The inverse medium problem in heterogeneous PML-truncated domains using scalar probing waves

Abstract

We discuss the inverse medium problem associated with semi-infinite domains. In particular, we attempt to image the spatial variability of shear moduli or shear wave velocities from scant surficial measurements of an arbitrarily heterogeneous semi-infinite domain’s response to prescribed dynamic excitations. We use a full waveform approach to drive the inversion process, within a PDE-constrained optimization framework. Due to the semi-infinite extent of the targeted domains, we introduce perfectly-matched-layers (PMLs) to arrive at finite computational domains. The numerical implementation is based on a mixed finite-element method that is used to resolve the ensuing state and adjoint boundary-value problems, both of which are PML-endowed. To alleviate the inherent solution multiplicity, we use Tikhonov and total variation (TV) regularization schemes, in conjunction with a regularization factor continuation scheme. To further improve the optimizer’s chances to converge, we also discuss a source-frequency continuation scheme. We report on two-dimensional numerical experiments using synthetic data. Included are layered profiles, and profiles involving inclined layers and inclusions. We also report on our methodology’s reconstruction of the highly-heterogeneous Marmousi benchmark velocity model.