Probabilistic Full-Waveform Inversion Considering the Discontinuities of the Material Properties of a Layered Half-Space

The goal of full-waveform inversion (FWI) is to extract quantitative information pertaining to the material and geometrical properties from measured wave fields with their full contents considered. As an inverse problem, FWI itself is associated with ill-posedness, which means instability and nonuniqueness of the solution, because the fields are measured only at some locations. Owing to these unfavorable conditions, several regularization techniques have been utilized for stable estimations, but it is difficult when using a regularization technique to select a regularization factor, which has no physical meaning. In this paper, the FWI approach is applied to estimate the material properties of a layered half-space. The thin-layered method, an efficient analysis method for wave propagation in a layered medium, is employed for this purpose. It is formulated in the maximum a posteriori (MAP) form, and Tikhonov regularization is expressed as a prior distribution, whose standard deviation replaces the role of the regularization factor to ensure an intuitive meaning. Additionally, a technique to remove outliers is newly introduced for the regularization technique; it captures discontinuities accurately in the material properties of a layered half-space. Through this additional technique, the limitation of the smoothness effect in existing regularization techniques is alleviated. The proposed MAP approach including the regularization-based prior and outlier-removal technique is applied to several numerical examples to estimate the profiles of the shear velocities of a layered half-space. The numerical investigations conducted here confirm the validity of the proposed approach with satisfactory accuracy.