固体介质中孤立波的传播及演化特征

由于地球介质中广泛存在断裂、微裂缝等地质现象，实际地震资料中会出现形似孤立波的非线性地震现象。因此，对固体介质中孤立波的研究有利于解释这些非线性地震现象的形成机制。本文基于KdV方程，以雷克子波作为初始条件，采用伸缩子机理构建体力模型，利用有限差分的方法模拟了孤立波的演化过程。理论结果表明，非线性地震纵波可以从雷克子波逐渐演化成孤立波，而且地震波的初始振幅和频散系数对模拟结果也有重要影响。通过与实际资料的对比也能说明这种演化的可能性。同时根据方程系数矩阵中元素带状分布的特征，采用稀疏矩阵的存取方法，可以减小计算内存，提高计算效率。

Propagation and Evolution of Solitary Waves in Solid Media

Because of the existence of geological structure such as fractures and small cracks in the earth, there are some nonlinear phenomena, which are similar to solitary waves in observed seismic data. Studies on solitary waves in solid media can help to explain their formation mechanism. Based on the KdV equation, using Ricker wavelet as initial condition and dilaton mechanism to construct body force, we simulated solitary waves in detail by finite difference method. Theoretical results indicate that solitary waves could be evolved from Ricker wavelet, and initial amplitude of seismic wave and dispersion coefficient can significantly influence the evolution process. The observed seismic data in this paper can also illustrate the possibility of this kind of evolution. In addition, according to the zonal distribution of the coefficient matrix, sparse matrix access method has been used, which can reduce the computation memory and improve the calculation efficiency.