True Amplitude Migration

A primary offset reflection of a point source from a smooth reflector within a laterally inhomogeneous velocity earth model is (within the framework of ray theory) defined by parameters pertaining to the reflected ray. The geometrical spreading factor - usually computed along the ray by dynamic ray tracing in a forward modeling approach - can be recovered from traveltime measurements at the surface. As a consequence, offset reflections can be time- and depthmigrated such that the geometrical spreading factor along the offset ray is removed. This leads to a. so-called "true amplitude migration. In this work, true-amplitude timemigrated reflections are obtained by nothing more than a simple Kirchhoff-type weighted diffraction stack, followed, essentially, by a time derivative of the diffraction-stack traces. For small transmission losses of primary offset reflections through intermediate layer boundaries, the true-amplitude time· migrated reflection provides a direct measure of the angle-dependent reflection coefficient at the reflecting lower end of the primary reflected ray. The time-migrated field-can easily be transformed into a depth migrated field with the help of image rays. The theory-described here is similar to the inversion approach derived by Bleistein (1987) based upon fundamental ideas expressed by Beylkin (1985). The similarities and differences will be elaborated.