共查询到20条相似文献，搜索用时 31 毫秒
1.
Reciprocity theorems for one-way wavefields 总被引：1，自引：0，他引：1
Acoustic reciprocity theorems have proved their usefulness in the study of forward and inverse scattering problems. The reciprocity theorems in the literature apply to the two-way (i.e. total) wavefield, and are thus not compatible with one-way wave theory, which is often applied in seismic exploration. By transforming the two-way wave equation into a coupled system of one-way wave equations for downgoing and upgoing waves it appears to be possible to derive 'one-way reciprocity theorems" along the same lines as the usual derivation of the 'two-way reciprocity theorems'. However, for the one-way reciprocity theorems it is not directly obvious that the 'contrast term' vanishes when the medium parameters in the two different states are identical. By introducing a modal expansion of the Helraholtz operator, its square root can be derived, which appears to have a symmetric kernel. This symmetry property appears to be sufficient to let the contrast term vanish in the above-mentioned situation.
The one-way reciprocity theorem of the convolution type is exact, whereas the one-way reciprocity theorem of the correlation type ignores evanescent wave modes. The extension to the elastodynamic situation is not trivial, but it can be shown relatively easily that similar reciprocity theorems apply if the (non-unique) decomposition of the elastodynamic two-way operator is done in such a way that the elastodynamic one-way operators satisfy similar symmetry properties to the acoustic one-way operators. 相似文献
The one-way reciprocity theorem of the convolution type is exact, whereas the one-way reciprocity theorem of the correlation type ignores evanescent wave modes. The extension to the elastodynamic situation is not trivial, but it can be shown relatively easily that similar reciprocity theorems apply if the (non-unique) decomposition of the elastodynamic two-way operator is done in such a way that the elastodynamic one-way operators satisfy similar symmetry properties to the acoustic one-way operators. 相似文献
2.
Multicomponent near-surface correction for land VSP data 总被引：1，自引：0，他引：1
Colin MacBeth Xinwu Zeng Xiang-Yang Li John Queen 《Geophysical Journal International》1995,121(1):301-315
Multicomponent seismic data collected using directional sources are degraded by the wave excitation process due to inaccurate control of the ground motion. unequal activation strengths or ground couplings between differently oriented sources, and misalignment of the pad. These acquisition uncertainties are exacerbated by the complicated near-surface scattering present in most seismic areas. Neither group of effects should be neglected in multicomponent analyses that make use of relative wavefield attributes derived from compressional and shear waves. These effects prevent analysis of the direct and reflected waves using procedures based on standard scalar techniques or a prima facia interpretation of the vector wavefield properties, even for the seemingly straightforward case of a near-offset vertical seismic profile (VSP). Near-surface correction, using a simple matrix operator designed from the shallowest recordings, alleviates many of these interpretational difficulties in near-offset VSP data. Results from application of this technique to direct waves from a nine-component VSP shot at the Conoco test-site facility, Oklahoma, are encouraging. The technique corrects for unexpected compressional-wave energy from shear-wave vibrators and collapses near-surface multiples, thus facilitating further processing for the upgoing wavefield. The method provides a simple and effective processing step for routine application to near-offset VSP analyses. 相似文献
3.
Kurt Lambeck 《Geophysical Journal International》1981,67(1):91-114
Summary. The response of a stratified elastic medium can be conveniently characterized by the Green's tensor for the medium. For coupled seismic wave propagation ( P—SV or fully anisotropic), the Green's tensor may be constructed directly from two matrices of linearly independent displacement solutions. Rather simple forms for the Green's tensor can be found if each displacement matrix satisfies one of the boundary conditions on the seismic field. This approach relates directly to 'reflection matrix' representations of the seismic field.
