共查询到20条相似文献，搜索用时 437 毫秒
1.
B.L.N.Kennett 《Geophysical Journal International》1998,133(1):159-174
A new formulation for the propagation of surface waves in three-dimensionally varying media is developed in terms of modal interactions. A variety of assumptions can be made about the nature of the modal field: a single set of reference modes, a set of local modes for the structure beneath a point, or a set of local modes for a laterally varying reference structure. Each modal contribution is represented locally as a spectrum of plane waves propagating in different directions in the horizontal plane. The influence of 3-D structure is included by allowing coupling between different modal branches and propagation directions. For anisotropic models, with allowance for attenuation, the treatment leads to a set of coupled 2-D partial differential equations for the weight functions for different modal orders.
The representation of the guided wavefield requires the inclusion of a full set of modes, so that, even for isotropic models, both Love and Rayleigh modes appear as different polarization states of the modal spectrum. The coupling equations describe the interaction between the different polarizations induced by the presence of the 3-D structure.
The level of lateral variation within the 3-D model is not required to be small. Horizontal refraction or reflection of the surface wavefield can be included by allowing for transfer between modes travelling in different directions. Approximate forms of the coupled equation system can be employed when the level of heterogeneity is small, for example the coupling between the fundamental mode and higher modes can often be neglected, or forward propagation can be emphasized by restricting the interaction to a limited band of plane waves covering the expected direction of propagation. 相似文献
The representation of the guided wavefield requires the inclusion of a full set of modes, so that, even for isotropic models, both Love and Rayleigh modes appear as different polarization states of the modal spectrum. The coupling equations describe the interaction between the different polarizations induced by the presence of the 3-D structure.
The level of lateral variation within the 3-D model is not required to be small. Horizontal refraction or reflection of the surface wavefield can be included by allowing for transfer between modes travelling in different directions. Approximate forms of the coupled equation system can be employed when the level of heterogeneity is small, for example the coupling between the fundamental mode and higher modes can often be neglected, or forward propagation can be emphasized by restricting the interaction to a limited band of plane waves covering the expected direction of propagation. 相似文献
2.
Hiroyuki Fujiwara 《Geophysical Journal International》1997,128(3):571-584
When full 3-D modelling is too costly or cumbersome, computations of 3-D elastic wave propagation in laterally heterogeneous, multilayered 2-D geological structures may enhance considerably our ability to predict strong ground motion for seismological and engineering purposes. Towards this goal, we extend the method based on the combination of the thin-layer finite-element and boundary-element methods (TLFE-BEM) and calculate windowend f - k spectra of the 3-D wavefield. The windowed f - k spectra are spatially localized spectra from which the local properties of the wavefield can be extracted. The TLFE-BEM is particularly suited for calculating the complete wavefield where surface waves are dominant in multilayered media. The computations are performed in the frequency domain, providing the f - k spectra directly. From the results for the 3-D wavefield excited by a point source in a 2-D multilayered, sloped structure, it can be said that the phase velocity of the fundamental-mode Rayleigh wave in a laterally heterogeneous multilayered medium, estimated from the windowed f - k spectra, varies with the location of the point source. For the model calculated in this article, the phase velocity varies between the value for the flat layered structure of the thick-layer side and that for the structure just under the centre of the window. The exact subsurface structure just under the centre of an array in a laterally heterogeneous medium cannot be obtained if we use the f - k spectral analysis assuming a flat layered structure. 相似文献
3.
Phil R. Cummins Nozomu Takeuchi Robert J. Geller 《Geophysical Journal International》1997,130(1):1-16
We use the Direct Solution Method (DSM) together with the modified operators derived by Geller & Takeuchi (1995) and Takeuchi, Geller & Cummins (1996) to compute complete synthetic seismograms and their partial derivatives for laterally heterogeneous models in spherical coordinates. The methods presented in this paper are well suited to conducting waveform inversion for 3-D Earth structure. No assumptions of weak perturbation are necessary, although such approximations greatly improve computational efficiency when their use is appropriate.
