Gaussian beam migration of common-shot records

Gaussian beam migration (GBM) (Hill, 1990, 2001) is an elegant, accurate, and efficient depth migration method. It has the ability to image complicated geologic structures with fidelity exceeding that of single-arrival Kirchhoff migration and approaching that of wave-equation migration. In fact, its accuracy can exceed that of most wave-equation migrations in imaging very steep dips, especially in three dimensions and especially in the presence of anisotropy. Poststack GBM is efficient, but a naïve implementation of prestack GBM can be relatively inefficient. Hill's (2001) implementation of prestack GBM takes advantage of symmetries available in common-offset, common-azimuth acquisition geometries to provide an extremely accurate method that is far more efficient than the naïve implementation. Unfortunately, different acquisition geometries, such as orthogonal land and marine bottom-cable geometries do not easily accommodate the requirements of common-azimuth migration. For these geometries, it might be more natural to perform migration on individual common-shot or common-receiver records. In this abstract, I adapt Hill's (2001) method to common-shot migration. The common-shot migration described here loses some accuracy compared with Hill's method, in the sense that it doesn't handle multiple arrivals as well. It is possible to overcome this problem (Gray, 2004), but the method described here will be sufficient for the purposes of this abstract, which is to point out some advantages of migrating common-shot records. In practice, this slight loss of accuracy needs to be weighed against (1) the difficulties (in some geometries) of obtaining regularly sampled regularly sampled common-offset, common-azimuth records for migration, and (2) the difficulties in regularizing common-offset, common-azimuth data for the premigration slant stack when surface elevations and velocities vary rapidly.