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Geophysical inversion and optimal transport

Sambridge, Malcolm and Jackson, Andrew and Valentine, Andrew P. (2022) 'Geophysical inversion and optimal transport.', Geophysical Journal International, 231 (1). pp. 172-198.


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.

Item Type:Article
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Publisher 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:
Date accepted:09 April 2022
Date deposited:29 April 2022
Date of first online publication:22 April 2022
Date first made open access:29 April 2022

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