Optimal Scaling of Seismic Migration

William Symes

The seismic industry estimates the structure of the subsurface from seismic reflection data by a process known as migration. This linear process amounts to application of the adjoint of a linearized prediction or modeling operator, linking perturbations of Earth mechanical parameters about a reference model to perturbations about the corresponding predicted data. This linearized modeling operator is almost unitary, in the sense that the its composition with its adjoint is "close" to the identity. The appropriate meaning of "close" is now fairly well understood, following work by Beylkin, Rakesh, Burridge, Bleistein, Nolan, de Hoop, ten Kroode, Stolk and others over the last twenty years: this composition is a pseudodifferential operator, under many circumstances. I will review this theory, and show how it leads to a simple and economical algorithm that turns migration into approximate inversion of the linear modeling operator.