Wavefield extrapolation with phase shift is currently a migration tool of importance. In this paper, we present a new prestack seismic depth migration algorithm using the Gabor transform with application to the Marmousi acoustic velocity model. The imaging results show a very promising depth imaging algorithm, which should compete with the best depth imaging algorithms. The Gabor depth imaging algorithm approximates generalized phase shift plus interpolation (GPSPI) wavefield extrapolation, in which exact lateral velocities are used in a wavefield extrapolator. Previously, Gaussian windows have been used in the Gabor wavefield extrapolation algorithm. Each of these Gaussian windows is a 'full-length' window, with the same dimension as lateral velocity structures. Programs have been coded with the adaptive windowing algorithm, which will substantially reduce redundancy of calculations in wavefield extrapolation related to repeated Fourier transforms. High computation efficiency is expected using these more compactly supported windows.
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