求解弹性波动方程的频率域近似解析离散化波场模拟方法

A nearly discrete analytic method of wave-field simulation for elastic wave equations in the frequency domain

为提高频率域弹性波动方程数值求解的计算效率,本文引入近似解析离散化(NAD)方法将其进行数值离散并得到大型线性代数方程组.在详细分析了相应系数矩阵的稀疏分块结构与数学性质之后,本文提出采用不精确旋转分块三角预处理子加速Krylov子空间迭代方法来快速求解该线性方程组,并利用数值试验证实这种方法在弹性波场模拟方面的数值效率.通过与另外两种经典数值方法(常规有限差分方法和交错网格有限差分方法)对多种介质模型进行波场模拟、数值频散分析以及与解析解的波形对比,NAD方法显示了其在压制数值频散和提高计算效率方面的优势以及对复杂介质模型弹性波场数值模拟的有效性.

To improve the computing efficiency of numerically solving frequency-domain elastic wave equation,this paper introduces nearly analytic discrete(NAD)method for numerically discretizing the frequency-domain elastic wave equation to obtain a large-scale linear algebraic system.After the detailed analysis for sparse block structure and mathematical property of the corresponding coefficient matrix,the inexact rotated block triangular preconditioners are proposed to accelerate Krylov subspace iteration methods to solve the linear system and the numerical efficiency of such methods for elastic wave simulation is examined by numerical experiments.When comparing with the other two classical numerical schemes(ordinary finite difference method and staggered grid method)in wave-field simulation,numerical dispersion analysis and waveform comparison with analytic solution for various models,NAD method shows its advantages of increasing computing efficiency,suppressing numerical dispersion and the effectiveness of numerical simulation in complicated media.