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Journal ArticleDOI

On seismic interferometry, the generalized optical theorem, and the scattering matrix of a point scatterer

27 Apr 2010-Geophysics (Society of Exploration Geophysicists)-Vol. 75, Iss: 3

AbstractWe have analyzed the far-field approximation of the Green's function representation for seismic interferometry. By writing each of the Green's functions involved in the correlation process as a superposition of a direct wave and a scattered wave, the Green's function representation is rewritten as a superposition of four terms. When the scattered waves are modeled with the Born approximation, it appears that a three-term approximation of the Green's function representation (omitting the term containing the crosscorrelation of the scattered waves) yields a nearly exact retrieval, whereas the full four-term expression leads to a significant nonphysical event. This is because the Born approximation does not conserve energy and therefore is an insufficient model to explain all aspects of seismic interferometry. We use the full four-term expression of the Green's function representation to derive the generalized optical theorem. Unlike other recent derivations, which use stationary phase analysis, our derivation uses reciprocity theory. From the generalized optical theorem, we derive the nonlinear scattering matrix of a point scatterer. This nonlinear model accounts for primary and multiple scattering at the point scatterer and conforms with well-established scattering theory of classical waves. The model is essential to explain fully the results of seismic interferometry, even when it is applied to the response of a single point scatterer. The nonlinear scattering matrix also has implications for modeling, inversion, and migration.

Topics: Born approximation (61%), Scattering theory (60%), Optical theorem (60%), Seismic interferometry (58%), Superposition principle (55%)

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Citations
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Journal ArticleDOI
Abstract: In the 1990s, the method of time-reversed acoustics was developed. This method exploits the fact that the acoustic wave equation for a lossless medium is invariant for time reversal. When ultrasonic responses recorded by piezoelectric transducers are reversed in time and fed simultaneously as source signals to the transducers, they focus at the position of the original source, even when the medium is very complex. In seismic interferometry the time-reversed responses are not physically sent into the earth, but they are convolved with other measured responses. The effect is essentially the same: The time-reversed signals focus and create a virtual source which radiates waves into the medium that are subsequently recorded by receivers. A mathematical derivation, based on reciprocity theory, formalizes this principle: The crosscorrelation of responses at two receivers, integrated over different sources, gives the Green’s function emitted by a virtual source at the position of one of the receivers and observed by the other receiver. This Green’s function representation for seismic interferometry is based on the assumption that the medium is lossless and nonmoving. Recent developments, circumventing these assumptions, include interferometric representations for attenuating and/or moving media, as well as unified representations for waves and diffusion phenomena, bending waves, quantum mechanical scattering, potential fields, elastodynamic, electromagnetic, poroelastic, and electroseismic waves. Significant improvements in the quality of the retrieved Green’s functions have been obtained with interferometry by deconvolution. A trace-by-trace deconvolution process compensates for complex source functions and the attenuation of the medium. Interferometry by multidimensional deconvolution also compensates for the effects of one-sided and/or irregular illumination.

189 citations


Journal ArticleDOI
Zvi Koren1, Igor Ravve1
Abstract: We present a new subsurface angle-domain seismic imaging systemforgeneratingandextractinghigh-resolutioninformation about subsurface angle-dependent reflectivity. The system enables geophysicists to use all recorded seismic data in a continuousfashiondirectlyinthesubsurfacelocalangledomainLAD, resulting in two complementary, full-azimuth, common-imageangle gather systems: directional and reflection. The complete setofinformationfrombothtypesofanglegathersleadstoaccurate, high-resolution, reliable velocity model determination and reservoir characterization. The directional angle decomposition enables the implementation of specular and diffraction imaging in real 3D isotropic/anisotropic geological models, leading to simultaneous emphasis on continuous structural surfaces and discontinuous objects such as faults and small-scale fractures. Structural attributes at each subsurface point, e.g., dip, azimuth andcontinuity,canbederiveddirectlyfromthedirectionalangle gathers. The reflection-angle gathers display reflectivity as a function of the opening angle and opening azimuth. These gathers are most meaningful in the vicinity of actual local reflecting surfaces,wherethereflectionanglesaremeasuredwithrespectto the derived background specular direction. The reflection-angle gathers are used for automatic picking of full-azimuth angle-domainresidualmoveoutsRMOwhich,togetherwiththederived background orientations of the subsurface reflection horizons, provide a complete set of input data to isotropic/anisotropic tomography. The full-azimuth, angle-dependent amplitude variations are used for reliable and accurate amplitude versus angle andazimuthAVAZanalysisandreservoircharacterization.The proposed system is most effective for imaging and analysis below complex structures, such as subsalt and subbasalt, high-velocity carbonate rocks, shallow low-velocity gas pockets, and others. In addition, it enables accurate azimuthal anisotropic imaging and analysis, providing optimal solutions for fracture detectionandreservoircharacterization.

