A new optimization approach for source-encoding full-waveform inversion

Moghaddam, Peyman P.; Keers, Henk; Herrmann, Felix J.; Mulder, W.A.

doi:10.1190/geo2012-0090.1

Cited by 48 publications

(20 citation statements)

References 47 publications

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“…In order to alleviate the large computational burden presented by sequential waveform inversion methods (e.g., Algorithm 1), a source encoding method has been proposed [22], [29], [41]. This method has been formulated as a stochastic optimization problem and solved by various stochastic gradient-based algorithms [30], [31]. In this section, we adapt the stochastic optimization-based formulation in [30] to find the solution of Eqn.…”

Section: B Stochastic Optimization-based Waveform Inversion With Soumentioning

confidence: 99%

See 1 more Smart Citation

Waveform inversion with source encoding for breast sound speed reconstruction in ultrasound computed tomography

Wang

Matthews

Anis

et al. 2015

IEEE Trans. Ultrason., Ferroelect., Freq. Contr.

146

158

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Ultrasound computed tomography (USCT) holds great promise for improving the detection and management of breast cancer. Because they are based on the acoustic wave equation, waveform inversion-based reconstruction methods can produce images that possess improved spatial resolution properties over those produced by ray-based methods. However, waveform inversion methods are computationally demanding and have not been applied widely in USCT breast imaging. In this work, source encoding concepts are employed to develop an accelerated USCT reconstruction method that circumvents the large computational burden of conventional waveform inversion methods. This method, referred to as the waveform inversion with source encoding (WISE) method, encodes the measurement data using a random encoding vector and determines an estimate of the sound speed distribution by solving a stochastic optimization problem by use of a stochastic gradient descent algorithm. Both computer-simulation and experimental phantom studies are conducted to demonstrate the use of the WISE method. The results suggest that the WISE method maintains the high spatial resolution of waveform inversion methods while significantly reducing the computational burden.

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Section: B Stochastic Optimization-based Waveform Inversion With Soumentioning

confidence: 99%

“…However, to accomplish this, the data fidelity term in Eqn. (9) is reformulated as the expectation of a random quantity as [29]- [31], [33], [41], [42]…”

Section: B Stochastic Optimization-based Waveform Inversion With Soumentioning

confidence: 99%

Waveform inversion with source encoding for breast sound speed reconstruction in ultrasound computed tomography

Wang

Matthews

Anis

et al. 2015

IEEE Trans. Ultrason., Ferroelect., Freq. Contr.

146

158

View full text Add to dashboard Cite

show abstract

“…This common limitation of non-convex problems can be partially mitigated by choosing the compression thresholds adaptively based on the norm of the gradient, thus gradually including more information. Similar strategies in the context of stochastic gradient methods have been applied successfully in full-waveform inversion (Li et al, 2012;Moghaddam et al, 2013), where randomly chosen subsets of sources introduce inexactness in the gradient. It has been observed by van Herrmann (2013, 2014) that the level of inexactness can be quite high during the first iterations and only needs to be refined once a local minimum is approached.…”

Section: Discussionmentioning

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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“…The computational cost is directly proportional to the sample size b = |I|, and thus a higher error in the gradient directly translates into a lower computational cost. Numerical experiments have shown that this approach is beneficial on 2D seismic inversion problems [49,28]. How to choose the rate of increase of the sample size in practice is an open problem.…”

Section: Source Subsamplingmentioning

confidence: 99%

3D Frequency-Domain Seismic Inversion with Controlled Sloppiness

Leeuwen¹,

Herrmann²

2014

SIAM J. Sci. Comput.

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Abstract. Seismic waveform inversion aims at obtaining detailed estimates of subsurface medium parameters, such as the spatial distribution of soundspeed, from multiexperiment seismic data. A formulation of this inverse problem in the frequency domain leads to an optimization problem constrained by a Helmholtz equation with many right-hand sides. Application of this technique to industry-scale problems faces several challenges: First, we need to solve the Helmholtz equation for high wave numbers over large computational domains. Second, the data consist of many independent experiments, leading to a large number of PDE solves. This results in high computational complexity both in terms of memory and CPU time as well as input/output costs. Finally, the inverse problem is highly nonlinear and a lot of art goes into preprocessing and regularization. Ideally, an inversion needs to be run several times with different initial guesses and/or tuning parameters. In this paper, we discuss the requirements of the various components (PDE solver, optimization method, . . . ) when applied to large-scale three-dimensional seismic waveform inversion and combine several existing approaches into a flexible inversion scheme for seismic waveform inversion. The scheme is based on the idea that in the early stages of the inversion we do not need all the data or very accurate PDE solves. We base our method on an existing preconditioned Krylov solver (CARP-CG) and use ideas from stochastic optimization to formulate a gradient-based (quasi-Newton) optimization algorithm that works with small subsets of the right-hand sides and uses inexact PDE solves for the gradient calculations. We propose novel heuristics to adaptively control both the accuracy and the number of right-hand sides. We illustrate the algorithms on synthetic benchmark models for which significant computational gains can be made without being sensitive to noise and without losing the accuracy of the inverted model. 1. Introduction. Detailed estimates of subsurface properties such as soundspeed and density can be obtained from seismic data by solving a PDE-constrained optimization problem [44]-also known as full-waveform inversion (FWI) in the seismic community-that involves multiple source experiments. The data in this setting consist of a collection of time series for many source-receiver pairs and are the result of either passive or active source experiments. The PDE is a wave equation with as many right-hand sides as there are sources. Applications of this technique include oil and gas exploration and global seismology. A common characteristic of these applications is the need to propagate the waves over large distances (i.e., several hundred wavelenghts) through strongly inhomogeneous media for a large number of sources.

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A new optimization approach for source-encoding full-waveform inversion

Cited by 48 publications

References 47 publications

Waveform inversion with source encoding for breast sound speed reconstruction in ultrasound computed tomography

Waveform inversion with source encoding for breast sound speed reconstruction in ultrasound computed tomography

Wavefield compression for adjoint methods in full-waveform inversion

3D Frequency-Domain Seismic Inversion with Controlled Sloppiness

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