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 back-projected 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 Kirchhoff tricks 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 hyperbolalike 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 hyperbola-like curve. For this reason I name this reformulation generalized diffraction stack migration (GDM). This formulation breathes the following new life into RTM. 1. A reverse-time common-offset migration operator is obtained without any approximation. This operator can be applied to common-offset gathers for any media, including those that induce turning waves. 2. Target-oriented RTM has been developed with the suggestion of Yi Luo. 3. A more efficient RTM method is developed that only uses first-arrival information to backpropagate arrivals. I called this wavefront wave-equation migration in a previous report. 4. GDM can be computed by any modeling method, including the reflectivity method. 5. Anti-aliasing, obliquity factors, and depth-dependent truncation of data aperture tricks can be applied to the GDM operator. In fact, a generalization of Gaussian-Beam and wavepath migration can be formulated. 6. The RTM reformulation leads to a theory for construction of the exact reverse-time migration operator from VSP data alone. No modeling computations or velocity model are needed, except simple convolutions of the VSP traces. This could be important in CDP imaging beneath salt domes where VSP data is available. In addition, migration operators for multiples can be derived from the VSP data as well.