Optimal Transport Based Seismic Inversion:Beyond Cycle Skipping

Full-waveform inversion (FWI) is today a standard process for the inverse problem of seismic imaging. PDE-constrained optimization used to determine unknown parameters in wave equation that represent geophysical properties. The objective function measures misfit between observed data and calculated synthetic data, it has traditionally been least-squares norm. In sequence papers, we introduced Wasserstein metric from optimal transport as an alternative mitigating so-called cycle skipping, which trapping local minima. this paper, first give sharper theorem regarding convexity function. We then focus on two new issues. One necessary normalization turning signals into probability such theory applies. other, beyond below reflecting interfaces. For first, propose class normalizations prove several favorable properties class. latter, demonstrate FWI using can recover domains where no waves travel through. finally illustrate these by realistic application imaging salt inclusions, significant challenge exploration geophysics. © 2021 Wiley Periodicals LLC.