Application of the Wasserstein metric to seismic signals

Seismic signals are typically compared using travel time difference or L₂ 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.