Three‐dimensional time‐slice migration

Abstract

Three‐dimensional migration of zero‐offset data using a velocity varying with depth can be performed in one pass using Fourier transforms of time slices. The migration process is carried out entirely in the two‐dimensional spatial Fourier domain. The algorithm consecutively filters and adds time slices of the 3-D data volume in a way that is equivalent to summing energy over the diffraction surface of a point scatterer. The partial energy being distributed along a circle in a time slice is properly added in each summation step. Time‐slice migration is based on an integral solution of the acoustic wave equation known as the “Kirchhoff integral.” The wavelet shape in a 3-D data volume is preserved throughout the entire migration process. The frequency characteristics are maintained by summing weighted differences between time slices instead of summing the time slices themselves. Automatic weighting is achieved by time slicing at equal increments of diffraction radius. Tapering the summation operator reduces effects introduced by limiting the summation window. Time‐slice migration preserves the frequency content of a 3-D data volume during summation in a natural way. Since the migration scheme assumes a constant velocity within the entire time slice, it is a local process in time which migrates a 3-D data volume with a constant velocity or with a velocity which varies with depth. The migration algorithm is applied to numerical and physical model data. This method is especially suitable for a migration of a targeted subset of the 3-D data volume.