A subsampled truncated-Newton method for multiparameter full-waveform inversion

Accounting for the Hessian in full-waveform inversion (FWI) can lead to higher convergence rates, improved resolution, and better mitigation of parameter trade-off in multiparameter problems. In spite of these advantages, the adoption of second-order optimization methods (e.g., truncated Newton [TN]) has been precluded by their high computational cost. We propose a subsampled TN (STN) algorithm for time-domain FWI with applications presented for the elastic isotropic case. By using uniform or nonuniform source subsampling during the computation of Hessian-vector products, we reduce the number of partial differential equation solves required per iteration when compared to the conventional TN algorithm. We evaluate the performance of STN through synthetic inversions on the Marmousi II and BP 2.5D models, using the limited-memory Broyden–Fletcher–Goldfarb–Shanno and TN algorithms as benchmarks. We determine that STN reaches a target misfit reduction at an overall cost comparable to first-order gradient methods, while retaining favorable convergence properties of TN methods. Furthermore, we evaluate an example in which nonuniform sampling outperforms uniform sampling in STN due to highly nonuniform source contributions to the Hessian.

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On-the-Fly Full Hessian Kernel Calculations Based upon Seismic-Wave Simulations

Seismological Research Letters ◽

10.1785/0220200410 ◽

2021 ◽

Author(s):

Yujiang Xie ◽

Catherine A. Rychert ◽

Nicholas Harmon ◽

Qinya Liu ◽

Dirk Gajewski

Keyword(s):

Wave Equations ◽

Convergence Rates ◽

Waveform Inversion ◽

Computational Cost ◽

Random Access ◽

Spectral Element ◽

Source Codes ◽

Full Waveform ◽

Trade Offs ◽

Adjoint Tomography

Abstract Full waveform inversion or adjoint tomography has routinely been performed to image the internal structure of the Earth at high resolution. This is typically done using the Fréchet kernels and the approximate Hessian or the approximate inverse Hessian because of the high-computational cost of computing and storing the full Hessian. Alternatively, the full Hessian kernels can be used to improve inversion resolutions and convergence rates, as well as possibly to mitigate interparameter trade-offs. The storage requirements of the full Hessian kernel calculations can be reduced by compression methods, but often at a price of accuracy depending on the compression factor. Here, we present open-source codes to compute both Fréchet and full Hessian kernels on the fly in the computer random access memory (RAM) through simultaneously solving four wave equations, which we call Quad Spectral-Element Method (QuadSEM). By recomputing two forward fields at the same time that two adjoint fields are calculated during the adjoint simulation, QuadSEM constructs the full Hessian kernels using the exact forward and adjoint fields. In addition, we also implement an alternative approach based on the classical wavefield storage method (WSM), which stores forward wavefields every kth (k≥1) timestep during the forward simulation and reads required fields back into memory during the adjoint simulation for kernel construction. Both Fréchet and full Hessian kernels can be computed simultaneously through the QuadSEM or the WSM code, only doubling the computational cost compared with the computation of Fréchet kernels alone. Compared with WSM, QuadSEM can reduce the disk space and input/output cost by three orders of magnitude in the presented examples that use 15,000 timesteps. Numerical examples are presented to demonstrate the functionality of the methods, and the computer codes are provided with this contribution.

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Optimized Model Parameterization using Compact Full Waveform Inversion

Geophysical Journal International ◽

10.1093/gji/ggaa175 ◽

2020 ◽

Author(s):

Linan Xu ◽

Edgar Manukyan ◽

Hansruedi Maurer

Keyword(s):

Large Scale ◽

Waveform Inversion ◽

Gradient Methods ◽

Significant Loss ◽

Inverse Model ◽

Eigenvalue Decomposition ◽

Model Parameters ◽

Full Waveform Inversion ◽

Full Waveform ◽

Model Parameterization

Summary Seismic Full Waveform Inversion (FWI) has the potential to produce high-resolution subsurface images, but the computational resources required for realistically sized problems can be prohibitively large. In terms of computational costs, Gauss-Newton algorithms are more attractive than the commonly employed conjugate gradient methods, because the former have favorable convergence properties. However, efficient implementations of Gauss-Newton algorithms require an excessive amount of computer memory for larger problems. To address this issue, we introduce Compact Full Waveform Inversion (CFWI). Here, a suitable inverse model parameterization is sought that allows representing all subsurface features, potentially resolvable by a particular source-receiver deployment, but using only a minimum number of model parameters. In principle, an inverse model parameterization, based on the Eigenvalue decomposition, would be optimal, but this is computationally not feasible for realistic problems. Instead, we present two alternative parameter transformations, namely the Haar and the Hartley transformations, with which similarly good results can be obtained. By means of a suite of numerical experiments, we demonstrate that these transformations allow the number of model parameters to be reduced to only a few percent of the original parameterization without any significant loss of spatial resolution. This facilitates efficient solutions of large-scale FWI problems with explicit Gauss-Newton algorithms.

