物探化探计算技术2025，Vol.47Issue(6)：845-855,11.DOI:10.12474/wthtjs.20241025-0002
基于最小范数优化三维有限差分系数的波动方程正演数值模拟
Wave equation forward numerical simulation based on minimum norm optimization of three-dimensional finite difference coefficients
摘要
Abstract
The finite difference method is widely used in the forward simulation of wave equations due to its advantages of easy implementation and high computational efficiency.However,the numerical dispersion error caused by mesh discretization in the finite difference method is unavoidable.The conventional optimization method for differential coefficients adopts unidirectional optimization,which optimizes the finite differential coefficients along a single spatial direction to suppress spatial dispersion.However,it cannot effectively reduce the inherent anisotropy of numerical dispersion on discrete grids.In order to meet the requirements of high-precision forward numerical simulation in three-dimensional space,this paper proposes a multi-directional optimization method that uses the minimum norm(norm)to constrain the differential approximation error of all propagation directions on the three-dimensional discrete grid,while suppressing spatial numerical dispersion and numerical dispersion anisotropy.Given the maximum absolute allowable error and grid spacing ratio,this article first determines the optimal differential order of the differential operator in each spatial direction.Then,the alternating direction multiplier method is used to solve and obtain the optimized differential coefficients.Theoretical analysis and numerical experiments show that for cubic and rectangular grids,the method proposed in this paper is superior to one-way optimization methods in suppressing spatial numerical dispersion and reducing numerical dispersion anisotropy.Under the condition of an absolute error of 0.5E-5 allowable error,multi-directional optimization has a more significant control effect on dispersion error in the medium and low wavenumber domains.It can also effectively reduce numerical dispersion anisotropy,thereby reducing the accumulation of errors in three-dimensional wave equation forward numerical simulation.关键词
L1范数/有限差分法/多方向优化/频散各向异性/误差积累Key words
L1 norm/finite difference method/multi directional optimization/dispersion anisotropy/error accumulation分类
天文与地球科学引用本文复制引用
林沛然,文晓涛..基于最小范数优化三维有限差分系数的波动方程正演数值模拟[J].物探化探计算技术,2025,47(6):845-855,11.基金项目
中国海洋石油有限公司"十四五"重大科技项目(KJGG2022-0903) （KJGG2022-0903）
