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151
Migration velocity analysis and waveform inversion:
 Geophysical Prospecting,
, 2008
"... SUMMARY Leastsquares inversion of seismic reflection waveform data can reconstruct remarkably detailed models of subsurface structure, and take into account essentially any physics of seismic wave propagation that can be modeled. However the waveform inversion objective has many spurious local min ..."
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Cited by 35 (3 self)
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SUMMARY Leastsquares inversion of seismic reflection waveform data can reconstruct remarkably detailed models of subsurface structure, and take into account essentially any physics of seismic wave propagation that can be modeled. However the waveform inversion objective has many spurious local minima, hence convergence of descent methods (mandatory because of problem size) to useful Earth models requires accurate initial estimates of longscale velocity structure. Migration velocity analysis, on the other hand, is capable of correcting substantially erroneous initial estimates of velocity at long scales. Migration velocity analysis is based on prestack depth migration, which is in turn based on linearized acoustic modeling (Born or singlescattering approximation). Two major variants of prestack depth migration, using binning of surface data and Claerbout's surveysinking concept respectively, are in widespread use. Each type of prestack migration produces an image volume depending on redundant parameters, and supplies a condition on the image volume which expresses consistency between data and velocity model, hence a basis for velocity analysis. The surveysinking (depthoriented) approach to prestack migration is less subject to kinematic artifacts than is the binningbased (surfaceoriented) approach. Because kinematic artifacts strongly violate the consistency or semblance conditions, this observation suggests that velocity analysis based on depthoriented prestack migration may be more appropriate in kinematically complex areas. Appropriate choice of objective (differential semblance) turns either form of migration velocity analysis into an optimization problem, for which Newtonlike methods exhibit little tendency to stagnate at nonglobal minima. The extended modeling concept links migration velocity analysis to the apparently unrelated waveform inversion approach to estimation of Earth structure: from this point of view, migration velocity analysis is a solution method for the linearized waveform inversion problem. Extended modeling also provides a basis for a nonlinear generalization of migration velocity analysis. Preliminary numerical evidence suggests a new approach to nonlinear waveform inversion which may combine the global convergence of velocity analysis with the physical fidelity of modelbased data fitting.
3d finitedifference frequencydomain modeling of viscoacoustic wave propagation using a massively parallel direct solver: A feasibility study:
 Geophysics,
, 2007
"... ABSTRACT We present a finitedifference frequencydomain method for 3D viscoacoustic wave propagation modeling. In the frequency domain, the underlying numerical problem is the resolution of a large sparse system of linear equations whose righthand side term is the source. This system is solved w ..."
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Cited by 33 (5 self)
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ABSTRACT We present a finitedifference frequencydomain method for 3D viscoacoustic wave propagation modeling. In the frequency domain, the underlying numerical problem is the resolution of a large sparse system of linear equations whose righthand side term is the source. This system is solved with a massively parallel direct solver. We first present an optimal 3D finitedifference stencil for frequencydomain modeling. The method is based on a parsimonious staggeredgrid method. Differential operators are discretized with secondorder accurate staggeredgrid stencils on different rotated coordinate systems to mitigate numerical anisotropy. An antilumped mass strategy is implemented to minimize numerical dispersion. The stencil incorporates 27 grid points and spans two grid intervals. Dispersion analysis shows that four grid points per wavelength provide accurate simulations in the 3D domain. To assess the feasibility of the method for frequencydomain fullwaveform inversion, we computed simulations in the 3D SEG/EAGE overthrust model for frequencies 5, 7, and 10 Hz. Results confirm the huge memory requirement of the factorization ͑several hundred Figabytes͒ but also the CPU efficiency of the resolution phase ͑few seconds per shot͒. Heuristic scalability analysis suggests that the memory complexity of the factorization is O͑35N 4 ͒ for a N 3 grid. Our method may provide a suitable tool to perform frequencydomain fullwaveform inversion using a large distributedmemory platform. Further investigation is still necessary to assess more quantitatively the respective merits and drawbacks of timeand frequencydomain modeling of wave propagation to perform 3D fullwaveform inversion.
Extended imaging conditions for waveequation migration
"... Wavefieldbased migration velocity analysis using the semblance principle requires computation of images in an extended space in which we can evaluate the imaging consistency as a function of overlapping experiments. Usual industry practice is to assemble those seismic images in commonimagegathers ..."
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Cited by 18 (6 self)
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Wavefieldbased migration velocity analysis using the semblance principle requires computation of images in an extended space in which we can evaluate the imaging consistency as a function of overlapping experiments. Usual industry practice is to assemble those seismic images in commonimagegathers (CIG) which represent reflectivity as a function depth and extensions, e.g. reflection angles. We introduce extended commonimagepoint (CIP) gathers constructed only as a function of the space and timelag extensions at sparse and irregularly distributed points in the image. Semblance analysis using CIPs constructed by this procedure is advantageous because we do not need to compute gathers at regular surface locations and we do not need to compute extensions at all depth levels. The CIPs also give us the flexibility to distribute them in the image at irregular locations aligned with the geologic structure. Furthermore, the CIPs remove the depth bias of CIGs constructed as a function of the depth axis. An interpretation of the CIPs using scattering theory shows that they are scattered wavefields associated with sources and receivers inside the subsurface. Thus, when the surface wavefields are correctly reconstructed, the extended CIPs are characterized by focused energy at the origin of the space and timelag axes. Otherwise, the energy defocuses from the origin of the lag axes proportionally with the cumulative velocity error in the overburden. This information can be used for wavefieldbased tomographic updates of the velocity model, and if the velocity used for imaging is correct, the coordinateindependent CIPs can be decomposed function of the angles of incidence.
