The Monge-Ampere equation and seismology

Björn Engquist
Institute for Computational Engineering and Sciences
University of Texas
Austin, Texas, USA


A fundamental inverse problem in seismology can be formulated as PDE constrained minimization where the miss-match between measured and computed signals plays an important role. We propose using optimal transport and the Wasserstein metric for this miss-match. The optimal transport can be given by the gradient of the solution to a Monge-Ampere equation. We will discuss numerical approximations of the viscosity solution to the Monge-Ampere equation and the application to exploration seismology.