3D F–K and finite‐difference dip moveout in cross‐spreads

Abstract

ABSTRACTA 3D F–K dip‐moveout (DMO) is developed, which is applicable to data acquired in an elementary single‐fold cross‐spread. The key idea is that a 3D log‐stretch transform and the inherent regularity of the cross‐spread geometry make it possible to transform 3D Fourier DMO. The derived theory generalizes the 2D Fourier shot‐gather DMO in the log‐stretch domain; 2D turns out to be a special case. Similarly to 2D, the cross‐spread DMO becomes convolutional after multidimensional logarithmic stretch. The proposed method works for orthogonal and slanted acquisition geometries; the cross‐spread DMO relationships are found to be independent of the intersection angle of the shot and receiver lines. In contrast to integral (Kirchhoff‐style) methods, the cross‐spread F–K DMO does not degrade from the inevitable irregularity in 3D sampling of offsets in a CMP gather. The newly derived F–K DMO operator can be approximated by finite‐difference (FD) schemes; the low‐order FD cross‐spread DMO equation is shown to be the 3D extension of the Bolondi and Rocca offset continuation. It is shown that F–K and low‐order FD operators are effective in a synthetic case.