For a stratified elastic half space the Green's tensor is used to give a spectral representation for coupled seismic waves. By means of a contour integration a general completeness relation is obtained for the 'body wave' and 'surface wave' parts of the seismic field. This relation is appropriate for SH and P–SV waves in an isotropic medium and also for full anisotropy. 相似文献
For a stratified elastic half space the Green's tensor is used to give a spectral representation for coupled seismic waves. By means of a contour integration a general completeness relation is obtained for the 'body wave' and 'surface wave' parts of the seismic field. This relation is appropriate for SH and P–SV waves in an isotropic medium and also for full anisotropy. 相似文献
4.
A. Kaslilar 《Geophysical Journal International》2007,171(1):352-367
An efficient inverse scattering method is developed for imaging near-surface heterogeneities using scattered surface waves. Three dimensional elastodynamic wave propagation and scattering in a laterally invariant embedding medium is considered. The Born Approximation is used and the scattered wavefield is expressed as a domain type integral representation. The computation time of Green's tensor elements is reduced by considering the radial symmetry of the medium. The method is validated by numerical tests. Ultrasonic laboratory data obtained from a scale model experiment are used for imaging the near-surface inhomogeneities caused by an epoxy-filled hole in the surface of an aluminum block. Both synthetic and the scale model tests show that the location, the actual density contrast and the depth of the inhomogeneities are reasonably well estimated. 相似文献
5.
6.
Synchronizing seismic networks with ambient noise 总被引：1，自引：0，他引：1
Christoph Sens-Schönfelder 《Geophysical Journal International》2008,174(3):966-970
The technique of retrieving Green's functions by pairwise correlation of a random wavefield is used to estimate the stability of the timing system of a seismic network. The method is demonstrated with data from a network consisting of stations with four independent clocks and GPS-receivers. For a two years period, daily measurements of the timing error of each of the four systems are obtained. These measurements can be used to correct the timing of the data in periods without GPS reception. The accuracy of this method can exceed the precision of the internal station clocks already after a single day of uncorrected drift. 相似文献
7.
Laiyu Lu Valerie Maupin Rongsheng Zeng Zhifeng Ding 《Geophysical Journal International》2008,174(3):857-872
The integral equation method is used to model the propagation of surface waves in 3-D structures. The wavefield is represented by the Fredholm integral equation, and the scattered surface waves are calculated by solving the integral equation numerically. The integration of the Green's function elements is given analytically by treating the singularity of the Hankel function at R = 0 , based on the proper expression of the Green's function and the addition theorem of the Hankel function. No far-field and Born approximation is made. We investigate the scattering of surface waves propagating in layered reference models imbedding a heterogeneity with different density, as well as Lamé constant contrasts, both in frequency and time domains, for incident plane waves and point sources. 相似文献
8.
A general correspondence principle is presented that relates any time-domain electromagnetic diffusion field to an electromagnetic wavefield in a 'corresponding' configuration. The principle applies to arbitrarily inhomogeneous and anisotropic media and arbitrary transmitters and receivers. For the correspondence between the two types of electromagnetic fields to hold, the electric conductivity in the diffusive case and the permittivity in the wavefield case should have the same spatial variation, while the permeability distributions in space in the two cases are to be identical. Essential steps in the derivation of the correspondence principle are the use of the time Laplace transformation of causal signals, taken at real, positive values of the transform parameter, the Schouten-Van der Pol theorem in the theory of the Laplace transformation, and the reliance upon Lerch's theorem of the uniqueness of the interrelation between causal field quantities and their time-Laplace-transform representations at real, positive values of the transform parameter. Correspondence is then established between the tensorial Green's functions in the two cases, where the Green's functions are the point-receiver responses (either electric or magnetic field) to point-transmitter excitations (either electric- or magnetic-current source).
Through the correspondence principle, all transient electromagnetic wavefields (where losses are neglected) have as a counterpart a transient diffusive electromagnetic field (where the electric displacement current is neglected). The interrelation yields the tool to compare quantitatively the potentialities of the two types of fields in transient electromagnetic geophysical prospecting.
