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

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


Malcolm Sambridge

Andrew Jackson


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.

Journal Article Type Article
Acceptance Date Dec 23, 2022
Online Publication Date Jan 5, 2023
Publication Date 2023-05
Deposit Date Feb 6, 2023
Journal Geophysical Journal International
Print ISSN 0956-540X
Electronic ISSN 1365-246X
Publisher Oxford University Press
Peer Reviewed Peer Reviewed
Volume 233
Issue 2
Pages 1488-1491
Public URL