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Geophysical inversion and optimal transport

Sambridge, Malcolm; Jackson, Andrew; Valentine, Andrew P.

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Authors

Malcolm Sambridge

Andrew Jackson



Abstract

We propose a new approach to measuring the agreement between two oscillatory time series, such as seismic waveforms, and demonstrate that it can be employed effectively in inverse problems. Our approach is based on Optimal Transport theory and the Wasserstein distance, with a novel transformation of the time series to ensure that necessary normalisation and positivity conditions are met. Our measure is differentiable, and can readily be employed within an optimization framework. We demonstrate performance with a variety of synthetic examples, including seismic source inversion, and observe substantially better convergence properties than achieved with conventional L2 misfits. We also briefly discuss the relationship between Optimal Transport and Bayesian inference.

Journal Article Type Article
Acceptance Date Apr 9, 2022
Online Publication Date Apr 22, 2022
Publication Date 2022-10
Deposit Date Apr 29, 2022
Publicly Available Date Apr 29, 2022
Journal Geophysical Journal International
Print ISSN 0956-540X
Electronic ISSN 1365-246X
Publisher Oxford University Press
Peer Reviewed Peer Reviewed
Volume 231
Issue 1
Pages 172-198
DOI https://doi.org/10.1093/gji/ggac151
Public URL https://durham-repository.worktribe.com/output/1207436

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Copyright Statement
This is a pre-copyedited, author-produced PDF of an article accepted for publication in Geophysical Journal International following peer review. The version of record: Sambridge, Malcolm, Jackson, Andrew & Valentine, Andrew P. (2022). Geophysical inversion and optimal transport. Geophysical Journal International 231(1): 172-198. is available online at: https://doi.org/10.1093/gji/ggac151





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