WAVE EXTRAPOLATION IN THE SPATIAL WAVELET DOMAIN WITH APPLICATION TO POSTSTACK REVERSE-TIME MIGRATION

A wavelet transformation is performed over each of the spatial coordin ates of the scalar wave equation. This transformed equation is solved directly with a finite-difference scheme for both homogeneous and smoo th inhomogeneous media. Wavefield extrapolation is performed completel y in the spatial wavelet domain without transforming back into the spa ce domain at each time step. The wavelet coefficients are extrapolated , rather than the wavefield itself. Thr numerical solution of the scal ar wave equation in the spatial wavelet domain is closely related to t he finite-difference method because of the compact support of the wave let bases. Poststack reverse-time migration is implemented as an appli cation. The resolution spaces of the wavelet transform provide a natur al framework for multigrid analysis. Migrated images are constructed f rom various resolution spaces.