Volume 28, Issue 1
Subspace Methods in Multi-Parameter Seismic Full Waveform Inversion

Yu Geng, Kristopher A. Innanen & Wenyong Pan

Commun. Comput. Phys., 28 (2020), pp. 228-248.

Published online: 2020-05

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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. 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.

  • Keywords

Waveform inversion, inverse problem, subspace method.

  • AMS Subject Headings

35L05, 35R30, 86A22

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

gengfish@gmail.com (Yu Geng)

k.innanen@ucalgary.ca (Kristopher A. Innanen)

wenyongp@lanl.gov (Wenyong Pan)

  • BibTex
  • RIS
  • TXT
@Article{CiCP-28-228, author = {Geng , Yu and Innanen , Kristopher A. and Pan , Wenyong }, title = {Subspace Methods in Multi-Parameter Seismic Full Waveform Inversion}, journal = {Communications in Computational Physics}, year = {2020}, volume = {28}, number = {1}, pages = {228--248}, 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. 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0087}, url = {http://global-sci.org/intro/article_detail/cicp/16835.html} }
TY - JOUR T1 - Subspace Methods in Multi-Parameter Seismic Full Waveform Inversion AU - Geng , Yu AU - Innanen , Kristopher A. AU - Pan , Wenyong JO - Communications in Computational Physics VL - 1 SP - 228 EP - 248 PY - 2020 DA - 2020/05 SN - 28 DO - http://doi.org/10.4208/cicp.OA-2018-0087 UR - https://global-sci.org/intro/article_detail/cicp/16835.html KW - Waveform inversion, inverse problem, subspace method. AB -

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. 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.

Yu Geng, Kristopher A. Innanen & Wenyong Pan. (2020). Subspace Methods in Multi-Parameter Seismic Full Waveform Inversion. Communications in Computational Physics. 28 (1). 228-248. doi:10.4208/cicp.OA-2018-0087
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