A new formalism and an old heuristic for seismic migration

Abstract

A new approach to seismic migration formalizes the early geometric methods such as the diffraction and wavefront stacks by relating them to linearized velocity inversion and the generalized Radon transform (GRT). This approach recasts migration as a form of tomography in which the problem is to reconstruct a function (velocity perturbation) from its integrals over a family of surfaces (isochrons). The theory rests on a solution of the wave equation by geometrical optics and an inversion formula for the GRT. This method can handle both lateral and vertical variations in velocity as well as arbitrary configurations of sources and receivers. Moreover, when specialized to constant background velocity and zero-offset seismic experiments, it yields an inversion algorithm that resembles standard Kirchhoff migration. Synthetic examples of a combined surface seismic and VSP experiment illustrate the resolution of the method for different combinations of sources and receivers.