An example calculation is presented in which the toroidal wavefield is calculated for an axisymmetric model for which velocity is dependent on depth and latitude but not longitude. The wavefield calculated using the DSM agrees well with wavefronts calculated by tracing rays. To demonstrate that our algorithm is not limited to weak, aspherical perturbations to a spherically symmetric structure, we consider a model for which the latitude-dependent part of the velocity structure is very strong. 相似文献
An example calculation is presented in which the toroidal wavefield is calculated for an axisymmetric model for which velocity is dependent on depth and latitude but not longitude. The wavefield calculated using the DSM agrees well with wavefronts calculated by tracing rays. To demonstrate that our algorithm is not limited to weak, aspherical perturbations to a spherically symmetric structure, we consider a model for which the latitude-dependent part of the velocity structure is very strong. 相似文献
4.
Today's numerical methods like the Spectral Element Method (SEM) allow accurate simulation of the whole seismic field in complex 3-D geological media. However, the accuracy of such a method requires physical discontinuities to be matched by mesh interfaces. In many realistic earth models, the design of such a mesh is difficult and quite ineffective in terms of numerical cost. In this paper, we address a limited aspect of this problem: an earth model with a thin shallow layer below the free surface in which the elastic and density properties are different from the rest of the medium and in which rapid vertical variations are allowed. We only consider here smooth lateral variations of the thickness and elastic properties of the shallow layer. In the limit of a shallow layer thickness very small compared to the smallest wavelength of the wavefield, by resorting to a second order matching asymptotic approximation, the thin layer can be replaced by a vertically smooth effective medium without discontinuities together with a specific Dirichlet to Neumann (DtN) surface boundary condition. Such a formulation allows to accurately take into account complex thin shallow structures within the SEM without the classical mesh design and time step constraints. Corrections at receivers and source—when the source is located within the thin shallow layer—have been also derived. Accuracy and efficiency of this formulation are assessed on academic tests. The stability and limitations of this formulation are also discussed. 相似文献
5.
Caroline de Linage Jacques Hinderer Yves Rogister 《Geophysical Journal International》2007,171(3):986-994
A data space approach to magnetotelluric (MT) inversion reduces the size of the system of equations that must be solved from M × M , as required for a model space approach, to only N × N , where M is the number of model parameter and N is the number of data. This reduction makes 3-D MT inversion on a personal computer possible for modest values of M and N . However, the need to store the N × M sensitivity matrix J remains a serious limitation. Here, we consider application of conjugate gradient (CG) methods to solve the system of data space Gauss–Newton equations. With this approach J is not explicitly formed and stored, but instead the product of J with an arbitrary vector is computed by solving one forward problem. As a test of this data space conjugate gradient (DCG) algorithm, we consider the 2-D MT inverse problem. Computational efficiency is assessed and compared to the data space Occam's (DASOCC) inversion by counting the number of forward modelling calls. Experiments with synthetic data show that although DCG requires significantly less memory, it generally requires more forward problem solutions than a scheme such as DASOCC, which is based on a full computation of J . 相似文献
6.
7.
In case of a complex overburden, the seismic data can be greatly improved by applying a full wavefield redatuming procedure. In practice, the application of the redatuming process to 3-D data acquired by conventional acquisition designs is non-trivial. Because of the large amount of data involved in the 3-D redatuming process and because of the sparseness of these data, it is impossible to apply conventional wave equation datuming directly.
We present a data mapping approach to redatuming (DMR), which follows the concept of Kirchhoff data mapping. A simplified background medium where no ray bending occurs is assumed for the medium below the datum in order to map an input data set referenced to the acquisition surface to an output data set referenced to the new datum level. The DMR method can be interpreted as a simplified version of the Kirchhoff summation redatuming (KSR) method, where one of the 2-D integrals over the acquisition coordinates can be solved analytically. Consequently, in this approach fewer traces are involved in the computation of one time sample (a 2-D integral is computed instead of a 4-D integral), which makes it particularly attractive for the application to 3-D data sets.
In this paper the theory underlying data mapping redatuming is discussed and the proposed approach is tested on fully sampled 2-D and 3-D synthetic data from models with both simple and complex velocity distributions in the subsurface.
