A New Approach of Rotated Staggered Grid FD Method With Unsplit Convolutional PML for GPR

Abstract

We introduce a novel implementation of a rotated staggered grid (RSG) finite difference (FD) method based on the unsplit convolutional perfectly matched layer (UCPML). The method is carried out using rotated staggered FD operators and a general complex frequency shifted stretching factor. It can offer a number of advantages over the RSG with split convolutional perfectly matched layer (SCPML), such as improving computational efficiency, overcoming the numerical dispersions resulting from the high-frequency propagation and strong contrasts in material, and specifically absorbing the evanescent modes at grazing incidence. A half-space numerical example with a lossy medium attached demonstrates that large-scale spurious reflections and evanescent modes at grazing incidence are absorbed efficiently by the UCPML in RSG scheme. Meanwhile, the comparison of the reflection error between the proposed algorithm and traditional approaches [using time-dependent reflection error (TDRE) and frequency-dependent reflection error (FDRE)] suggests that the proposed algorithm of RSG provides a preferable improvement in absorbing low-frequency coda wave of evanescent modes, particularly in the lossy medium that possesses inhomogeneous discontinuities.