Compound Regularization of Full-Waveform Inversion for Imaging Piecewise Media

Full-waveform inversion (FWI) is an iterative nonlinear waveform matching procedure, which seeks to reconstruct unknown model parameters from partial waveform measurements. The nonlinear and ill-posed nature of FWI requires sophisticated regularization techniques to solve it. In most applications, the model parameters may be described by physical properties (e.g., wave speeds, density, attenuation, and anisotropy) that are piecewise functions of space. Compound regularizations are, thus, beneficial to capture these different functions by FWI. We consider different implementations of compound regularizations in the wavefield reconstruction inversion (WRI) method, a formulation of FWI that extends its search space and mitigates the so-called cycle skipping pathology. Our hybrid regularizations rely on the Tikhonov and total variation (TV) functionals, from which we build two classes of hybrid regularizers: the first class is simply obtained by a convex combination (CC) of the two functionals, while the second relies on their infimal convolution (IC). In the former class, the model parameters are required to simultaneously satisfy different priors, while in the latter, the model is broken into its basic components, each satisfying a distinct prior (e.g., smooth, piecewise constant, and piecewise linear). We implement these compound regularizations in WRI using the alternating direction method of multipliers (ADMM). Then, we assess our regularized WRI for seismic imaging applications. Using a wide range of subsurface models, we conclude that the compound regularizer based on IC leads to the lowest error in the parameter reconstruction compared to that obtained with the CC counterpart and the Tikhonov and TV regularizers when used independently.