The tests clearly show that the objective of producing results that are comparable to the conventional KSR has been achieved. The redatumed traces are dynamically and kinematically correct. Furthermore, these results confirm that the dependency of the new approach on the assumed medium below the datum level is, indeed, weak because the assumption of a velocity medium where no ray bending occurs is already sufficient to produce correct results. 相似文献
We present a data mapping approach to redatuming (DMR), which follows the concept of Kirchhoff data mapping. A simplified background medium where no ray bending occurs is assumed for the medium below the datum in order to map an input data set referenced to the acquisition surface to an output data set referenced to the new datum level. The DMR method can be interpreted as a simplified version of the Kirchhoff summation redatuming (KSR) method, where one of the 2-D integrals over the acquisition coordinates can be solved analytically. Consequently, in this approach fewer traces are involved in the computation of one time sample (a 2-D integral is computed instead of a 4-D integral), which makes it particularly attractive for the application to 3-D data sets.
In this paper the theory underlying data mapping redatuming is discussed and the proposed approach is tested on fully sampled 2-D and 3-D synthetic data from models with both simple and complex velocity distributions in the subsurface.
The tests clearly show that the objective of producing results that are comparable to the conventional KSR has been achieved. The redatumed traces are dynamically and kinematically correct. Furthermore, these results confirm that the dependency of the new approach on the assumed medium below the datum level is, indeed, weak because the assumption of a velocity medium where no ray bending occurs is already sufficient to produce correct results. 相似文献
8.
We present a new approach of the Indirect Boundary Element Method (IBEM) for 3-D topographic problems which can be used to deal with an infinitely spread free surface owing to the introduction of a reference solution, that is the analytical solution for the half-space with a flat free surface. This approach is an efficient countermeasure for the non-physical waves owing to the domain truncation which contaminates the computed results in the ordinary approach. Theoretical consideration shows that this newly proposed approach is a higher-grade approximation than some existing ones and achieves a higher efficacy and accuracy than those of existing ones. The discretization of the resulting boundary integral equation for this formulation is carried out with triangular elements. Their contributions to the solution are calculated by Gaussian numerical integration except in the case where the wavefield is evaluated on the source element itself. For this case, we present an analytical formula based on the reasonable assumption that the elements are much smaller than the wavelengths appearing in the calculation. Several numerical examples used for validation show acceptably precise results. 相似文献
9.
Tarje Nissen-Meyer Alexandre Fournier F. A. Dahlen 《Geophysical Journal International》2008,174(3):873-888
We portray a dedicated spectral-element method to solve the elastodynamic wave equation upon spherically symmetric earth models at the expense of a 2-D domain. Using this method, 3-D wavefields of arbitrary resolution may be computed to obtain Fréchet sensitivity kernels, especially for diffracted arrivals. The meshing process is presented for varying frequencies in terms of its efficiency as measured by the total number of elements, their spacing variations and stability criteria. We assess the mesh quantitatively by defining these numerical parameters in a general non-dimensionalized form such that comparisons to other grid-based methods are straightforward. Efficient-mesh generation for the PREM example and a minimum-messaging domain decomposition and parallelization strategy lay foundations for waveforms up to frequencies of 1 Hz on moderate PC clusters. The discretization of fluid, solid and respective boundary regions is similar to previous spectral-element implementations, save for a fluid potential formulation that incorporates the density, thereby yielding identical boundary terms on fluid and solid sides. We compare the second-order Newmark time extrapolation scheme with a newly implemented fourth-order symplectic scheme and argue in favour of the latter in cases of propagation over many wavelengths due to drastic accuracy improvements. Various validation examples such as full moment-tensor seismograms, wavefield snapshots, and energy conservation illustrate the favourable behaviour and potential of the method. 相似文献
10.
Summary. Two methods of computing body wave synthetic seismograms in three-dimensional laterally varying media are discussed. Both these methods are based on the summation of Gaussian beams. In the first, the initial beam parameters are chosen at the source, in the second at the beam endpoints. Both these variants eliminate the ray method singularities. The expansion of the wavefield into plane waves may be considered as the limiting case of the first approach and the Chapman–Maslov method as the limiting case of the second approach. Computer algorithms are briefly described and numerical examples presented. In the first numerical example, the comparisons of the two approaches, based on summing Gaussian beams, with the reflectivity method indicate that the computed synthetic seismograms are satisfactorily accurate even in the caustic region. The next example suggests that the two methods discussed can be simply and effectively applied to 3-D laterally inhomogeneous structures. 相似文献
11.