Finally, a general medium-parameter scaling law for time-domain electromagnetic wavefields is presented. 相似文献
Through the correspondence principle, all transient electromagnetic wavefields (where losses are neglected) have as a counterpart a transient diffusive electromagnetic field (where the electric displacement current is neglected). The interrelation yields the tool to compare quantitatively the potentialities of the two types of fields in transient electromagnetic geophysical prospecting.
Finally, a general medium-parameter scaling law for time-domain electromagnetic wavefields is presented. 相似文献
9.
Summary . Born inverse methods give accurate and stable results when the source wavelet is impulsive. However, in many practical applications (reflection seismology) an impulsive source cannot be realized and the inversion needs to be generalized to include an arbitrary source function. In this paper, we present a Born solution to the seismic inverse problem which can accommodate an arbitrary source function and give accurate and stable results. It is shown that the form of the generalized inversion algorithm reduces to a Wiener shaping ***filter, which is solved efficiently using a Levinson recursion algorithm. Numerical examples of synthetic and real field data illustrate the validity of our method. 相似文献
10.
Synthetic SH seismograms in a laterally varying medium by the discrete wavenumber method 总被引：1，自引：0，他引：1
Summary. We present a new method to calculate the SH wavefield produced by a seismic source in a half-space with an irregular buried interface. The diffracting interface is represented by a distribution of body forces. The Green's functions needed to solve the boundary conditions are evaluated using the discrete wavenumber method. Our approach relies on the introduction of a periodicity in the source-medium configuration and on the discretization of the interface at regular spacing. The technique developed is applicable to boundaries of arbitrary shapes and is valid at all frequencies. Some examples of calculation in simple configurations are presented showing the capabilities of the method. 相似文献
11.
Sylvie Kelner Michel Bouchon & Olivier Coutant 《Geophysical Journal International》1999,137(1):197-206
We study the propagation of P waves through media containing open fractures by performing numerical simulations. The important parameter in such problems is the ratio between crack length and incident wavelength. When the wavelength of the incident wavefield is close to or shorter than the crack length, the scattered waves are efficiently excited and the attenuation of the primary waves can be observed on synthetic seismograms. On the other hand, when the incident wavelength is greater than the crack length, we can simulate the anisotropic behaviour of fractured media resulting from the scattering of seismic waves by the cracks through the time delay of the arrival of the transmitted wave. The method of calculation used is a boundary element method in which the Green's functions are computed by the discrete wavenumber method. For simplicity, the 2-D elastodynamic diffraction problem is considered. The rock matrix is supposed to be elastic, isotropic and homogeneous, while the cracks are all empty and have the same length and strike direction. An iterative method of calculation of the diffracted wavefield is developed in the case where a large number of cracks are present in order to reduce the computation time. The attenuation factor Q −1 of the direct waves passing through a fractured zone is measured in several frequency bands. We observe that the attenuation factor Q −1 of the direct P wave peaks around kd = 2, where k is the incident wavenumber and d the crack length, and decreases proportionally to ( kd ) −1 in the high-wavenumber range. In the long-wavelength domain, the velocity of the direct P wave measured for two different crack realizations is very close to the value predicted by Hudson's theory on the overall elastic properties of fractured materials. 相似文献
12.
Summary . The spectral function of a perfectly elastic, horizontally stratified medium has been demonstrated previously to provide an attractive formulation to describe the properties of the one-dimensional synthetic seismogram (Robinson & Treitel). Here we examine the mathematical framework of the Model in still greater detail. Knowledge of this fine structure of the synthetic seismogram leads to the solution of two particular seismic inverse problems. First, we consider a layered medium with an arbitrary surface reflection coefficient c o , where | c o |<1, and which contains an impulsive source immediately above the surface. Given the corresponding synthetic seismogram, we develop an inverse, or backward recursion formalism which recovers the entire series of original reflection coefficients. Second, we consider a similar problem for an impulsive source located just below the surface. Both inversion procedures constitute a continuation of the work of Goupillaud and of Sherwood & Trorey, and represent a generalization of the classical technique originally proposed by Kunetz which, however, only holds for the marine case, co =±1. The present approach is not so constrained and thereby becomes applicable to land seismograms as well.
