In seismic exploration a wave field is generated at the surface and reflections from the earths interior are recorded. The purpose is to find properties such as wave velocity and location of reflecting sub layers. This can be done in an inverse problem where the measurements are compared to a computed ware field with unknown coefficients in the wave equation. We will discuss the choice of Wasserstein metric in this comparison. We will also comment on numerical methods for the related Monge-Ampere equation and applications to registration.
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