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.
Resumo. O foco do presente trabalho consiste na aplicação de um Método de Galerkin Descontínuo Estabilizado para a aproximação numérica do modelo bidimensional do Traçador-Passivo. Especificamente, serão exploradas as boas propriedades de estabilidade local no tempo dos métodos da classe Runge-Kutta em conjunto com funções de fluxo numérico estáveis com destaque para o uso de uma estratégia de estabilização baseada na Técnica de Reconstrução do Gradiente para a estabilização do problema hiperbólico associado.
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.
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