If products of third or higher order in the reflection coefficients can be neglected, significant simplifications arise in the theory. In that event the usual representation of the synthetic seismogram as a ratio of two polynomials in the complex variable z becomes particularly revealing. The numerator polynomial is then approximately equal to the z transform of the reflection coefficient series, while the denominator polynomial is approximately equal to the z transform of the autocorrelation of these reflection coefficients. The resulting simplified theory affords important computational savings in the appropriate backward recursion algorithms. 相似文献
If products of third or higher order in the reflection coefficients can be neglected, significant simplifications arise in the theory. In that event the usual representation of the synthetic seismogram as a ratio of two polynomials in the complex variable z becomes particularly revealing. The numerator polynomial is then approximately equal to the z transform of the reflection coefficient series, while the denominator polynomial is approximately equal to the z transform of the autocorrelation of these reflection coefficients. The resulting simplified theory affords important computational savings in the appropriate backward recursion algorithms. 相似文献
13.
Three-dimensional inversion without blocks 总被引：12，自引：0，他引：12
Summary. We propose a method for solving non-linear inverse problems in the case where the unknown is a function of the spatial coordinates and the data set is discrete and finite. The method is based on a generalized leastsquares criterion, it is defined directly for non-linear problems (without previous linearization of the forward problem), and in the particular linear case it gives the same results (although slightly more general) than the Backus & Gilbert approach. As an example, we apply the method to the three-dimensional seismic velocity inverse problem, using as data the arrival times of seismic waves. The following paper (Nercessian et al .) shows some esults obtained using the present method. 相似文献
14.
Tatsuhiko Hara 《Geophysical Journal International》1997,130(1):251-256
We present a new method for centroid moment tensor (CMT) inversion, in which we employ the Green's function computed for aspherical earth models using the Direct Solution Method. We apply this method to CMT inversion of low-frequency seismic spectra for the 1994 Bolivia and 1996 Flores Sea deep earthquakes. The estimated centroid locations agree well with those obtained by multiple-shock analyses using body-wave data. This shows that it is possible to obtain reliable CMT solutions by analyses of low-frequency seismic spectra using accurate Green's functions computed for present 3-D earth models. 相似文献
15.
Summary. The one-dimensional acoustic wave equation has been transformed to two coupled first-order equations whose inverse solution is obtained through application of the Gopinath and Sondhi integral equation. A scattering solution of the Schrödinger wave equation for an explosive source leads us to express the kernel of the Gopinath–Sondhi integral equation in terms of a seismic reflection response. A numerical solution of the integral equation obtained by a trapezoidal rule yields a continuous impedance profile whose derivative has step-like discontinuities. The method is illustrated with computer model studies. 相似文献
16.
Jose Pujol Thomas Bohlen Thies Beilecke Wolfgang Rabbel 《Geophysical Journal International》2007,169(2):563-578
VSP data collected in the KTB (Germany) borehole to a depth of 8.5 km in 1999 show a surprising spectral modulation of the downgoing wavefield. After filtering the data with the singular value decomposition technique it was found that below about 6.2 km there are two depth intervals where the modulation can be explained in terms of a basic wavelet plus two weighted and delayed copies of that wavelet, with the delay for each wavelet remaining almost constant in each interval. The boundary between the two intervals is at about 7.25 km depth and above and below this depth the delay for the second wavelet is almost the same, while the delay for the third wavelet is significantly different. Neither the modulation nor its depth variation are source related and cannot be explained in terms of multiple reflections in a subhorizontal low-velocity layer. On the other hand, finite difference synthetic data show that subvertical layering (which is prevalent in the borehole area) provides a mechanism that can explain the observations. This mechanism has analogies with the generation of the standard refracted (i.e. head) waves. When a plane wave front propagates perpendicular to the boundaries of a vertical low-velocity layer surrounded by two vertical high-velocity layers, refracted wave fronts are generated in the low-velocity layer, which in turn generate secondary wave fronts in the high-velocity layers. These wave fronts trail the primary wave fronts by a constant delay whose magnitude has a simple dependence on the thickness of the low-velocity layer and the velocities involved. This process creates multipath arrivals that in geological settings with steeply inclined and faulted layers may appear and disappear rather abruptly, which may contribute to a scattered appearance of the wavefield. 相似文献
17.
