Interpolating wavelet for adaptive simulation of wave propagation in layered media

An interpolating wavelet collocation method (IWCM) for adaptive solution of wave propagation in layered media with non-periodic boundary condition is presented. The method is based on the use of multi-resolution analysis and Deslaurier-Dubuc interpolating theory. Thus, the problem is solved in the multi-resolution interpolating subspace rather than traditional Euclidian space. Due to the one-to-one correspondence between the wavelet coefficients and point values in physical space, the treatment of boundary conditions and the nonlinear operations such as differentiation and multiplication is simple and in sparse point representation. The adaptively compressive storage of non-uniform response is performed automatically by changing the interpolating wavelet coefficients. Thus, the computational effectiveness and the memory requirement are improved. Numerical results in geophysics exploration demonstrate the potential of the method.