Abstract: 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.

Key words: Solitary waves, KdV equation, Finite-difference method, Sparse matrix access