Subspace Methods in Multi-Parameter Seismic Full Waveform Inversion

Geng, Yu; Innanen, Kristopher A.; Pan, Wenyong

doi:10.4208/cicp.oa-2018-0087

Title: Subspace Methods in Multi-Parameter Seismic Full Waveform Inversion

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Abstract

In full waveform inversion (FWI) high-resolution subsurface model parameters are sought. FWI is normally treated as a nonlinear least-squares inverse problem, in which the minimum of the corresponding misfit function is found by updating the model parameters. When multiple elastic or acoustic properties are solved for, simple gradient methods tend to confuse parameter classes. This is referred to as parameter cross-talk; it leads to incorrect model solutions, poor convergence and strong dependence on the scaling of the different parameter types. Determining step lengths in a subspace domain, rather than directly in terms of gradients of different parameters, is a potentially valuable approach to address this problem. The particular subspace used can be defined over a span of different sets of data or different parameter classes, provided it involves a small number of vectors compared to those contained in the whole model space. Additionally, in a subspace method, the basis vectors are defined first, and a local minimum is found in the space spanned by these. We examine the application of the subspace method within acoustic FWI in determining simultaneously updates for velocity and density. We first discuss the choice of basis vectors to construct the spanned space, from linear updatesmore »« less

Authors:

Geng, Yu ^[1]; Innanen, Kristopher A. ^[1];

^[2]

Univ. of Calgary, AB (Canada)
Univ. of Calgary, AB (Canada); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Publication Date:: Mon Jun 01 00:00:00 EDT 2020

Research Org.:: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE; Natural Science and Engineering Research Council of Canada (NSERC)

OSTI Identifier:: 1770098

Report Number(s):: LA-UR-18-22898
Journal ID: ISSN 1815-2406; TRN: US2206789

Grant/Contract Number:: 89233218CNA000001; CRDPJ 461179-13

Resource Type:: Accepted Manuscript

Journal Name:: Communications in Computational Physics

Additional Journal Information:: Journal Volume: 28; Journal Issue: 1; Journal ID: ISSN 1815-2406

Publisher:: Global Science Press

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; full-waveform inversion; waveform inversion; inverse problem; subspace method

Citation Formats


                    Geng, Yu, Innanen, Kristopher A., and Pan, Wenyong. Subspace Methods in Multi-Parameter Seismic Full Waveform Inversion.  United States: N. p., 2020. 
Web.  doi:10.4208/cicp.oa-2018-0087.

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                    Geng, Yu, Innanen, Kristopher A., & Pan, Wenyong. Subspace Methods in Multi-Parameter Seismic Full Waveform Inversion.  United States.  https://doi.org/10.4208/cicp.oa-2018-0087

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                    Geng, Yu, Innanen, Kristopher A., and Pan, Wenyong. Mon .  
"Subspace Methods in Multi-Parameter Seismic Full Waveform Inversion".  United States.  https://doi.org/10.4208/cicp.oa-2018-0087.  https://www.osti.gov/servlets/purl/1770098.

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@article{osti_1770098,

  title        = {Subspace Methods in Multi-Parameter Seismic Full Waveform Inversion},

  author       = {Geng, Yu and Innanen, Kristopher A. and Pan, Wenyong},

  abstractNote = {In full waveform inversion (FWI) high-resolution subsurface model parameters are sought. FWI is normally treated as a nonlinear least-squares inverse problem, in which the minimum of the corresponding misfit function is found by updating the model parameters. When multiple elastic or acoustic properties are solved for, simple gradient methods tend to confuse parameter classes. This is referred to as parameter cross-talk; it leads to incorrect model solutions, poor convergence and strong dependence on the scaling of the different parameter types. Determining step lengths in a subspace domain, rather than directly in terms of gradients of different parameters, is a potentially valuable approach to address this problem. The particular subspace used can be defined over a span of different sets of data or different parameter classes, provided it involves a small number of vectors compared to those contained in the whole model space. Additionally, in a subspace method, the basis vectors are defined first, and a local minimum is found in the space spanned by these. We examine the application of the subspace method within acoustic FWI in determining simultaneously updates for velocity and density. We first discuss the choice of basis vectors to construct the spanned space, from linear updates by distinguishing only the contributions of different parameter classes towards nonlinear updates by adding the contributions of higher-order perturbations of each parameter class. The numerical character of FWI solutions generated via subspace methods involving different basis vectors is then analyzed and compared with traditional FWI methods. The subspace methods can provide better reconstructions of the model, especially for the velocity, as well as improved convergence rates, while the computational costs are still comparable with the traditional FWI methods.},

  doi          = {10.4208/cicp.oa-2018-0087},

  journal      = {Communications in Computational Physics},

  number       = 1,

  volume       = 28,

  place        = {United States},

  year         = {Mon Jun 01 00:00:00 EDT 2020},

  month        = {Mon Jun 01 00:00:00 EDT 2020}

}

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