Effectiveness and computational efficiency of absorbing boundary conditions for full-waveform inversion

Abstract. Full-Waveform Inversion (FWI) is a high-resolution numerical technique for seismic waves used to estimate the physical characteristics of a subsurface region. The continuous problem involves solving an inverse problem on an infinite domain, which is impractical from a computational perspective. In limited area models, absorbing boundaries conditions (ABCs) are usually imposed, to avoid wave reflections. Several relevant ABCs have been proposed, with extensive literature on their effectiveness on the direct wave problem. Here, we investigate and compare the theoretical and computational characteristics of several ABCs in the full inverse problem. After a brief review of the most widely used ABCs, we derive their formulations in their respective adjoint problems. The different ABCs are implemented in a highly optimized domain-specific language (DLS) computational framework, Devito, which targets seismic modeling problems. We evaluate the effectiveness, computational efficiency, and memory requirements of the ABC methods, considering from simple models to realistic ones. Our findings reveal that, even though the popular Perfectly Matching Layers (PMLs) are effective in avoiding wave reflections on the boundaries, they can be computationally more demanding than less used Hybrid ABCs. We show here that a proposed Hybrid ABC formulation, with nested Higdon's boundary conditions, is the most cost-effective method among the methods considered here, being as effective, or more, as PML and other schemes, but being computationally more efficient.