Seismic Depth Imaging with the Gabor Transform

Wavefield extrapolation by spatially variable phase shift is currently a migration tool of importance. In this paper, we present a new prestack seismic migration algorithm using the Gabor transform with application to the Marmousi acoustic dataset. The imaging results show a very promising depth imaging algorithm, which is competitive with the best depth imaging algorithms. The Gabor depth imaging algorithm approximates generalized phase shift plus interpolation (GPSPI) wavefield extrapolation using the Gabor, or windowed Fourier, transform to localize the wavefield. The key to an efficient algorithm is to develop an adaptive windowing scheme that only localizes the wavefield as required by the lateral velocity variation. If there is no lateral velocity variation then no localization (windowing) is required. When velocity varies rapidly, then many, relatively narrow, windows are required for accurate wavefield extrapolation. We present the details of an adaptive windowing method that has a controlled phase error. Programs have been coded with the adaptive windowing algorithm, which substantially reduces the computational burden in wavefield extrapolation when compared to the full GPSPI integral. We will illustrate the performance of this algorithm with images from prestack depth migration of the Marmousi dataset.