Summary. The equations describing seismic waves in a stratified earth have a number of symmetry properties, one of which has recently been used by Garmany to derive a simple expression for the inverse of the matrix of eigenvectors appearing in the solution of the equations. We review these symmetries of the wave equation in several notations to demonstrate that the property used by Garmany is distinct from the usual symmetries found in the seismological literature. Like the others, the new symmetry has implications for the reflection and transmission properties of a medium. These implications are briefly reviewed in order to show how the new symmetry is placed relative to the others. A limited discussion of the physical origins of the symmetries is given and, though the overall picture is incomplete, it is noted that the new symmetry yields conservation of energy for reflection/transmission at a single interface in all types of media (anisotropic, lossy, etc.). 相似文献
18.
Summary. For the determination of lateral velocity or absorption inhomogeneities, methods such as the generalized matrix inversion and its damped versions, for example the stochastic inverse, are usually applied in seismology to travel-time or amplitude anomalies. These methods are not appropriate for the solution of very extensive systems of equations. Reconstruction techniques as developed for computer tomography are suitable for operations with extremely large numbers of equations and unknown parameters. In this paper solutions obtained with the BPT (Back Projection Technique), ART (Algebraic Reconstruction Technique) and SIRT (Simultaneous Iterative Reconstruction Technique) are compared with those obtained from a damped version of the generalized inverse method. Data of 2-D model-seismic experiments are presented for demonstration. 相似文献
19.
David W. Eaton 《Geophysical Journal International》2006,166(3):1249-1258
The Kirchhoff (or tangent plane) approximation, derived from the theoretically complete Kirchhoff–Helmholtz integral representation for the seismic wavefield, has been used extensively for the analysis of seismic-wave scattering from irregular interfaces; however, the accuracy of this method for curved interfaces has not been rigorously established. This paper describes an efficient Kirchhoff algorithm to simulate scattered waves from an arbitrarily curved interface in an elastic medium. Synthetic seismograms computed using this algorithm are compared with exact synthetics computed using analytical formulae for scattering of plane P waves by a spherical elastic inclusion. A windowing technique is used to remove strong internal reverberations from the analytical solution. Although the Kirchhoff method tends to underestimate the total scattering intensity, the accuracy of the approximation improves with increasing value of the wavenumber-radius product, kR . The arrival times and pulse shapes of primary reflections from the sphere are well approximated using the Kirchhoff approach regardless of curvature of the scattering surface, but the amplitudes are significantly underestimated for kR ≤ 5. The results of this work provide some new guidelines to assess the accuracy of Kirchhoff-synthetic seismograms for curved interfaces. 相似文献
20.
Eystein S. Husebye ers Christoffersson Keiiti Aki Christine Powell 《Geophysical Journal International》1976,46(2):319-340
About 1500 readings of teleseismic P -time residuals obtained from the US Geological Survey seismograph network in central California have been used to obtain a three-dimensional image of seismic velocity anomalies for this area by the method of Aki, Christoffersson & Husebye We found that the California network is less suitable than the LASA and NORSAR arrays for this kind of studies because of its greater proportion of peripheral blocks in which the resolution is very poor for the stochastic inverse solution and the random error effect is severe for the generalized inverse solution. Nevertheless, the resultant velocity anomalies show a remarkable correlation with the San Andreas fault zone to a depth of 75 km. The anomaly pattern changes drastically as the depth exceeds 75 km, suggesting that the asthenosphere has been reached. 相似文献