Simulation of acoustic wave propagation in complex media using MRFD method

This paper is devoted to the simulation of acoustic wave propagation in com plex media, applying the finite difference scheme and the orthonormal compa ctly supported wavelet transform approximation, to the time and the space d imension of the wave equation, respectively. A new method, which is a fast adaptive arithmetic, named Multiresolution Finite Difference (MRFD) is firs t proposed to solve the problem of the wave propagation in multi - layered medium with nonperiodic boundary condition. Thus the problem is solved in t he wavelet domain rather than in the traditional Euclidian space. Due to ad aptive and vanishing-moment property of the wavelet basis, the difference o perator and solution vector have sparseness in the wavelet domain. MRFD is a promising method because of some advantages such as lighter computational burden, efficiency of convergence and robustness. Numerical results in geo physics exploration show the effectiveness and potential of the method.