We present a new method for prestack depth migration that is based on the double plane-wave decompositions of the original seismic data along both source and offset directions. Initially the data are slanted-stacked along the offset direction for each shot and then organized into common offset ray parameter sections (p0). Each constant po section is migrated separately in a manner similar to a poststack migration procedure using Gaussian beam method based on microlocalization, except for an additional term related to the offset ray parameter using an interval velocity in depth. It extends the Gaussian beam method to migrate the plane wave gathers and combines the numerous advantages of the plane wave migration and Gaussian beam migration.
Migration is a process of mapping reflection energy back to its true subsurface location. Most migration algorithms are derived from imaging principles such as exploding reflectors, down-going continuation and the like (Claerbout, 1976, 1985; Stolt, 1978; Stolt and Benson, 1986; Stoffa et al., 1990). Plane-wave migration methods use data transformed to the tau-p domain (Stoffa et al., 1981; Akbar et al., 1996; Xu and Lambare, 1998; Sun and Schuster, 1999; De Hoop and Brandsberg-Dahl, 2000; Albertin et al., 2001); an appropriate extrapolation operator is then designed to continue the wavefield (characterized by its surface ray parameter) downward in depth. Stoffa et al. (2006) considered depth migration methods based on one or more plane wave decompositions of the original seismic data. Based on an ART approximation, they developed a new depth migration method using both source and receiver plane wave decompositions of the seismic data. Their method can be improved using a multi-valued ray tracing method. However, it still only deals with the caustics problem one by one based on Maslov solutions (Foster et al., 2002). Gaussian beam migration (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. It can deal with multiple caustics easily. Gaussian beam migration also can solve the multi-pathing problem by locally decomposing the wavefields at the source or receiver into beams and then extrapolating the wavefield using these beams with highly accurate ray tracers. Each beam propagates individually and is guided by a ray tube. They can overlap and allow multiple paths for the energy to travel. Therefore, a Gaussian beam migration is a better generalization of a conventional Kirchhoff migration. However, the conventional Gaussian beam migration can be improved by using the plane wave domain to avoid the traveltime injection condition failure in cases of common shot and common offset migrations (Nolan and Symes, 1996). We propose a new plane wave Gaussian beam migration method that utilizes plane wave decomposition on the receiver side and Gaussian beam decomposition on the source side based on microlocalization. This use of the Gaussian beam method in plane wave domain can improve the caustic-free effects and stationary phase approximationsin ART path integral evaluations.
