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

Abstract

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 boundary 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 (DSL) computational framework, Devito, which is primarily used for seismic modelling 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 at avoiding wave reflections at 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, for being as effective as or more effective than PML and other schemes but also for being computationally more efficient.

Efficient hyperbolic–parabolic models on multi‐dimensional unbounded domains using an extended DG approach

“…Accurate computational representation of physical phenomena on unbounded domains remains a challenge for numerical methods for transient differential problems, with fields of interest ranging from cell growth modeling 1 to upper atmosphere dynamics 2 and space weather. 3,4 In the quest to make the inherently infinite problem tractable, numerical treatments based on absorbing (also called sponge) layers are usually preferred to analytical approaches relying on nonreflecting boundary conditions [5][6][7][8] (though see also 9 for a recent study challenging that convention). The former class of methods typically relies on dividing the computational domain into a bounded region of interest to the physical phenomena relevant to the problem at hand (e.g., the troposphere and lower stratosphere in currently operational atmospheric models 10,11 ) and an unbounded buffer region for damping the outgoing signals.…”