Efficient calculation of partial derivative wavefield using reciprocity for seismic imaging and inversion

Shin, Changsoo; Yoon, Kang Sup; Marfurt, Kurt J.

doi:10.1190/1.1816196

Cited by 29 publications

(46 citation statements)

References 11 publications

(14 reference statements)

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“…We first consider the traditional Hessian approximations (e.g., diagonal pseudo-Hessian and diagonal Gauss-Newton Hessian) as the preconditioners. The pseudo-Hessian H is constructed by replacing the Fréchet derivative wavefield with the virtual sourcef s (x, ω) in the correlation process (Shin et al, 2001b):f…”

Section: Diagonal Hessian Approximation Preconditionersmentioning

confidence: 99%

Accelerating Hessian-free Gauss-Newton full-waveform inversion via improved preconditioning strategies

Pan

Innanen

Liao

2016

SEG Technical Program Expanded Abstracts 2016

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Gradient-based methods for full-waveform inversion (FWI) have the potential to converge globally but suffer from a slow convergence rate. Newton-type methods provide quadratic convergence, but they are computationally burdensome for large-scale inverse problems. The Hessian-free (HF) optimization method represents an attractive alternative to these above-mentioned optimization methods. At each iteration, the HF approach obtains the search direction by approximately solving the Newton linear system using a conjugate-gradient (CG) algorithm. One issue with HF optimization is that the CG algorithm requires many iterations. In this paper, we develop and compare different preconditioning schemes for the CG algorithm to accelerate the HF Gauss-Newton method. Traditionally, the preconditioners are designed as diagonal Hessian approximations or inverse Hessian approximations. In this research, we propose to construct the l-BFGS inverse Hessian preconditioner with the diagonal Hessian approximations as initial guess. It is shown that the quasi-Newton l-BFGS preconditioning scheme with the pseudo diagonal Gauss-Newton Hessian as initial guess shows the best performances in accelerating the HF Gauss-Newton FWI.

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Section: Diagonal Hessian Approximation Preconditionersmentioning

confidence: 99%

Accelerating Hessian-free Gauss-Newton full-waveform inversion via improved preconditioning strategies

Pan

Innanen

Liao

2016

SEG Technical Program Expanded Abstracts 2016

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“…Even though setting up the adjoint state problem requires additional work to solve for an adjoint variable which has no primary physical interest in the solution of the inverse problem, this method is appealing because the computation of the gradient with respect to a model parameter requires two evaluations of the partial differential equations. The alternative method, which consists in the explicit computation of the Fréchet derivatives, is expensive to compute, as it requires one forward modeling for each non redundant position of source and receiver (Shin et al, 2001).…”

Section: Adjoint State Equation For the Conservative Formulationmentioning

confidence: 99%

Algorithmic and methodological developments towards full waveform inversion in 3D elastic media

Castellanos

Etienne

et al. 2011

SEG Technical Program Expanded Abstracts 2011

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We present some methodological aspects of full waveform inversion (FWI) in 3D elastic media. FWI is a local optimization scheme aiming to update the initial model with perturbations in order to minimize the misfit between the computed and observed data. The pertubations are found in the opposite direction of the gradient which can be evaluated efficiently with the adjoint state method. While this method is generally applied to a second order expression of the wave equation, we develop our inversion scheme on a first-order velocity-stress formulation which provides a great flexibility to recast the wave equation in pseudo-conservative form. We show how to take advantage of this formalism to develop the gradient of the misfit function with the adjoint-state method in a straightforward way. The inversion is implemented in the frequency domain, while the seismic modeling is performed in time. We propose also an abstraction concept between the forward and inverse problems that allows us to use different modeling engines in the inversion code and to perform target-oriented imaging.

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“…The diagonal of the approximate Hessian provides a preconditioner of the gradient which properly scales the perturbation model (Shin et al, 2001). The damping parameter ε is used to avoid numerical instability (i.e.…”

Section: Frequency-domain Full-waveform Inversionmentioning

confidence: 99%

3D acoustic frequency‐domain full‐waveform inversion

Ali¹,

Operto²,

Virieux³

et al. 2007

SEG Technical Program Expanded Abstracts 2007

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We present one of the first attempt at implementing a massively parallel frequency-domain full-waveform inversion algorithm for imaging 3D acoustic media. The inverse method is based on a classic steepest-descent algorithm. The algorithm was designed so that one or several frequencies are inverted at a time. Wave propagation modeling, a key component of the inversion algorithm, is performed with a finite-difference frequency-domain method which requires 4 grid points per wavelength. Frequency-domain methods for wave propagation modeling requires to solve a huge sparse system of linear equations whose solutions are the computed wavefields and right-hand side (RHS) terms are the sources. We solve this system with a massively parallel direct solver in order to compute efficiently multiple-source solutions. The massively parallel direct solver leaves the multiple solutions distributed over the processors. We take advantage of this distributed storage to compute in parallel the gradient of the cost function in the inversion. The algorithm was validated with preliminary synthetic examples of limited dimensions.

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Efficient calculation of partial derivative wavefield using reciprocity for seismic imaging and inversion

Cited by 29 publications

References 11 publications

Accelerating Hessian-free Gauss-Newton full-waveform inversion via improved preconditioning strategies

Accelerating Hessian-free Gauss-Newton full-waveform inversion via improved preconditioning strategies

Algorithmic and methodological developments towards full waveform inversion in 3D elastic media

3D acoustic frequency‐domain full‐waveform inversion

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