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Open accessJournal ArticleDOI: 10.1103/PHYSREVRESEARCH.3.013206

Focusing and Green's function retrieval in three-dimensional inverse scattering revisited: A single-sided Marchenko integral for the full wave field

04 Mar 2021-Vol. 3, Iss: 1, pp 013206
Abstract: The authors present a framework for Marchenko-type integrals in three-dimensional full wavefield inverse scattering by introducing the homogeneous Green's function of the second kind.

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Topics: Green's function (64%), Inverse scattering problem (60%), Field (physics) (53%) ... read more
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13 results found


Open accessProceedings Article
01 Jan 1993-
Abstract: Wave field splitting, invariant imbedding, and phase space methods reformulate the Helmholtz wave propagation problem in terms of an operator scattering matrix characteristic of the modeled environment. The subsequent equations for the reflection and transmission operators are of first-order (one-way) in range, nonlinear (Riccati-like), and, in general, nonlocal. The reflection and transmission operator equations provide the framework for constructing inverse algorithms based on, in principle, exact solution methods

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Topics: Wave propagation (62%), Reflection (physics) (56%), Helmholtz equation (56%) ... read more

44 Citations


Open access
01 May 2010-
Abstract: SUMMARY Seismic interferometry, also known as Green’s function retrieval by crosscorrelation, has a wide range of applications, ranging from surface wave tomography using ambient noise, to creating virtual sources for improved reflection seismology. Despite its successful applications, the crosscorrelation approach also has its limitations. The main underlying assumptions are that the medium is lossless and that the wave field is equipartitioned. These assumptions are in practice often violated: the medium of interest is often illuminated from one side only, the sources may be irregularly distributed, and, particularly for EM applications, losses may be significant. These limitations may partly be overcome by reformulating seismic interferometry as a multidimensional deconvolution (MDD) process. We present a systematic analysis of seismic interferometry by crosscorrelation and by MDD. We show that for the non-ideal situations mentioned above, the correlation function is proportional to a Green’s function with a blurred source. The source blurring is quantified by a so-called point-spread function which, like the correlation function, can be derived from the observed data (i.e., without the need to know the sources and the medium). The source of the Green’s function obtained by the correlation method can be deblurred by deconvolving the correlation function for the point-spread function. This is the essence of seismic interferometry by MDD. We illustrate the crosscorrelation and MDD methods for controlled-source and passive data applications with numerical examples and discuss the advantages and limitations of both methods.

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Topics: Seismic interferometry (71%), Deconvolution (62%)

16 Citations


Open accessJournal ArticleDOI: 10.1190/GEO2020-0854.1
01 Sep 2021-Geophysics
Abstract: With the Marchenko method, it is possible to retrieve Green’s functions between virtual sources in the subsurface and receivers at the surface from reflection data at the surface and focusi...

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Topics: Reflection (physics) (61%)

10 Citations


Open accessJournal ArticleDOI: 10.1093/GJI/GGAB220
Abstract: Marchenko methods are based on integral representations which express Green’s functions for virtual sources and/or receivers in the subsurface in terms of the reflection response at the surface. An underlying assumption is that inside the medium the wave field can be decomposed into downgoing and upgoing waves and that evanescent waves can be neglected. We present a new derivation of Green’s function representations which circumvents these assumptions, both for the acoustic and the elastodynamic situation. These representations form the basis for research into new Marchenko methods which have the potential to handle refracted and evanescent waves and to more accurately image steeply dipping reflectors.

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Topics: Reflection (physics) (51%), Green's function (51%)

5 Citations


Open accessJournal ArticleDOI: 10.1190/GEO2020-0939.1
01 Sep 2021-Geophysics
Abstract: Reconstructing the details of subsurface structures deep beneath complex overburden structures, such as subsalt, remains a challenge for seismic imaging. Over the past few years, the Marche...

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Topics: Overburden (56%), Geophysical imaging (54%)

2 Citations


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56 results found


Open accessJournal ArticleDOI: 10.1145/355984.355989
Abstract: An iterative method is given for solving Ax ~ffi b and minU Ax b 112, where the matrix A is large and sparse. The method is based on the bidiagonalization procedure of Golub and Kahan. It is analytically equivalent to the standard method of conjugate gradients, but possesses more favorable numerical properties. Reliable stopping criteria are derived, along with estimates of standard errors for x and the condition number of A. These are used in the FORTRAN implementation of the method, subroutine LSQR. Numerical tests are described comparing I~QR with several other conjugate-gradient algorithms, indicating that I~QR is the most reliable algorithm when A is ill-conditioned.

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Topics: Sparse approximation (58%), Iterative method (56%), Bidiagonalization (56%) ... read more

3,828 Citations


Journal ArticleDOI: 10.1190/1.3238367
Jean Virieux1, Stéphane Operto2Institutions (2)
01 Nov 2009-Geophysics
Abstract: Full-waveform inversion FWI is a challenging data-fitting procedure based on full-wavefield modeling to extract quantitative information from seismograms. High-resolution imaging at half the propagated wavelength is expected. Recent advances in high-performance computing and multifold/multicomponent wide-aperture and wide-azimuth acquisitions make 3D acoustic FWI feasible today. Key ingredients of FWI are an efficient forward-modeling engine and a local differential approach, in which the gradient and the Hessian operators are efficiently estimated. Local optimization does not, however, prevent convergence of the misfit function toward local minima because of the limited accuracy of the starting model, the lack of low frequencies, the presence of noise, and the approximate modeling of the wave-physics complexity. Different hierarchical multiscale strategiesaredesignedtomitigatethenonlinearityandill-posedness of FWI by incorporating progressively shorter wavelengths in the parameter space. Synthetic and real-data case studies address reconstructing various parameters, from VP and VS velocities to density, anisotropy, and attenuation. This review attempts to illuminate the state of the art of FWI. Crucial jumps, however, remain necessary to make it as popular as migration techniques. The challenges can be categorized as 1 building accurate starting models with automatic procedures and/or recording low frequencies, 2 defining new minimization criteria to mitigate the sensitivity of FWI to amplitude errors and increasing the robustness of FWI when multiple parameter classes are estimated, and 3 improving computational efficiency by data-compression techniquestomake3DelasticFWIfeasible.

