Prestack depth migration by symmetric nonstationary phase shift

Robert James Ferguson, Gary F. Margrave

A new depth imaging method is presented that is based on nonstationary filter theory. It is suitable for imaging media whose velocity structure varies in all spatial coordinates. The well-known phase-shift-plus-interpolation method and the recently introduced nonstationary phase-shift method, both implemented as nonstationary filters, are combined into a single symmetric operator. The symmetric operator is used to compute incident and reflected wavefields at different depths using, respectively, a source waveform and geophone recordings. The ratio of the resulting incident and reflected wavefields is used to estimate seismic reflectivity. Reflectivity is then immediately useful in providing a kinematic image of the subsurface. A practical implementation of the symmetric operator is possible when the required velocity model is made piecewise constant laterally. Depth imaging then proceeds by a sequence of phase shifts, spatial windows and integrations over temporal frequency. Migration of the Marmousi synthetic data set by this method provides a very good image.