Lift and relax for waveform inversion
Name
segam2020-3427933.1.pdf
Description
Published version
Size
8.57 MB
Format
Adobe PDF
Checksum (MD5)
4c466b6dccac688f92ad23116fbab367
Author(s)
Fang, Zhilong
Demanet, Laurent
Date Issued
September 30, 2020
Journal
SEG Technical Program Expanded Abstracts 2020
Publisher
Society of Exploration Geophysicists
Citation
Zhilong Fang, Laurent Demanet; September 1, 2020. "Lift and relax for waveform inversion." Proceedings of the SEG Technical Program Expanded Abstracts 2020. SEG Technical Program Expanded Abstracts 2020. (pp. pp. 785-789). ASME.
Version
Final published version
Abstract
We present Lift and Relax for Waveform Inversion (LRWI), an approach that mitigates the cycle-skipping issue in full waveform inversion via a combination of two convexification techniques. The first technique (Lift) extends the set of variables in the optimization problem to products of those variables, arranged as a moment matrix. This algebraic idea is a celebrated way to replace a hard polynomial optimization problem by a semidefinite programming approximation. Concretely, both the model and the wavefield are lifted from vectors to rank-2 matrices. The second technique (Relax) invites to consider the wave equation, not as a hard constraint, but as a soft constraint to be satisfied only approximately – a technique known as wavefield reconstruction inversion (WRI). WRI weakens wave-equation constraints by introducing wave-equation misfits as a weighted penalty term in the objective function. The relaxed penalty formulation enables balancing the data and wave-equation misfits by tuning a penalty parameter. Together, “Lift” and “Relax” help reformulate FWI as a set of constraints on a rank-2 moment matrix in a higher dimensional space. Such a lifting strategy permits a good data and wave-equation fit throughout the inversion process, while leaving the numerical rank of the rank-2 moment matrix to be minimized down to one. Numerical examples indicate that the proposed rank-2 lifting approach with the wave-equation relaxation is capable of reconstructing geologically plausible subsurface models from poor initial models without stagnation at suboptimal models encountered by conventional FWI.
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Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1190/segam2020-3427933.1
