Kinematic Analysis of Different Phase-shift-type Migration Methods

In this paper I propose a method for comparing kinematics of different phase-shift migration algorithms based on the double-square-root (DSR) equation. Kinematics of wave propagation is described by the Hamiltonian (characteristic equation) associated with the wave equation. Singularities (waves) are propagating along rays - solutions to a system of Hamilton equations derived from this Hamiltonian. Similarly, kinematics of the DSR migration is described by the DSR Hamiltonian and corresponding DSR rays. The proposed method of studying kinematics of various phase-shift migration algorithms is computationally efficient as it is based on ray tracing. Possible applications include comparison of different generalizations of the phase-shift method as well as checking their usefulness for constructing common-image gathers for migration velocity analysis.