Curvelet-based migration preconditioning and scaling

Herrmann, Felix J.; Brown, Cody R.; Erlangga, Yogi A.; Moghaddam, Peyman P.

doi:10.1190/1.3124753

Cited by 47 publications

(24 citation statements)

References 25 publications

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“…However, contrary to many inverse problems, the Hessian of seismic imaging is relatively well behaved-i.e, it is near unitary for linerarizations with respect to velocity models that are close to the actual velocity model. In that case, the highfrequency behavior of the Hessian can be approximated with diagonal scalings Symes, 2008), which can lead to effective preconditioners (Herrmann et al, 2009a). In this paper, we exploit the relatively well-behaved reduced Hessian differently by using techniques from compressive sensing to reduce the dimensionality of the linearized system.…”

Section: Theorymentioning

confidence: 99%

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%

Full‐waveform inversion from compressively recovered model updates

Herrmann

2010

SEG Technical Program Expanded Abstracts 2010

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“…where B is a positive-definite scaling matrix and L is a discrete LaplacianSymes (2008); Herrmann et al (2008Herrmann et al ( , 2009. From this factorization, we expect a very low mutual coherence between the columns of the scattering operator.…”

Section: Modified Gauss-newton Methods For Saa Approachmentioning

confidence: 99%

A modified, sparsity-promoting, Gauss-Newton algorithm for seismic waveform inversion

Herrmann

Aravkin

et al. 2011

SPIE Proceedings

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Images obtained from seismic data are used by the oil and gas industry for geophysical exploration. Cutting-edge methods for transforming the data into interpretable images are moving away from linear approximations and high-frequency asymptotics towards Full Waveform Inversion (FWI), a nonlinear data-fitting procedure based on full data modeling using the wave-equation. The size of the problem, the nonlinearity of the forward model, and ill-posedness of the formulation all contribute to a pressing need for fast algorithms and novel regularization techniques to speed up and improve inversion results. In this paper, we design a modified Gauss-Newton algorithm to solve the PDEconstrained optimization problem using ideas from stochastic optimization and compressive sensing. More specifically, we replace the Gauss-Newton subproblems by randomly subsampled, 1 regularized subproblems. This allows us us significantly reduce the computational cost of calculating the updates and exploit the compressibility of wavefields in Curvelets. We explain the relationships and connections between the new method and stochastic optimization and compressive sensing (CS), and demonstrate the efficacy of the new method on a large-scale synthetic seismic example.

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“…Miller et al (2005) use the dual-tree complex wavelet transform as a basis for the reflectivity and demonstrate that such a change of basis leads to a better reduction in noise and migration artifacts, whereas at the same time, the discontinuities are preserved better than standard LSM for very sparse data. Herrmann et al (2009) and Herrmann and Li (2012) use curvelets, and Dutta (2015, 2017 use seislets as basis functions for the reflectivity and show that with sparsity promoting imaging techniques, it is possible to recover high-quality images from undersampled or noisy data.…”

Section: Introductionmentioning

confidence: 99%

Least-squares reverse time migration with local Radon-based preconditioning

et al. 2017

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Least-squares migration (LSM) can produce images with better balanced amplitudes and fewer artifacts than standard migration. The conventional objective function used for LSM minimizes the L2-norm of the data residual between the predicted and the observed data. However, for field-data applications in which the recorded data are noisy and undersampled, the conventional formulation of LSM fails to provide the desired uplift in the quality of the inverted image. We have developed a leastsquares reverse time migration (LSRTM) method using local Radon-based preconditioning to overcome the low signal-tonoise ratio (S/N) problem of noisy or severely undersampled data. A high-resolution local Radon transform of the reflectivity is used, and sparseness constraints are imposed on the inverted reflectivity in the local Radon domain. The sparseness constraint is that the inverted reflectivity is sparse in the Radon domain and each location of the subsurface is represented by a limited number of geologic dips. The forward and the inverse mapping of the reflectivity to the local Radon domain and vice versa is done through 3D Fourier-based discrete Radon transform operators. The weights for the preconditioning are chosen to be varying locally based on the relative amplitudes of the local dips or assigned using quantile measures. Numerical tests on synthetic and field data validate the effectiveness of our approach in producing images with good S/N and fewer aliasing artifacts when compared with standard RTM or standard LSRTM.

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Curvelet-based migration preconditioning and scaling

Cited by 47 publications

References 25 publications

Full‐waveform inversion from compressively recovered model updates

Full‐waveform inversion from compressively recovered model updates

A modified, sparsity-promoting, Gauss-Newton algorithm for seismic waveform inversion

Least-squares reverse time migration with local Radon-based preconditioning

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