Electromagnetic Full Waveform Inversion Based on Quadratic Wasserstein Metric

Abstract

Electromagnetic full waveform inversion (FWI) is a high-resolution method to reveal the distribution of dielectric parameters of the medium. Traditionally, the electromagnetic FWI is usually performed using the L-2 norm misfit function, which suffers severely local minimum problems since the L-2 norm misfit function is nonconvex in the model space. To mitigate the local minimum problem, the quadratic Wasserstein metric (W-2) derived from the optimal transport theory is proposed to replace the L-2 norm to define the misfit function. Since the computation of the W-2 metric requires the signal to be mass conservation and nonnegativity, the softplus function is applied to rescale the signal to meet these two requirements. Based on the softplus scaling method, a hierarchy inversion strategy that involves multiple scaling coefficients is proposed to mitigate the local minimum problem without sacrificing the inversion resolution. The numerical experiments prove that the FWI based on W-2 (W-2-FWI) is more independent on the initial model than the FWI based on the L-2 norm (L-2-FWI), and the W-2-FWI could be more robust to zero-mean random noise than the L-2-FWI. Finally, a comprehensive numerical experiment related to asteroid radar tomography is carried out to show the potential of W-2-FWI in realistic applications.