As indicated by numerical tests, the computation of synthetic seismograms based on the modal summation technique, for 2-D or 3-D media, requires the computation of the transmission and reflection coupling coefficients, at sharp lateral heterogeneities, with a formulation that takes into account the possible non-Poissonian character of the media. 相似文献
12.
Inversion of time domain three-dimensional electromagnetic data 总被引：7，自引：0，他引：7
Eldad Haber Douglas W. Oldenburg R. Shekhtman 《Geophysical Journal International》2007,171(2):550-564
We present a general formulation for inverting time domain electromagnetic data to recover a 3-D distribution of electrical conductivity. The forward problem is solved using finite volume methods in the spatial domain and an implicit method (Backward Euler) in the time domain. A modified Gauss–Newton strategy is employed to solve the inverse problem. The modifications include the use of a quasi-Newton method to generate a pre-conditioner for the perturbed system, and implementing an iterative Tikhonov approach in the solution to the inverse problem. In addition, we show how the size of the inverse problem can be reduced through a corrective source procedure. The same procedure can correct for discretization errors that inevidably arise. We also show how the inverse problem can be efficiently carried out even when the decay time for the conductor is significantly larger than the repetition time of the transmitter wave form. This requires a second processor to carry an additional forward modelling. Our inversion algorithm is general and is applicable for any electromagnetic field ( E , H , d B / dt ) measured in the air, on the ground, or in boreholes, and from an arbitrary grounded or ungrounded source. Three synthetic examples illustrate the basic functionality of the algorithm, and a result from a field example shows applicability in a larger-scale field example. 相似文献
13.
Summary. In a paper by Červený & Pšenčik, high-frequency Gaussian beams in elastic 2-D, laterally inhomogeneous, smooth media were investigated as asymptotic high-frequency solutions of elastodynamic equations, concentrated close to rays of P - and S -waves. This paper generalizes the above results for 2-D, laterally inhomogeneous, layered structures. Gaussian beams concentrated close to any multiply-reflected, possibly converted, ray are investigated. Gaussian beams are regular everywhere, including caustic regions. The paraxial ray approximation, which allows the wavefield in the zero-order ray approximation to be evaluated not only directly on the ray, but also in its vicinity, is derived as a limiting case of the Gaussian beams. 相似文献
14.
We present a technique based on the single-scattering approximation that relates time-lapse localized changes in the propagation velocity to changes in the traveltime of singly scattered waves. We describe wave propagation in a random medium with homogeneous statistical properties as a single-scattering process where the fluctuations of the velocity with respect to the background velocity are assumed to be weak. This corresponds to one of two end-member regimes of wave propagation in a random medium, the first being single scattering, and the second multiple scattering. We present a formulation that relates the change in the traveltime of the scattered waves to a localized change in the propagation velocity by means of the Born approximation for the scattered wavefield. We validate the methodology with synthetic seismograms calculated with finite differences for 2-D acoustic waves. Potential applications of this technique include non-destructive evaluation of heterogeneous materials and time-lapse monitoring of heterogeneous reservoirs. 相似文献
15.
Traveltime computation methods for strongly heterogeneous 3-D media developed during recent years are well suited for earthquake location. We present here a new method based on the traveltime algorithm of Podvin-Lecomte, related to the inverse problem formulation of Tarantola & Valette. The Podvin-Lecomte method, based on the Huygens principle, is very robust and allows arbitrary surface topography and station placement even for borehole instruments. First arrival traveltimes are computed for each of the recording stations using a fine 3-D velocity mesh (up to 106 cells on a workstation). The traveltime grid allows the use of the Tarantola & Valette formulation, which enables a full non-linear approach. The solution is given as a 3-D probability density function of hypocentre coordinates, which accounts for the arrival time measurements as well as a priori information for the location, the accuracy of both the arrival time readings and the computation of the theoretical traveltimes. This powerful method called 3DGRIDLOC gives the location of the induced seismicity of the gas field of Lacq (France) using 443 520 cells of a 3-D velocity mesh and the observations from nine recording stations, one of which is located at the bottom of a 3880 m deep borehole. Location of synthetic foci as well as more than 500 actual earthquakes shows the real advantages of this new method versus the classical HYPO71. A new insight into the induced seismicity is now possible: induced seismicity may occur as far away as 10 km from the gas reservoir and involve a much greater volume of rock than expected using earlier locations. 相似文献
16.
