Björn Engquist: "Monge-Ampère equation and seismology"

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