Reply to comment on Geophysical inversion and Optimal Transport, 231, 172–198, by Okazaki & Ueda

Malcolm Sambridge, Andrew Jackson, Andrew P. Valentine

Research output: Contribution to journalArticlepeer-review

Abstract

Concerns raised by Okazaki & Ueda (2022) on the paper by Sambridge et al. (2022) are addressed. Two issues are discussed and some new numerical results presented. The first concerns whether the properties of the Wasserstein time-series misfit introduced in our earlier paper will translate to model space non-uniqueness in a seismic waveform inversion setting. It is argued that this is unlikely, given the special conditions, which must exist between all observed/predicted seismic waveform pairs for non-uniqueness to result. The second issue discussed is the efficacy of using the Sliced Wasserstein algorithm of Bonneel et al. (2015) as an alternate to the marginal Wasserstein algorithm, as proposed by Okazaki & Ueda (2022). It is argued that for optimization-based waveform fitting, the Sliced Wasserstein algorithm is a viable alternate provided care is taken to ensure that conditions arise which do invalidate analytical derivative expressions of the resulting Wasserstein misfit. In practice, this would likely mean recasting the 2D Optimal Transport problem posed in our earlier paper onto unstructured grids.

Original languageEnglish
Pages (from-to)1488-1491
Number of pages4
JournalGeophysical Journal International
Volume233
Issue number2
DOIs
Publication statusPublished - 1 May 2023

Fingerprint

Dive into the research topics of 'Reply to comment on Geophysical inversion and Optimal Transport, 231, 172–198, by Okazaki & Ueda'. Together they form a unique fingerprint.

Cite this