17.
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
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
18.
Wavepath traveltime tomography 总被引：1，自引：1，他引：1
The elastic-wave equation is used to construct sensitivity kernels relating perturbations in elastic parameters to traveltime deviations. Computation of the functions requires a correlation of the forward-propagating seismic wavefield with a backward propagation of the residual wavefield. The computation of the wavefields is accomplished using a finite difference algorithm and is efficiently executed on a CM-2 parallel processor. The source and receiver locations have maximum sensitivity to velocity structure. The sensitivity kernels or wavepaths are well suited for transmission traveltime inversion such as cross-borehole tomography and vertical seismic profiling. Conventional ray tomography and wavepath tomography are applied to a set of P -wave arrival times, from a cross-borehole experiment at Kesterson, California. Because the wavepaths have increased sensitivity near the source and receiver there are differences in resolution of the velocity structure. Both techniques recover the same relative variations in velocity where the coverage is adequate. The wavepath solution is more laterally continuous and the dominant variation is vertical, as is expected for the layered sediments in this region. 相似文献
19.
C. P. A. Wapenaar 《Geophysical Journal International》1996,127(1):178-188
A general one-way representation of seismic data can be obtained by substituting a Green's one-way wavefield matrix into a reciprocity theorem of the convolution type for one-way wavefields. From this general one-way representation, several special cases can be derived.
By introducing a Green's one-way wavefield matrix for primaries , a generalized Bremmer series representation is obtained. Terminating this series after the first-order term yields a primary representation of seismic reflection data. According to this representation, primary seismic reflection data are proportional to a reflection operator, 'modified' by primary propagators for downgoing and upgoing waves. For seismic imaging, these propagators need to be inverted. Stable inverse primary propagators can easily be obtained from a one-way reciprocity theorem of the correlation type.
By introducing a Green's one-way wavefield matrix for generalized primaries , an alternative representation is obtained in which multiple scattering is organized quite differently (in comparison with the generalized Bremmer series representation). According to the generalized primary representation, full seismic reflection data are proportional to a reflection operator, 'modified' by generalized primary propagators for downgoing and upgoing waves. Internal multiple scattering is fully included in the generalized primary propagators {either via a series expansion or in a parametrized way). Stable inverse generalized primary propagators can be obtained from the one-way reciprocity theorem of the correlation type. These inverse propagators are the nucleus for seismic imaging techniques that take the angle-dependent dispersion effects due to fine-layering into account. 相似文献
By introducing a Green's one-way wavefield matrix for primaries , a generalized Bremmer series representation is obtained. Terminating this series after the first-order term yields a primary representation of seismic reflection data. According to this representation, primary seismic reflection data are proportional to a reflection operator, 'modified' by primary propagators for downgoing and upgoing waves. For seismic imaging, these propagators need to be inverted. Stable inverse primary propagators can easily be obtained from a one-way reciprocity theorem of the correlation type.
By introducing a Green's one-way wavefield matrix for generalized primaries , an alternative representation is obtained in which multiple scattering is organized quite differently (in comparison with the generalized Bremmer series representation). According to the generalized primary representation, full seismic reflection data are proportional to a reflection operator, 'modified' by generalized primary propagators for downgoing and upgoing waves. Internal multiple scattering is fully included in the generalized primary propagators {either via a series expansion or in a parametrized way). Stable inverse generalized primary propagators can be obtained from the one-way reciprocity theorem of the correlation type. These inverse propagators are the nucleus for seismic imaging techniques that take the angle-dependent dispersion effects due to fine-layering into account. 相似文献
20.
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