Young Researchers Workshop: Kinetic descriptions in theory and applications

Optimal transport base approaches for nonlinear seismic inverse problems

Yunan Yang

New York University

Full waveform inversion (FWI) is a nonlinear inverse technique that inverts the model parameters by minimizing the difference between the synthetic data from numerical simulations and the observed data at the surface of the earth. The least-squares (L2) norm of this difference is the traditional objective function for FWI, but it is sensitive to the initial model, the data spectrum, the noise in the measurement, and other issues related to optimization. We proposed that the quadratic Wasserstein (W2) metric of the Optimal Transport theory to FWI is a global metric which considers both the amplitude dierences and the phase mismatches. However, its application to seismic data is not straightforward: Optimal Transport assumes positivity and mass balance between compared quantities while seismic data is non-positive. Integrating OT within FWI also requires fast and robust numerical methods for solving the optimal transport problem. I will discuss the recent progress in this area.