Introduction

Working on migration to zero-offset (MZO) in variable velocity media, I encountered a problem with the formulation of my MZO operator: while the operator is accurate in depth variable velocity, it is defined in the offset-wavenumber domain, and therefore has to be applied to all the offsets at the same time. As people apply DMO to constant-offset sections, I had to look at how to separate the operator so it could be applied to individual offsets. My MZO formulation (Popovici, 1993) is very similar to prestack migration in Fourier domain which also applies a phase-shift operator in offset-wavenumber domain. Therefore I decided to apply the offset separation technique to prestack Fourier domain migration as it is a well known operator and researchers are more familiar with its formulation.

I present two methods for applying phase-shift migration to separate constant-offset sections. One method is faster when applied to all the offsets at the same time. However, this method migrates all the constant-offsets at the same time, so it is inefficient when a single constant-offset migrated image is desired. The second method migrates one constant-offset at a time, but requires more time to migrate all the offsets.

I also discuss the source of artifacts present in offset domain and explain how they can be avoided by a careful implementation of the algorithm.