discuss the implications for crustal anisotropy in that region. 相似文献
12.
Stuart Crampin Ralph A. Stephen Robert McGonigle 《Geophysical Journal International》1982,68(2):477-485
Summary. The paper examines P -wave propagation in anisotropic solids, and demonstrates the effect of anisotropy on the polarizations of quasi P -waves. The deviation of the polarization of the quasi P -wave from the propagation vector may be significant, but is in almost the same direction as the deviation of the group-velocity vector. Since the group-velocity, or energy propagation, vector follows seismic ray paths, the apparent deviation is the difference of the polarization and group-velocity deviations and is small. Consequently, it may be easily overlooked, hidden by noise, or attributed to the effects of inhomogeneity. 相似文献
13.
First-arrival waveforms remain underutilized in crustal refraction–reflection seismology by mostly reducing them to traveltime picks. However, as in earthquake seismology, the waveforms also contain important information about shallow near-receiver structures. We illustrate the use of three-component waveform analysis on the records from the ACCRETE wide-angle data set (SE Alaska and British Columbia; 1994), apply the Receiver Function (RF) methodology to the codas of P -wave arrivals, and draw two important conclusions. First, the P -wave polarization azimuths are found to be controlled by the near-receiver structures and virtually unrelated to the source–receiver backazimuths, from which they deviate by up to ∼40°. This observation might be important for studies of anisotropy and also for earthquake RF studies. Second, after correcting for the polarization azimuths, clear P / S mode conversions are reliably detected within 80–400 ms following the primary arrivals. The conversions are interpreted as originating at the base of the sedimentary cover of the fjord channel. In most cases, imaging of the basement requires only several records; however, notable exceptions are also found and interpreted as caused by multipathing, localized scattering, and onsets of crustal and Moho reflections. The ACCRETE example shows that RF methodology could be useful for constraining sediment thickness and deriving P - and S -wave receiver statics in land refraction surveys where collocated reflection profiles are not available. In addition, RFs from repeatable controlled sources could be useful for testing and calibration of RF techniques. 相似文献
14.
S. I. Koshubin N. I. Pavlenkova A. V. Yegorkin 《Geophysical Journal International》1984,76(1):221-226
Summary. The analysis of data of seismic crustal studies in the USSR, obtained from waves propagating at different azimuths, reveals considerable horizontal and vertical inhomogeneity of the crust. Against this background it is difficult to predict what kind of velocity anisotropy can be expected in the continental crust. The rare cases of disagreement in velocities on intersecting profiles can be attributed both to anisotropy and to horizontal crustal inhomogeneity. There is a definite disagreement in layer velocities measured by reflected waves: fine layers in the crust and upper mantle have been found to have anomalously high velocities. The role of anisotropy in these events is not clear. The frequently observed splitting of S -wave with different polarization, however, positively implies anisotropy in the Earth's crust. 相似文献
15.
Yun-Hao Wu En-Chao Yeh Jia-Jyun Dong Li-Wei Kuo Jui-Yu Hsu Jih-Hao Hung 《Geophysical Journal International》2008,174(3):949-965
Taiwan Chelungpu-fault Drilling Project (TCDP) was initiated to understand the physical mechanisms involved in the large displacements of the 1999 Taiwan Chi-Chi earthquake. Continuous measurements of cores (including laboratory work) and a suite of geophysical downhole logs, including P - and S -wave sonic velocity, gamma ray, electrical resistivity, density, temperature, electrical borehole images and dipole-shear sonic imager, were acquired in Hole-A over the depth of 500–2003 m. Integrated studies of cores and logs facilitate qualitative and quantitative comparison of subsurface structures and physical properties of rocks. A total of 10 subunits were divided on the basis of geophysical characteristics. Generally, formation velocity and temperature increase with depth as a result of the overburden and thermal gradient, respectively. Gamma ray, resistivity, formation density, shear velocity anisotropy and density-derived porosity are primarily dependent on the lithology. Zones with changes of percentage of shear wave anisotropy and the fast shear polarization azimuth deduced from Dipole Shear-Imager (DSI) are associated with the appearance of fractures, steep bedding and shear zones. The fast shear wave azimuth is in good agreement with overall dip of the bedding (approximately 30° towards SE) and maximum horizontal compressional direction, particularly in the Kueichulin Formation showing strong shear wave velocity anisotropy. Bedding-parallel fractures are prevalent within cores, whereas minor sets of high-angle, NNW–SSE trending with N- and S-dipping fractures are sporadically distributed. The fault zone at depth 1111 m (FZA1111) is the Chi-Chi earthquake slip zone and could be a fluid conduit after the earthquake. The drastic change in fast shear wave polarization direction across the underlying, non-active Sanyi thrust at depth 1710 m reflects changes in stratigraphy, physical properties and structural geometry. 相似文献
16.
