An Application of waveletª²Based Method for Wave Propagation
Ma Jianwei, Yang Huizhu
(Department of Engineering Mechanics, Tsinghua University, Beijing 100084)

Abstract: Two waveletª²based methods, named multi-resolution symplectic scheme and interpolating wavelet collocation scheme for fast adaptive solution of wave propagation with general boundary condition are presented by introducing Hamilton system and interpolating subdivision scheme. Computational effectiveness and memory requirement are improved due to the vanishing moments, localization and multi-resolution analysis of the wavelet. Then, a new method of multi-resolution inversion for wave equation is proposed using interpolating wavelet. Finally, the advantage and disadvantage of these methods are discussed and several prospects are put forward. Numerical results in geophysics exploration show the potential of the methods.
Keywords: Symplectic, Interpolating wavelet, Wave Propagation, Multi-resolution inversion.