Phase‐shift migration with a variable‐length spatial transform–an algorithm for moderately varying lateral velocities1

Abstract

AbstractA migration algorithm appropriate for moderately varying lateral velocity changes is developed as an extension of phase‐shift migration by using a variable‐length spatial transform. This process significantly reduces the number of lateral wave‐numbers necessary to downward continue the data, and it replaces the spatial FFT with a simple recursion relationship. For a given frequency and position x, ten lateral wavenumbers are typically sufficient, and the migration algorithm produces accurate images when the velocity structure V (X, z) changes over a few depth intervals of thickness Δz, with lateral velocity gradients up to 1.4 to 1.0.