Geophysical inversion and optimal transport. Issue 1 (22nd April 2022)

• Record Type: Journal Article
• Authors: Sambridge, Malcolm; Jackson, Andrew; Valentine, Andrew P
• Is Part Of: Geophysical journal international. Volume 231:Issue 1(2022)
• Page Start: 172
• Page End: 198
• Publication Date: 2022-04-22
• Subjects: Inversion -- Waveform analysis -- Gradient -- Numerical techniques; Geophysics -- Periodicals; 550
• DOI: 10.1093/gji/ggac151
• Languages: English
• ISSNs: 0956-540X

Abstract

SUMMARY: We propose a new approach to measuring the agreement between two oscillatory time-series, such as seismic waveforms, and demonstrate that it can be used 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 normalization and positivity conditions are met. Our measure is differentiable, and can readily be used 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 L 2 misfits. We also briefly discuss the relationship between Optimal Transport and Bayesian inference.