Abstract: A frame expansion method of operator is used to the phase shift operator of split-step Fourier propagator.A local split-step Fourier propagator for wavefield propagation is presented and used in a wave equation prestack depth migration.The local split-step Fourier propagator consists of a phase shift operator in phase-space-frequency domain and a windowed time shift operator in space-frequency domain.Different from the global phase shift operator in wavenumber-frequency domain,the phase shift operator in phase-space-frequency domain shows good space localization.A numerical test of wave equation prestack depth migration on the international standard SEG-EAGE 2D salt dome model shows that the local split-step Fourier propagator is stable and is applicable to the media with velocity strong lateral variation.

Key words: wave equation, local propagator, windowed Fourier frame, expansion, prestack depth migration