Seismic Inversion and the Data Normalization for Optimal Transport

Understand

Full waveform inversion (FWI) has recently become a favorite technique for the inverse problem of finding properties in the earth from measurements of vibrations of seismic waves on the surface.

• Mathematically, FWI is PDE constrained optimization where model parameters in a wave equation are adjusted such that the misfit between the computed and the measured dataset is minimized.
• In a sequence of papers, we have shown that the quadratic Wasserstein distance from optimal transport is to prefer as misfit functional over the standard $L^2$ norm.
• Datasets need however first to be normalized since seismic signals do not satisfy the requirements of optimal transport.