Analysis of Seismic Inversion with Optimal Transportation and Softplus Encoding

TL;DR

This paper introduces a novel softplus encoding approach to improve the convexity and reduce cycle-skipping in seismic full waveform inversion by leveraging optimal transportation metrics, supported by theoretical analysis and numerical experiments.

Contribution

It provides a mathematical analysis of OT-based objective functions and introduces a softplus encoding method to enhance FWI performance.

Findings

Improved convexity of the objective function.

Reduced cycle-skipping in seismic inversion.

Validated effectiveness on Marmousi model.

Abstract

This paper is devoted to theoretical and numerical investigation of the local minimum issue in seismic full waveform inversion (FWI). This paper provides a mathematical analysis of optimal transportation (OT) type objective function's differentiability and proves that the gradient obtained in the adjoint-state method does not depend on the particular choice of the Kantorovich potentials. A novel approach using the softplus encoding method is presented to generalize and impose the OT metric on FWI. This approach improves the convexity of the objective function and mitigates the cycle-skipping problem. The effectiveness of the proposed method is demonstrated numerically on an inversion task with the benchmark Marmousi model.