Communications in Mathematical Sciences
Volume 14 (2016)
Optimal transport for seismic full waveform inversion
Pages: 2309 – 2330
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 the Wasserstein 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.
optimal transport, Wasserstein metric, computational seismology, full waveform inversion
2010 Mathematics Subject Classification
35J96, 49N45, 65K10, 65N06, 86A15