Optimal transport for seismic full waveform inversion

Full waveform inversion is a successful procedure for determining properties of the Earth from surface measurements in seismology. This inverse problem is solved by PDE constrained optimization where unknown coefficients in a computed wavefield are adjusted to minimize the mismatch with the measured data. We propose using theWasserstein metric, which is related to optimal transport, for measuring this mismatch. Several advantageous properties are proved with regards to convexity of the objective function and robustness with respect to noise. The Wasserstein metric is computed by solving a Monge-Ampère equation. We describe an algorithm for computing its Fréchet gradient for use in the optimization. Numerical examples are given.