A hybrid absorbing boundary condition for frequency-domain finite-difference modelling

Abstract

Liu and Sen (2010 Geophysics 75 A1?6; 2012 Geophys. Prospect. 60 1114?32) proposed an efficient hybrid scheme to significantly absorb boundary reflections for acoustic and elastic wave modelling in the time domain. In this paper, we extend the hybrid absorbing boundary condition (ABC) into the frequency domain and develop specific strategies for regular-grid and staggered-grid modelling, respectively. Numerical modelling tests of acoustic, visco-acoustic, elastic and vertically transversely isotropic (VTI) equations show significant absorptions for frequency-domain modelling. The modelling results of the Marmousi model and the salt model also demonstrate the effectiveness of the hybrid ABC. For elastic modelling, the hybrid Higdon ABC and the hybrid Clayton and Engquist (CE) ABC are implemented, respectively. Numerical simulations show that the hybrid Higdon ABC gets better absorption than the hybrid CE ABC, especially for S-waves. We further compare the hybrid ABC with the classical perfectly matched layer (PML). Results show that the two ABCs cost the same computation time and memory space for the same absorption width. However, the hybrid ABC is more effective than the PML for the same small absorption width and the absorption effects of the two ABCs gradually become similar when the absorption width is increased.