Communications in Mathematical Sciences

Volume 12 (2014)

Number 5

Application of the Wasserstein metric to seismic signals

Pages: 979 – 988

(Fast Communication)

DOI: http://dx.doi.org/10.4310/CMS.2014.v12.n5.a7

Authors

Björn Engquist (Department of Mathematics and ICES, University of Texas, Austin, Tx., U.S.A.)

Brittany D. Froese (Department of Mathematics and ICES, University of Texas, Austin, Tx., U.S.A.)

Abstract

Seismic signals are typically compared using travel time difference or $L_2$ difference. We propose the Wasserstein metric as an alternative measure of fidelity or misfit in seismology. It exhibits properties from both of the traditional measures mentioned above. The numerical computation is based on the recent development of fast numerical methods for the Monge-Ampère equation and optimal transport. Applications to waveform inversion and registration are discussed and simple numerical examples are presented.

Keywords

Wasserstein metric, seismology, optimal transport, waveform inversion, registration

2010 Mathematics Subject Classification

62E99, 65K99, 65N06, 86A15

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