Modeling Seismic Wave Propagation in TTI Media Using Residual Perfectly Matched Layer

TL;DR

This paper introduces a novel residual PML method for seismic wave simulation in TTI media, enhancing absorption and stability while reducing computational complexity compared to existing PML approaches.

Contribution

The paper presents a new residual PML formulation, RPML-2, that improves wave absorption and stability in TTI media simulations with higher efficiency.

Findings

RPML-2 outperforms ADEPML and NPML in absorption and stability.

High-order spatial discretization is unnecessary with RPML-2, increasing accuracy.

MCFS-RPML-2 further enhances stability and absorption using complex frequency shift technology.

Abstract

The perfectly matched layer(PML) is commonly used in wave propagation, radiation and diffraction problems in unbounded space domains. A new implementation scheme of PML is presented. The PML formulation is pre-defined, and the wave field absorption is achieved by calculating the residual between the PML equation and original equation through backward induction. Two forms of the Residual PML (RPML) are presented: RPML-1, which defines the residual as the difference between the original and PML equations, and RPML-2, which defines the residual as the difference between the original and PML wave fields. RPML-2 is the simplest and easiest to extend, as it does not alter the original equation and only has one time partial derivative term in the residual equation. Additionally, since the residual equation has no spatial partial derivative term, high-order spatial difference discretization is unnecessary, which results in higher accuracy and computational efficiency. Furthermore, simulating a wave field in TTI media requires a high absorption effect and stability of PML. The numerical simulation demonstrates that RPML-2 provides better absorption performance and stability compared to ADEPML and NPML. To meet the needs of wave field simulation for complex media, a multiaxial complex frequency shifted RPML-2 (MCFS-RPML-2) is introduced, which employs double damping profiles and complex frequency shift technology to achieve higher stability and absorption effects.