插值小波自适应求解层状介质波传问题

利用多尺度插值小波理论,提出一种适合于求解一般边界层状介质波传问题的快速自适应配点算法.将问题放在多尺度插值空间中进行,其插值小波系数与物理空间点一一对应,可简单快速地处理非线性、边界等.使非均匀变化的响应得到自适应压缩存储,改善了计算效率.地震勘探中数值实例显示了方法良好的潜力.

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.