A numerical method is presented for calculating complete theoretical seismograms, under the assumption that the earth models have velocity, density and attenuation profiles which are arbitrary piece-wise continuous functions of depth only. Solutions for the stress-displacement vectors in the medium are expanded in terms of orthogonal cylindrical functions. Our method for solving the resulting two-point boundary value problems differs from that of other investigators in three ways. First, collocation is used in traditionally troublesome situations, e.g. for highly evanescent waves, at turning points, and in regions having large gradient in material properties. Second, in some situations (high frequencies and small gradients) P and S -waves decouple and we use a different solution method for each wave type, instead of trying to force a single method to find all solutions. For example, above the P - and S -waves turning points an approximate fundamental matrix may be used for each wave type. At the P -wave turning point, the fundamental matrix may be used for the S -wave components but collocation is used for the P -wave. Between the P - and S -wave turning points collocation is used for the evanescent P -wave and the fundamental matrix is used for the S -wave. At the S -wave turning point and below, collocation is used for both. Third, the computational algorithm chooses the appropriate solution method and depth domain upon which it is employed based upon a specified error tolerance and the known inaccuracies of the various approximations employed. Once solutions of the boundary value problems are obtained, a Fourier—Bessel transform is then applied to get back into the space-time domain. 相似文献
17.
Summary. A combination of analytic solutions and numerical computations has been used to obtain the low-frequency, far-field P - and S -wave radiation patterns from Heaviside-loaded ellipsoid cavities of fixed volume and varying eccentricity (including the sphere and the finite cylinder) in an unbounded elastic solid. Results show that as the spherical cavity becomes a prolate ellipsoid, S -waves are radiated with strength proportional to the increasing aspect ratio ( A R ) (major axis/minor axis). With large aspect ratios ( A R > 10) both P - and S -wave radiation strengths approach asymptotically a limit for which the maximum P -wave amplitude is twice as large as the maximum S -wave amplitude, irrespective of Poisson's ratio.
A representation of the radiation pattern is obtained whose mathematical form can be interpreted as due to the action of a centre of dilatation plus a vector linear dipole, both appropriately weighted. the weights are nonlinear functions of AR . On the basis of numerical results, we have obtained an approximate formula that relates those weights to A R . the radiation patterns thus obtained are in excellent agreement with the experimental results reported by Gupta & Kisslinger. the results may be of some importance to the investigation of explosions in non-spherical cavities and in the study of the origin and mechanisms of volcanic (explosive) earthquakes. 相似文献
A representation of the radiation pattern is obtained whose mathematical form can be interpreted as due to the action of a centre of dilatation plus a vector linear dipole, both appropriately weighted. the weights are nonlinear functions of A
18.
This paper presents an updated interpretation of seismic anisotropy within the uppermost mantle of southern Germany. The dense network of reversed and crossing refraction profiles in this area made it possible to observe almost 900 traveltimes of the Pn phase that could be effectively used in a time-term analysis to determine horizontal velocity distribution immediately below the Moho. For 12 crossing profiles, amplitude ratios of the Pn phase compared to the dominant crustal phase were utilized to resolve azimuthally dependent velocity gradients with depth. A P -wave anisotropy of 3–4 per cent in a horizontal plane immediately below the Moho at a depth of 30 km, increasing to 11 per cent at a depth of 40 km, was determined. For the axis of the highest velocity of about 8.03 km s−1 at a depth of 30 km a direction of N31°F was obtained. The azimuthal dependence of the observed Pn amplitude is explained by an azimuth-dependent sub-Moho velocity gradient decreasing from 0.06 s−1 in the fast direction to 0 s−1 in the slow direction of horizontal P -wave velocity. From the seismic results in this study a petrological model suggesting a change of modal composition and percentage of oriented olivine with depth was derived. 相似文献
19.
Jordi Julià 《Geophysical Journal International》2007,171(1):286-301
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
20.
Upper mantle beneath the Eger Rift (Central Europe): plume or asthenosphere upwelling? 总被引：4，自引：0，他引：4
Jaroslava Plomerová Ulrich Achauer Vladislav Babu&#;ka Lud&#;k Vecsey BOHEMA working group 《Geophysical Journal International》2007,169(2):675-682
We present the first results of a high-resolution teleseismic traveltime tomography and seismic anisotropy study of the lithosphere–asthenosphere system beneath the western Bohemian Massif. The initial high-resolution tomography down to a depth of 250 km did not image any columnar low-velocity anomaly which could be interpreted as a mantle plume anticipated beneath the Eger Rift, similar to recent findings of small plumes beneath the French Massif Central and the Eifel in Germany. Alternatively, we interpret the broad low-velocity anomaly beneath the Eger Rift by an upwelling of the lithosphere–asthenosphere transition. We also map lateral variations of seismic anisotropy of the mantle lithosphere from spatial variations of P -wave delay times and the shear wave splitting. Three major domains characterised by different orientations of seismic anisotropy correspond to the major tectonic units—Saxothuringian, Moldanubian and the Teplá-Barrandian—and their fabrics fit to those found in our previous studies of mantle anisotropy on large European scales. 相似文献