Total wavefield-based inversion in PML-truncated domains

Abstract

We discuss a total wavefield-based inversion approach for the reconstruction of the material profile of heterogeneous semi-infinite domains, directly in the time domain, based on scant surficial measurements of the domain's response to prescribed wave illumination. Of particular interest is the ability to recover the in-depth profile of moduli/wave velocities typically associated with small-scale geotechnical site characterization applications. We address four key issues associated with the wavefield-based inversion: a) to limit the semi-infinite extent of the physical domain, a perfectly-matched-layer (PML) is introduced at truncation interfaces to render a finite computational domain; b) to account for the introduction of the PML, while retaining the second-order temporal character of the hyperbolic problem, we discuss a new mixed unsplit-field formulation for the coupled PML-regular-domain problem; c) to tackle the inversion, we adopt a PDE-constrained optimization framework that formally leads to a classic (time-dependent) KKT (Karush-Kuhn-Tucker) system; and d) to alleviate solution multiplicity, we discuss a first-order Tikhonov regularization scheme endowed with a regularization factor continuation algorithm. We report on one- and two-dimensional experiments that lead efficiently to the reconstruction of heterogeneous profiles involving both horizontal and inclined layers, as well as of inclusions within layered systems.