Application of perfectly matched layer for scalar arbitrarily wide-angle wave equations

Abstract

Arbitrarily wide-angle wave equation (AWWE) is a space domain, high-order one-way wave equation (OWWE). Its accuracy can be arbitrarily increased, and it is amenable to easy numerical implementation. Those properties make it outstanding among the existing OWWEs and further enable it to be a desirable tool for migration. We extend the perfectly matched layer (PML) to 3D scalar AWWE to provide a good approach to suppress artifacts arising at truncation boundaries. We follow the concept of complex coordinate stretching, and the derivation procedure of PML for AWWE is straightforward. An existing finite-difference scheme is adopted to fit the split PML formulation and its stability is observed through numerical examples. The performance of the developed PML condition is compared with two different wave-equation based absorbing boundary conditions. Numerical results illustrate that the PML condition used in AWWE propagator can effectively absorb the propagating waves and evanescent waves at a price of limited additional computation cost.

Application of unsplit convolutional perfectly matched layer for scalar arbitrarily wide-angle wave equation

“…It is seen that the HABC absorbs the propagating waves a little more than the 20-layer split PML, but the latter absorbs the evanescent waves more efficiently (see the white arrows for a comparison). The result agrees with previous numerical observations (Chen et al, 2013). Unfortunately, in case P1, the absorption effect is unacceptable.…”

“…The parameters d i , α i , and k i ði ¼ x; yÞ constitute a general CFS stretching factor, d i is the damping profile in the PML layers, whereas α i and k i are expected to take effect in absorbing propagating waves with large incident angles and evanescent waves. A special CFS operator corresponding to α x ðxÞ ¼ 0 and k x ðxÞ ¼ 1 underlies the existing split PML for the second-order AWWE (Chen et al, 2013). The staggered-grid FD method (Virieux, 1984) is adopted to discretize equation 11, and the details are presented in Appendix A.…”

“…Four different settings of ABCs are used for comparison, and they are, respectively, denoted as C, H, P1, and P2; C represents a 10-layer CPML for the first-order AWWE and H represents a three-layer, highly accurate ABC (HABC) proposed by Heidari and Guddati (2006) for the second-order AWWE. The P1 and P2 stand for, respectively, a 10-layer and a 20-layer split PML for the second-order AWWE (Chen et al, 2013). For a clear comparison, the wavefield snapshots at the same time are displayed in the same amplitude range (amplified by a factor of 10).…”

“…When the number of auxiliary variables increases, the computational cost increases dramatically. Chen et al (2013) apply a split PML to the scalar AWWE to suppress artificial edge reflections. The split PML obviously further increases the elapsed time and memory consumption.…”