基于谱元法的三维地震波场数值模拟与分析

Spectral Element Method-Based Numerical Simulation and Analysis of 3D Seismic Wavefield

摘要: 本文采用谱元法(Spectral Element Method, SEM)对三维介质中的地震波传播过程进行数值模拟，并以三维无限均匀介质中的点源球面波解析解作为理论参照。数值模型采用六面体单元进行空间剖分，在单元内部布置Gauss-Lobatto-Legendre (GLL)节点，通过高阶拉格朗日多项式对波场进行空间逼近，时间方向采用显式差分格式推进。结果表明，在本文所建立的三维均匀介质模型和计算参数条件下，波前具有较好的连续性，观测点处的数值解波形与解析解波形在初至位置、主要波峰和波谷位置以及整体振荡特征方面具有较好的一致性。峰值归一化后，数值解与解析解之间的均方根误差为1.01%，表明当前数值模型和计算程序能够较好地描述三维介质中的地震波传播过程。

Abstract: In this paper, the Spectral Element Method (SEM) is adopted to numerically simulate the propagation of seismic waves in three-dimensional media. The analytical solution of spherical waves excited by a point source in a three-dimensional infinite homogeneous medium is used as the theoretical reference. The numerical model is spatially discretized using hexahedral elements. Gauss-Lobatto-Legendre (GLL) nodes are arranged within each element, and high-order Lagrange polynomials are employed for spatial approximation of the wavefield. An explicit difference scheme is utilized for time integration. The results show that under the established three-dimensional homogeneous medium model and computational parameters, the wavefront maintains good continuity. At observation points, the waveforms of numerical solutions are in good agreement with analytical solutions in terms of first-arrival time, positions of major peaks and troughs, and overall oscillation characteristics. After peak normalization, the root mean square error (RMSE) between numerical and analytical solutions is 1.01%, demonstrating that the proposed numerical model and computational program can well describe the propagation of seismic waves in three-dimensional media.