An effective method for parameter estimation with PDE constraints with multiple right hand sides
, 2010
"... Many parameter estimation problems involve with a parameterdependent PDEs with multiple right hand sides. The computational cost and memory requirements of such problems increases linearly with the number of right hand sides. For many applications this is the main bottleneck of the computation. In ..."
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Cited by 17 (9 self)
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Many parameter estimation problems involve with a parameterdependent PDEs with multiple right hand sides. The computational cost and memory requirements of such problems increases linearly with the number of right hand sides. For many applications this is the main bottleneck of the computation. In this paper we show that problems with multiple right hand sides can be reformulated as stochastic optimization problems that are much cheaper to solve. We discuss the solution methodology and use the direct current resistivity and seismic tomography as model problems to show the effectiveness of our approach.
Nonlinear extended images via imagedomain interferometry
 Geophysics
, 2010
"... Abstract Waveequation, finitefrequency imaging and inversion still faces considerable challenges in addressing the inversion of highly complex velocity models as well as in dealing with nonlinear imaging (e.g., migration of multiples, amplitudepreserving migration). Extended images (EI's), ..."
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Cited by 16 (3 self)
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Abstract Waveequation, finitefrequency imaging and inversion still faces considerable challenges in addressing the inversion of highly complex velocity models as well as in dealing with nonlinear imaging (e.g., migration of multiples, amplitudepreserving migration). Extended images (EI's), as we present here, are particularly important for designing imagedomain objective functions aimed at addressing standing issues in seismic imaging such as twoway migration velocity inversion or imaging/inversion using multiples. Using general twoand oneway representations for scattered wavefields, we describe and analyze EI's obtained in waveequation imaging. The presented formulation explicitly connects the wavefield correlations done in seismic imaging with the theory and practice of seismic interferometry. We define extended images as locally scattered fields reconstructed by modeldependent, imagedomain interferometry. Because we use the same twoand oneway scattering representations that are used for seismic interferometry, the reciprocitybased EI's can in principle account for all possible nonlinear effects in the imaging process, i.e., migration of multiples, amplitude corrections, etc. In that case, the practice of twoway imaging departs considerably from that of the oneway approach. Here we elaborate on the differences between these approaches in the context of nonlinear imaging, describing these differences both in the wavefield extrapolation steps as well as in imposing the extended imaging conditions. When invoking singlescattering and ignoring amplitude effects in generating EI's, the oneand twoway approaches become essentially the same as those employed in today's migration practice, with the straightforward addition of spaceand timelags I. Vasconcelos et al. 2 Nonlinear extended images via interferometry in the correlationbased imaging condition. Our formal description of the EI's and the insight that they are scattered fields in the imagedomain may be useful in further development of imaging and inversion methods: either in the context of linear, migrationbased velocity inversion, or in more sophisticated imagedomain nonlinear inverse scattering approaches.
Waveequation migration velocity analysis using extended images
"... Waveequation migration velocity analysis (WEMVA) is a velocity estimation technique designed to invert for velocity information using migrated images. Its capacity for handling multipathing makes it appropriate in complex subsurface regions characterized by strong velocity variation. WEMVA operate ..."
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Cited by 7 (2 self)
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Waveequation migration velocity analysis (WEMVA) is a velocity estimation technique designed to invert for velocity information using migrated images. Its capacity for handling multipathing makes it appropriate in complex subsurface regions characterized by strong velocity variation. WEMVA operates by establishing a linear relation between a velocity model perturbation and a corresponding migrated image perturbation. The linear relationship is derived from conventional extrapolation operators and it inherits the main properties of frequencydomain wavefield extrapolation. A key step in implementing WEMVA is to design an appropriate procedure for constructing image perturbations. Using timelag extended images, one can characterize the error in migrated images by defining the focusing error as the shift of the focused reflection along the timelag axis. Under the linear approximation, the focusing error can be transformed into an image perturbation by multiplying it with an image derivative taken relative to the timelag parameter. The resulting image perturbation is thus a mapping of the velocity error in image space. This approach is computationally efficient and simple to implement, and no further assumptions about smoothness and homogeneity of the velocity model and reflector geometry are needed. Synthetic examples demonstrate the successful application of our method to a complex velocity model.
Velocity estimation for seismic data exhibiting focusingeffect AVO
"... Transmission anomalies sometimes create AVO effects by focusing the reflected seismic wavefields, which impedes AVO analysis. The AVO anomalies caused by focusing are distinguishable by surface consistent patterns. We analyze the previous efforts to define, describe and eliminate spurious AVO anomal ..."
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Cited by 6 (6 self)
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Transmission anomalies sometimes create AVO effects by focusing the reflected seismic wavefields, which impedes AVO analysis. The AVO anomalies caused by focusing are distinguishable by surface consistent patterns. We analyze the previous efforts to define, describe and eliminate spurious AVO anomalies. We also propose using wave equation migration velocity analysis to build an accurate velocity model. The transmissionrelated AVO can then be eliminated by downward continuation through this velocity model.