  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-Ampere equation and
optimal transport. Applications to waveform inversion and registration are
discussed and simple numerical examples are presented.
