Reverse-time migration = generalized diffraction stack migration

The standard reverse-time migration (RTM) algorithm is usually described as zero-lag correlation of the backprojected data with the source wavefield. The data are backprojected by a finite-difference algorithm, where each trace acts as a source-time history of a point source at the geophone location. This is a simple and easily understood migration method, but appears inflexible to improvement by the usual Kirchhofftricks such as obliquity factors, first-arrival restrictions, angle-dependent truncation of data aperture or intrinsic anti-aliasing filters. In this paper, I reformulate the equations of reverse-time migration so that they can be interpreted as summing data along a series of hyperbola-like curves, each one representing a different type of event such as a reflection or multiple. This is a generalization of the familiar diffraction-stack algorithm where the migration image at a point is a sum of data along an appropriate hyperbolalike curve. For this reason I name this reformulation generalized diffraction stack migration (GDM). This formulation breathes new life into RTM, including a more efficient form of RTM denoted as wave-equation wavefront migration, a means for computing the exact RTM operator from RVSP data, a common-offset migration scheme for RTM, and the ability to apply Kirchhofffiltering tricks like obliquity factors and anti-aliasing filters to RTM operators. The caveat is that the full-blown GDM can be computationally more expensive than standard RTM, but reduced versions can make it more efficient.