修正辛-准粒子法地震波数值模拟

基于Hamilton力学，从分子动力学角度建立了针对地震波传播的空间离散的准粒子体系，在该体系中各个粒子仅与上、下、左、右和4个对角粒子发生相互作用，且认为其作用力和相对位移呈近似线性关系，给出了粒子间的相互作用系数，并将该体系变换至Hamilton系统。在时间离散上，通过在二阶辛格式的基础上构建了一个新的修正辛格式，该格式具有三阶时间精度，并在理论上分析了其数值频散和稳定性。修正辛格式所有的系数均为正系数，符合时间演进方向，且具有长时间计算能力。为了测试修正辛格式和空间准粒子体系的准确性，利用拉梅问题验证对弹性波数值模拟的计算精度和效率，为了测试稳定性，选取Sigsbee 2B速度模型进行验证。结果表明，修正辛格式在数值频散压制和数值稳定性提升等方面具有明显的优势。

Seismic wave modeling based on modified symplectic scheme and quasi-particles method

Based on Hamilton mechanics,we develop a quasi-particles system to discretize seismic wave equation from the viewpoint of molecular dynamics.Each particle in the system only interacts with the particles which located at the upper,the lower,the left,and the right,and the four diagonal particles.The force and the relative displacement between the particles can be considered as approximately linear.In this paper,the interaction coefficients of the particles are derived.We get a modified symplectic scheme with third-order on the basis of two-order symplectic schemes to deal with temporal discretization.Theoretical analysis shows the new scheme possesses weaker numerical dispersion and larger stability than those of the conventional symplectic schemes.The modified symplectic scheme is suitable for long-term computational owing to all positive symplectic coefficients which consistent with iterative computation.In order to test the accuracy of the symplectic scheme and the spatial quasi-particles system,we adopt Lamb's problem to investigate the accuracy and efficiency of the numerical simulation of elastic wave.In addition,the Sigsbee2B velocity model is selected to test the stability of the proposed method.Numerical experiments demonstrate improvements in the numerical dispersion suppression and numerical stability of the modified symplectic scheme.