A Newton-CG method for large-scale three-dimensional elastic full-waveform seismic inversion

Epanomeritakis, I.; Akçelik, Volkan; Ghattas, Omar; Bielak, Jacobo

doi:10.1088/0266-5611/24/3/034015

Cited by 193 publications

(146 citation statements)

References 39 publications

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“…For simplicity, we always use the L 2 -norm as misfit functional, but, of course, more sophisticated measures can be used as well. Furthermore, we apply a free-surface condition at the top boundary and dashpot absorbing boundary conditions (Epanomeritakis et al, 2008) on all other faces of the computational domain.…”

Section: Resultsmentioning

confidence: 99%

Wavefield compression for adjoint methods in full-waveform inversion

et al. 2016

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Adjoint methods are a key ingredient of gradient-based full-waveform inversion schemes. While being conceptually elegant, they face the challenge of massive memory requirements caused by the opposite time directions of forward and adjoint simulations and the necessity to access both wavefields simultaneously for the computation of the sensitivity kernel. To overcome this bottleneck, we present lossy compression techniques that significantly reduce the memory requirements with only a small computational overhead. Our approach is tailored to adjoint methods and utilizes the fact that the computation of a sufficiently accurate sensitivity kernel does not require the fully-resolved forward wavefield. The collection of methods comprises re-interpolation with a coarse temporal grid as well as adaptively chosen polynomial degree and floating-point precision to represent spatial snapshots of the forward wavefield on hierarchical grids. Furthermore, the first arrivals of adjoint waves are used to identify "shadow zones" that do not contribute to the sensitivity kernel. Numerical experiments show the high potential of this approach achieving an effective compression factor of three orders of magnitude with only a minor reduction in the rate of convergence. Moreover, it is computationally cheap and straightforward to integrate in finite-element wave propagation codes with possible extensions to finite-difference methods.

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Section: Resultsmentioning

confidence: 99%

Wavefield compression for adjoint methods in full-waveform inversion

et al. 2016

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“…Similar problems in seismology are discussed in [8,32]. In our experiment we use a single low frequency as a model problem.…”

Section: Experiments With Seismic Tomographymentioning

confidence: 95%

“…In our experiment we use a single low frequency as a model problem. More complex problems (that require other sophistication such as continuation in frequency and mesh) are discussed in [8].…”

Section: Experiments With Seismic Tomographymentioning

confidence: 99%

An Effective Method for Parameter Estimation with PDE Constraints with Multiple Right-Hand Sides

Haber¹,

Chung²,

Herrmann³

2012

SIAM J. Optim.

108

165

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Abstract. Often, parameter estimation problems of parameter-dependent PDEs involve multiple right-hand sides. The computational cost and memory requirements of such problems increase 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 programming problems by combining the right-hand sides into a few "simultaneous" sources. This effectively reduces the cost of the forward problem and results in problems that are much cheaper to solve. We discuss two solution methodologies: namely sample average approximation and stochastic approximation. To illustrate the effectiveness of our approach we present two model problems, direct current resistivity and seismic tomography.

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“…In FWI, computationally intensive wavefield modeling has been considered a major numerical challenge although efficient modeling algorithms and massively parallel computers are increasingly available. Another difficulty associated with FWI is the convergence of the FWI misfit function toward local minimums because of the lack of reliable low-frequency data (Epanomeritakis et al, 2008;Plessix, 2009).…”

Section: Introductionmentioning

confidence: 99%

Iterative finite-difference solution analysis of acoustic wave equation in the Laplace-Fourier domain

Commer

Newman

2012

GEOPHYSICS

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We have investigated numerical characteristics of iterative solutions to the acoustic wave equation in the LaplaceFourier (LF) domain. We transformed the time-domain acoustic wave equation into the LF domain; the transformed equation was discretized with finite differences and was solved with iterative methods. Finite-difference modeling experiments demonstrate that iterative methods require an infinitesimal stopping tolerance to accurately compute the pressure field especially at long offsets. To understand the requirement for such infinitesimal tolerance values, we analyzed the evolution of intermediate solution vectors, residual vectors, and search direction vectors during the iteration. The analysis showed that the requirement arises from the fact that in the solution space, the amplitude of the pressure field varies more than sixty orders of magnitude on the common log scale. Accordingly, we propose a rule of thumb for choosing a proper stopping tolerance value. We also examined numerical dispersion errors in terms of the grid sampling resolutions per skin depth and wavelength. We found that despite the similarity of the form of the acoustic wave and electromagnetic diffusion equations, the former is different from the latter due to the fact that in the LF domain, the skin depth of the acoustic wave equation is decoupled from its wavelength. This aspect requires that in the LF domain, its grid size be determined by considering the minimum grid sampling resolutions based not only the wavelength but also the skin depth.

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A Newton-CG method for large-scale three-dimensional elastic full-waveform seismic inversion

Cited by 193 publications

References 39 publications

Wavefield compression for adjoint methods in full-waveform inversion

Wavefield compression for adjoint methods in full-waveform inversion

An Effective Method for Parameter Estimation with PDE Constraints with Multiple Right-Hand Sides

Iterative finite-difference solution analysis of acoustic wave equation in the Laplace-Fourier domain

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