Analysis and Application of Optimal Transport For Challenging Seismic Inverse Problems
For geophysicists using FWI, the method overcomes a key challenge in seismic inversion by enabling sub-reflection recovery, though the approach is incremental over prior optimal transport-based work.
The paper addresses the limitations of least-squares full-waveform inversion (FWI) by using the quadratic Wasserstein distance from optimal transport theory, which improves convexity and enables recovery of sub-reflection structures. New results demonstrate enhanced reconstruction below reflecting layers.
In seismic exploration, sources and measurements of seismic waves on the surface are used to determine model parameters representing geophysical properties of the earth. Full-waveform inversion (FWI) is a nonlinear seismic inverse technique that inverts the model parameters by minimizing the difference between the synthetic data from the forward wave propagation and the observed true data in PDE-constrained optimization. The traditional least-squares method of measuring this difference suffers from three main drawbacks including local minima trapping, sensitivity to noise, and difficulties in reconstruction below reflecting layers. Unlike the local amplitude comparison in the least-squares method, the quadratic Wasserstein distance from the optimal transport theory considers both the amplitude differences and the phase mismatches when measuring data misfit. We will briefly review our earlier development and analysis of optimal transport-based inversion and include improvements, for example, a stronger convexity proof. The main focus will be on the third "challenge" with new results on sub-reflection recovery.