In seismic-wave migration imaging, the conjugate-transpose matrix stands for the back-propagation of the observed wavefield. Therefore, the wavefield propagators are the basis for seismic-wave imaging.

For constructing a wavefield propagator, we introduce the following methods: (1) a hybrid wavefield propagator, that is, the split-step-Fourier propagator plus optimal interpolation with a self-adaptive reference velocity choice; and (2) a local and directional wavefield propagator, which can be designed with the local Fourier transform and local plane wave/Gaussian beam, for target-oriented imaging (, , ).

5/3/2005