Modern Perspectives in Applied Mathematics: Theory and Numerics of PDEs

Wasserstein metric and Texas oil

Bjorn Engquist

The University of Texas at Austin

Full waveform inversion is an essential step in modern seismic imaging. In this process, PDE constrained optimization is used to find the seismic wave velocity field in the earth by matching a computed wave field to measured data. We will describe advantages and difficulties from choosing a Wasserstein distance for computing the mismatch. For a fast algorithm the measure is determined from a numerical approximation of the viscosity solution of the Monge-Ampere equation.