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A subsampled truncated Newton approach for multiparameter full-waveform inversion

10.1190/segam2018-2997924.1 ◽

2018 ◽

Author(s):

Gian Matharu ◽

Mauricio D. Sacchi

Keyword(s):

Waveform Inversion ◽

Full Waveform Inversion ◽

Full Waveform ◽

Truncated Newton

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A Time-Domain Preconditioned Truncated Newton Approach to Visco-acoustic Multiparameter Full Waveform Inversion

SIAM Journal on Scientific Computing ◽

10.1137/17m1126126 ◽

2018 ◽

Vol 40 (4) ◽

pp. B1101-B1130 ◽

Cited By ~ 16

Author(s):

Pengliang Yang ◽

Romain Brossier ◽

Ludovic Métivier ◽

Jean Virieux ◽

Wei Zhou

Keyword(s):

Time Domain ◽

Waveform Inversion ◽

Full Waveform Inversion ◽

Full Waveform ◽

Truncated Newton

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A GPU implementation of the second order adjoint state theory to quantify the uncertainty on FWI results

CT&F - Ciencia Tecnología y Futuro ◽

10.29047/01225383.86 ◽

2018 ◽

Vol 8 (2) ◽

Cited By ~ 1

Author(s):

Sergio Alberto Abreo ◽

Ana Beatríz Ramírez- Silva ◽

Oscar Mauricio Reyes- Torres

Keyword(s):

Wave Equation ◽

Probability Distribution ◽

Hessian Matrix ◽

Waveform Inversion ◽

Computational Cost ◽

State Theory ◽

Second Order ◽

Full Waveform Inversion ◽

Full Waveform ◽

Adjoint State

The second order scattering information provided by the Hessian matrix and its inverse plays an important role in both, parametric inversion and uncertainty quantification. On the one hand, for parameter inversion, the Hessian guides the descent direction such that the cost function minimum is reached with less iterations. On the other hand, it provides a posteriori information of the probability distribution of the parameters obtained after full waveform inversion, as a function of the a priori probability distribution information. Nevertheless, the computational cost of the Hessian matrix represents the main obstacle in the state-of-the-art for practical use of this matrix from synthetic or real data. The second order adjoint state theory provides a strategy to compute the exact Hessian matrix, reducing its computational cost, because every column of the matrix can be obtained by performing two forward and two backward propagations. In this paper, we first describe an approach to compute the exact Hessian matrix for the acoustic wave equation with constant density. We then provide an analysis of the use of the Hessian matrix for uncertainty quantification of the full waveform inversion of the velocity model for a synthetic example, using the 2D acoustic and isotropic wave equation operator in time.

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Accelerating numerical wave propagation by wavefield adapted meshes. Part II: full-waveform inversion

Geophysical Journal International ◽

10.1093/gji/ggaa065 ◽

2020 ◽

Vol 221 (3) ◽

pp. 1591-1604 ◽

Cited By ~ 4

Author(s):

Solvi Thrastarson ◽

Martin van Driel ◽

Lion Krischer ◽

Christian Boehm ◽

Michael Afanasiev ◽

...

Keyword(s):

Wave Propagation ◽

Wave Equation ◽

Waveform Inversion ◽

Computational Cost ◽

Spectral Element ◽

Full Waveform Inversion ◽

Full Waveform ◽

Order Of Magnitude ◽

Numerical Wave ◽

Expected Complexity

SUMMARY We present a novel full-waveform inversion (FWI) approach which can reduce the computational cost by up to an order of magnitude compared to conventional approaches, provided that variations in medium properties are sufficiently smooth. Our method is based on the usage of wavefield adapted meshes which accelerate the forward and adjoint wavefield simulations. By adapting the mesh to the expected complexity and smoothness of the wavefield, the number of elements needed to discretize the wave equation can be greatly reduced. This leads to spectral-element meshes which are optimally tailored to source locations and medium complexity. We demonstrate a workflow which opens up the possibility to use these meshes in FWI and show the computational advantages of the approach. We provide examples in 2-D and 3-D to illustrate the concept, describe how the new workflow deviates from the standard FWI workflow, and explain the additional steps in detail.

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