A new depth migration method suitable for heterogeneous media is presented. The well-known phase shift plus interpolation (PSPI) method and the recently introduced nonstationary phase-shift (NSPS) method are combined into a single symmetric operator with improved accuracy and stability and with similar computational effort. For prestack depth migration, the symmetric operator is used in a recursive wavefield extrapolation to compute incident and reflected wavefields at any desired depth, and the ratio of the incident and reflected wavefields at a particular depth is used to estimate seismic reflectivity. When the velocity model is made piecewise constant laterally, the symmetric extrapolation operator can be computed efficiently using ordinary phase-shift extrapolation for a series of reference velocities and appropriate spatial windowing. Migration of the Marmousi synthetic data set by symmetric nonstationary phase shift (SNPS) provides an image that compares favorably with an image of the zero-offset reflectivity derived from the Marmousi velocity model.

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