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2,460 Citations


Open accessJournal ArticleDOI: 10.1190/1.2213955
Kees Wapenaar1, Jacob T. Fokkema1Institutions (1)
17 Aug 2006-Geophysics
Abstract: The term seismic interferometry refers to the principle of generating new seismic responses by crosscorrelating seismic observations at different receiver locations. The first version of this principle was derived by Claerbout (1968), who showed that the reflection response of a horizontally layered medium can be synthesized from the autocorrelation of its transmission response. For an arbitrary 3D inhomogeneous lossless medium it follows from Rayleigh's reciprocity theorem and the principle of time-reversal invariance that the acoustic Green's function between any two points in the medium can be represented by an integral of crosscorrelations of wavefield observations at those two points. The integral is along sources on an arbitrarily shaped surface enclosing these points. No assumptions are made with respect to the diffusivity of the wavefield. The Rayleigh-Betti reciprocity theorem leads to a similar representation of the elastodynamic Green's function. When a part of the enclosing surface is the earth's free surface, the integral needs only to be evaluated over the remaining part of the closed surface. In practice, not all sources are equally important: The main contributions to the reconstructed Green's function come from sources at stationary points. When the sources emit transient signals, a shaping filter can be applied to correct for the differences in source wavelets. When the sources are uncorrelated noise sources, the representation simplifies to a direct crosscorrelation of wavefield observations at two points, similar as in methods that retrieve Green's functions from diffuse wavefields in disordered media or in finite media with an irregular bounding surface.

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Topics: Seismic interferometry (61%), Green's function (54%), Reflection (physics) (51%) ... read more

640 Citations


Open accessJournal ArticleDOI: 10.2528/PIER01061103
Abstract: We discuss the problem of the reconstruction of the profile of an inhomogeneous object from scattered field data. Our starting point is the contrast source inversion method, where the unknown contrast sources and the unknown contrast are updated by an iterative minimization of a cost functional. We discuss the possibility of the presence of local minima of the nonlinear cost functional and under which conditions they can exist. Inspired by the successful implementation of the minimization of total variation and other edgepreserving algorithms in image restoration and inverse scattering, we have explored the use of these image-enhancement techniques as an extra regularization. The drawback of adding a regularization term to the cost functional is the presence of an artificial weighting parameter in the cost functional, which can only be determined through considerable numerical experimentation. Therefore, we first discuss the regularization as a multiplicative constraint and show that the weighting parameter is now completely prescribed by the error norm of the data equation and the object equation. Secondly, inspired by the edge-preserving algorithms, we introduce a new type of regularization, based on a weighted L2 total variation norm. The advantage is that the updating parameters in the contrast source inversion method can be determined explicitly, without the usual line minimization. In addition this new regularization shows excellent edge-preserving properties. Numerical experiments illustrate that the present multiplicative regularized inversion scheme is very robust, handling noisy as well as limited data very well, without the necessity of artificial regularization parameters. 190 Van den Berg and Abubakar

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Topics: Weighting (51%), Inverse scattering problem (51%), Norm (mathematics) (51%) ... read more

293 Citations


Open accessJournal ArticleDOI: 10.1190/1.3457445
Kees Wapenaar1, Deyan Draganov1, Roel Snieder2, Xander Campman3  +1 moreInstitutions (3)
14 Sep 2010-Geophysics
Abstract: Seismic interferometry involves the crosscorrelation of responses at different receivers to obtain the Green’s function between these receivers. For the simple situation of an impulsive plane wave propagating along the x-axis, the crosscorrelation of the responses at two receivers along the x-axis gives the Green’s function of the direct wave between these receivers. When the source function of the plane wave is a transientas in exploration seismology or a noise signalas in passive seismology, then the crosscorrelation gives the Green’s function, convolved with the autocorrelation of the source function. Direct-wave interferometry also holds for 2D and 3D situations, assuming the receivers are surrounded by a uniform distribution of sources. In this case, the main contributions to the retrieved direct wave between the receivers come from sources in Fresnel zones around stationary points. The main application of direct-wave interferometry is the retrieval of seismic surface-wave responses from ambient noise and the subsequent tomographic determination of the surfacewave velocity distribution of the subsurface. Seismic interferometry is not restricted to retrieving direct waves between receivers. In a classic paper, Claerbout shows that the autocorrelation of the transmission response of a layered medium gives the plane-wave reflection response of that medium. This is essentially 1D reflected-wave interferometry. Similarly, the crosscorrelation of the transmission responses, observed at two receivers, of an arbitrary inhomogeneous medium gives the 3D reflection response of that medium. One of the main applications of reflected-wave interferometry is retrieving the seismic reflection response from ambient noise and imaging of the reflectors in the subsurface. A common aspect of direct- and reflected-wave interferometry is that virtual sources are created at positions where there are only receivers without requiring knowledge of the subsurface medium parameters or of the positions of the actual sources.

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Topics: Seismic interferometry (73%), Interferometry (56%), Reflection (physics) (55%) ... read more

292 Citations


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