155 citations


Journal ArticleDOI
TL;DR: The specific aspects of borehole radar are discussed and recent developments to become more sensitive to orientation and to exploit the supplementary information in different components in polarimetric uses of radar data are described.
Abstract: During the past 80 years, ground-penetrating radar (GPR) has evolved from a skeptically received glacier sounder to a full multicomponent 3D volume-imaging and characterization device. The tool can be calibrated to allow for quantitative estimates of physical properties such as water content. Because of its high resolution, GPR is a valuable tool for quantifying subsurface heterogeneity, and its ability to see nonmetallic and metallic objects makes it a useful mapping tool to detect, localize, and characterize buried objects. No tool solves all problems; so to determine whether GPR is appropriate for a given problem, studying the reasons for failure can provide an understanding of the basics, which in turn can help determine whether GPR is appropriate for a given problem. We discuss the specific aspects of borehole radar and describe recent developments to become more sensitiveto orientation and to exploit the supplementary information in different components in polarimetric uses of radar data. Multicomponent GPR data contain more diverse geometric information than single-channel data, and this is exploited in developed dedicated imaging algorithms. The evolution of these imaging schemes is discussed for ground-coupled and air-coupled antennas. For air-coupled antennas, the measured radiated wavefield can be used as the basis for the wavefield extrapolator in linear-inversion schemes with an imaging condition, which eliminates the source-time function and corrects for the measured radiation pattern. A handheld GPR system coupled with a metal detector is ready for routine use in mine fields. Recent advances in modeling, tomography, and full-waveform inversion, as well as Green's function extraction through correlation and deconvolution, show much promise in this field.

144 citations


Book
01 Feb 2012
Abstract: Only for you today! Discover your favourite seismic wave propagation and scattering in the heterogeneous earth second edition book right here by downloading and getting the soft file of the book. This is not your time to traditionally go to the book stores to buy a book. Here, varieties of book collections are available to download. One of them is this seismic wave propagation and scattering in the heterogeneous earth second edition as your preferred book. Getting this book b on-line in this site can be realized now by visiting the link page to download. It will be easy. Why should be here?

142 citations


Cites background from "On seismic interferometry, the gene..."

  • ...We note that the Green’s function retrieval for a scattering medium is strongly linked with the generalized optical theorem in the framework of scattering theory (Lu et al. 2011; Margerin and Sato 2011a,b; Snieder and Fleury 2010; Wapenaar et al. 2010)....

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Journal ArticleDOI
Abstract: Iterative substitution of the coupled Marchenko equations is a novel methodology to retrieve the Green's functions from a source or receiver array at an acquisition surface to an arbitrary location in an acoustic medium. The methodology requires as input the single-sided reflection response at the acquisition surface and an initial focusing function, being the time-reversed direct wavefield from the acquisition surface to a specified location in the subsurface. We express the iterative scheme that is applied by this methodology explicitly as the successive actions of various linear operators, acting on an initial focusing function. These operators involve multidimensional crosscorrelations with the reflection data and truncations in time. We offer physical interpretations of the multidimensional crosscorrelations by subtracting traveltimes along common ray paths at the stationary points of the underlying integrals. This provides a clear understanding of how individual events are retrieved by the scheme. Our interpretation also exposes some of the scheme's limitations in terms of what can be retrieved in case of a finite recording aperture. Green's function retrieval is only successful if the relevant stationary points are sampled. As a consequence, internal multiples can only be retrieved at a subsurface location with a particular ray parameter if this location is illuminated by the direct wavefield with this specific ray parameter. Several assumptions are required to solve the Marchenko equations. We show that these assumptions are not always satisfied in arbitrary heterogeneous media, which can result in incomplete Green's function retrieval and the emergence of artefacts. Despite these limitations, accurate Green's functions can often be retrieved by the iterative scheme, which is highly relevant for seismic imaging and inversion of internal multiple reflections.

114 citations


Cites background from "On seismic interferometry, the gene..."

  • ...This effect is also observed in Green’s function retrieval by seismic interferometry (Wapenaar et al. 2010)....

    [...]


References
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Journal ArticleDOI
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.

640 citations