Compressive simultaneous full-waveform simulation

Herrmann, Felix J.; Erlangga, Yogi A.; Lin, Tim

doi:10.1190/1.3115122

Cited by 104 publications

(83 citation statements)

References 25 publications

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“…The simultaneous super shots themselves are obtained by phase encoding with random phases θ θ θ 1···n s = Uniform([0, 2π]), followed by the selection of one or more simultaneous sources with the restriction matrix R Σ i . Because the cost of evaluating the gradient and Newton updates depends on the number of sources (n s ) and frequencies (n f ), the computational costs are reduced as long as N × n s < n s and N × n f < n f (Herrmann et al, 2009b;Neelamani et al, 2008;Herrmann and Li, 2010;Krebs et al, 2009b). After applying this sampling operator, the nonlinear least-squares problem reduces to min m…”

Section: Theorymentioning

confidence: 99%

“…2,2 , where the underbarred quantities refer to compressively sampled wavefieldsi.e., δ P : Herrmann et al, 2009b, for details).…”

Section: Theorymentioning

confidence: 99%

“…The proposed methodology follows in the footsteps of attempts towards cost reductions for the computation of gradients, which are central to imaging and inversion, through phase-encoded simultaneous sources (Romero et al, 2000;Herrmann et al, 2009b), possibly in combination with the removal of subsets of angular frequencies (Sirgue and Pratt, 2004;Mulder and Plessix, 2004;Lin et al, 2008;Herrmann et al, 2009b). The advantage of this approach are fourfold.…”

Section: Introductionmentioning

confidence: 99%

“…These developments in conjunction with the recent resurgence of simultaneous sources (Beasley, 2008;Berkhout, 2008;Krebs et al, 2009a;Herrmann et al, 2009b;Herrmann, 2009) allow us to replace conventional impulsive sources by a limited number of of simultaneous phase-encoded sources to reduce the computational complexity of computing the gradients (migration). These randomly phase-encoded sources render source crosstalk harmless by turning these artifatcs into incoherent noise.…”

Section: Introductionmentioning

confidence: 99%

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Full‐waveform inversion from compressively recovered model updates

Herrmann

2010

SEG Technical Program Expanded Abstracts 2010

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SUMMARYFull-waveform inversion relies on the collection of large multiexperiment data volumes in combination with a sophisticated back-end to create high-fidelity inversion results. While improvements in acquisition and inversion have been extremely successful, the current trend of incessantly pushing for higher quality models in increasingly complicated regions of the Earth reveals fundamental shortcomings in our ability to handle increasing problem size numerically. Two main culprits can be identified. First, there is the so-called "curse of dimensionality" exemplified by Nyquist's sampling criterion, which puts disproportionate strain on current acquisition and processing systems as the size and desired resolution increases. Secondly, there is the recent "departure from Moore's law" that forces us to lower our expectations to compute ourselves out of this. In this paper, we address this situation by randomized dimensionality reduction, which we adapt from the field of compressive sensing. In this approach, we combine deliberate randomized subsampling with structure-exploiting transform-domain sparsity promotion. Our approach is successful because it reduces the size of seismic data volumes without loss of information. With this reduction, we compute Newton-like updates at the cost of roughly one gradient update for the fully-sampled wavefield.

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Section: Theorymentioning

confidence: 99%

“…2,2 , where the underbarred quantities refer to compressively sampled wavefieldsi.e., δ P : Herrmann et al, 2009b, for details).…”

Section: Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Full‐waveform inversion from compressively recovered model updates

Herrmann

2010

SEG Technical Program Expanded Abstracts 2010

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“…Alternatively a far less expensive procedure relies upon a recently developed data reduction technique based on the idea of 'simultaneous sources' [2,20,11,17,19]. Here the estimate is based on a weighted combination of the form d(w) = wjdj.…”

Section: Introductionmentioning

confidence: 99%

Optimal design of simultaneous source encoding

Haber

Doel

Horesh

2014

Inverse Problems in Science and Engineering

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A broad range of parameter estimation problems involve the collection of an excessively large number of observations N . Typically each such observation involves excitation of the domain through injection of energy at some pre-defined sites and recording of the response of the domain at another set of locations. It has been observed that similar results can often be obtained by considering a far smaller number K of multiple linear superpositions of experiments with K << N . This allows the construction of the solution to the inverse problem in time O(K) instead of O(N ). Given these considerations it should not be necessary to perform all the N experiments but only a much smaller number of K experiments with simultaneous sources in superpositions with certain weights. Devising such procedure would results in a drastic reduction in acquisition time.The question we attempt to rigorously investigate in this work is: what are the optimal weights ? We formulate the problem as an optimal experimental design problem and show that by leveraging techniques from this field an answer is readily available. Designing optimal experiments requires some statistical framework and therefore the statistical framework that one chooses to work with plays a major role in the selection of the weights.

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Optimization Methods for Inverse Problems

Roosta-Khorasani

Cui

2019

MATRIX Book Series

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Optimization plays an important role in solving many inverse problems. Indeed, the task of inversion often either involves or is fully cast as a solution of an optimization problem. In this light, the mere non-linear, non-convex, and large-scale nature of many of these inversions gives rise to some very challenging optimization problems. The inverse problem community has long been developing various techniques for solving such optimization tasks. However, other, seemingly disjoint communities, such as that of machine learning, have developed, almost in parallel, interesting alternative methods which might have stayed under the radar of the inverse problem community. In this survey, we aim to change that. In doing so, we first discuss current state-of-the-art optimization methods widely used in inverse problems. We then survey recent related advances in addressing similar challenges in problems faced by the machine learning community, and discuss their potential advantages for solving inverse problems. By highlighting the similarities among the optimization challenges faced by the inverse problem and the machine learning communities, we hope that this survey can serve as a bridge in bringing together these two communities and encourage cross fertilization of ideas.

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Compressive simultaneous full-waveform simulation

Cited by 104 publications

References 25 publications

Full‐waveform inversion from compressively recovered model updates

Full‐waveform inversion from compressively recovered model updates

Optimal design of simultaneous source encoding

Optimization Methods for Inverse Problems

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