A non-balanced staggered-grid finite-difference scheme for the first-order elastic wave-equation modeling

TL;DR

This paper presents a novel non-balanced staggered-grid finite-difference scheme for 2D elastic wave modeling, combining mixed operators to improve efficiency while maintaining accuracy, validated through dispersion analysis and modeling examples.

Contribution

It introduces a non-balanced SGFD scheme using mixed operators, offering computational efficiency without sacrificing accuracy in elastic wave simulations.

Findings

Similar accuracy to balanced SGFD methods

Reduced computational cost

Validated by dispersion analysis and modeling examples

Abstract

We introduce an efficient and accurate staggered-grid finite-difference (SGFD) method to solve the two-dimensional elastic wave equation. We use a coupled first-order stress-velocity formulation. In the standard implementation of SGFD method the same SGFD operator is used to approximate the spatial derivatives. However, we propose a numerical method based on mixed SGFD operators which happen to be more efficient with similar accuracy in comparison to uniform SGFD operator. We refer the proposed method as the non-balanced SGFD numerical scheme which means combining high-order SGFD operators with second-order SGFD operators. A very care attention is directed at the derivation of the SGFD operator coefficients. The correctness of proposed scheme is proven by dispersion analysis. Through SGFD modeling examples, we verify/demonstrate that the proposed non-balanced operator offers a similar level of accuracy with a cheaper computation cost compared to the more expensive balanced SGFD method.