Sparsity-promoting Migration with Surface-related Multiples

Tu, Ning; Lin, Tim; Herrmann, Felix J.

doi:10.3997/2214-4609.20149208

Cited by 3 publications

References 14 publications

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Modified Gauss-Newton full-waveform inversion explained — Why sparsity-promoting updates do matter

Esser

Herrmann

2016

GEOPHYSICS

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Full-waveform inversion (FWI) can be formulated as a nonlinear least-squares optimization problem. This nonconvex problem can be computationally expensive because it requires repeated solutions of the wave equation. Randomized subsampling techniques allow us to work with small subsets of (monochromatic) source experiments, reducing the computational cost. However, this subsampling may weaken subsurface illumination or introduce subsampling-related incoherent artifacts. These subsampling-related artifacts — in conjunction with the desire to obtain high-fidelity inversion results — motivate us to come up with a technique to regularize this inversion problem. Following earlier work, we have taken advantage of the fact that curvelets represent subsurface models and model perturbations parsimoniously. At first impulse, promoting sparsity on the model directly seemed the most natural way to proceed, but we have determined that in certain cases it can be advantageous to promote sparsity on the Gauss-Newton updates instead. Although constraining the one norm of the descent directions did not change the underlying FWI objective, the constrained model updates remained descent directions, removed subsampling-related artifacts, and improved the overall inversion result. We have empirically observed this phenomenon in situations where the different model updates occurred at roughly the same locations in the curvelet domain. We have further investigated and analyzed this behavior, in which nonlinear inversions benefit from sparsity-promoting constraints on the updates, by means of a set of carefully selected examples including the phase retrieval problem and time-harmonic FWI. In all cases, we have observed a faster decay of the residual and model error as a function of the number of iterations.

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Modified Gauss-Newton full-waveform inversion explained — Why sparsity-promoting updates do matter

Esser

Herrmann

2016

GEOPHYSICS

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Low-cost time-lapse seismic with distributed compressive sensing — Part 1: Exploiting common information among the vintages

et al. 2017

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Time-lapse seismic is a powerful technology for monitoring a variety of subsurface changes due to reservoir fluid flow. However, the practice can be technically challenging when one seeks to acquire colocated time-lapse surveys with high degrees of replicability among the shot locations. We have determined that under “ideal” circumstances, in which we ignore errors related to taking measurements off the grid, high-quality prestack data can be obtained from randomized subsampled measurements that are observed from surveys in which we choose not to revisit the same randomly subsampled on-the-grid shot locations. Our acquisition is low cost because our measurements are subsampled. We have found that the recovered finely sampled prestack baseline and monitor data actually improve significantly when the same on-the-grid shot locations are not revisited. We achieve this result by using the fact that different time-lapse data share information and that nonreplicated (on-the-grid) acquisitions can add information when prestack data are recovered jointly. Whenever the time-lapse data exhibit joint structure — i.e., they are compressible in some transform domain and share information — sparsity-promoting recovery of the “common component” and “innovations,” with respect to this common component, outperforms independent recovery of the prestack baseline and monitor data. The recovered time-lapse data are of high enough quality to serve as the input to extract poststack attributes used to compute time-lapse differences. Without joint recovery, artifacts — due to the randomized subsampling — lead to deterioration of the degree of repeatability of the time-lapse data. We tested this method by carrying out experiments with reliable statistics from thousands of repeated experiments. We also confirmed that high degrees of repeatability are achievable for an ocean-bottom cable survey acquired with time-jittered continuous recording.

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Imaging with multiples accelerated by message passing

Tu¹,

Herrmann²

2012

SEG Technical Program Expanded Abstracts 2012

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With the growing realization that multiples can provide valuable information, there is a paradigm shift from removing them to using them. For instance, primary estimation by sparse inversion has demonstrated its superiority over surface-related multiple removal in many aspects. Inspired by this shift, we propose a method to image directly from the total up-going wavefield, including surface-related multiples, by sparse inversion. To address the high computational cost associated with this method, we propose to speed up the inversion by having the wave-equation solver carry out the multi-dimensional convolutions implicitly and cheaply by randomized subsampling. We improve the overall performance of this algorithm by selecting new independent copies of the randomized modeling operator, which leads to a cancellation of correlations that hamper the speed of convergence of the solver. We show the merits of our approach on a number of examples.

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Sparsity-promoting Migration with Surface-related Multiples

Cited by 3 publications

References 14 publications

Modified Gauss-Newton full-waveform inversion explained — Why sparsity-promoting updates do matter

Modified Gauss-Newton full-waveform inversion explained — Why sparsity-promoting updates do matter

Low-cost time-lapse seismic with distributed compressive sensing — Part 1: Exploiting common information among the vintages

Imaging with multiples accelerated by message passing

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