Seismic migration and mathematical mapping

Abstract

This paper is concerned with fundamental properties of seismic imaging (forward modelling) and migration (inverse modelling). The precise mathematical nature of the transformations connecting model space and data space are analyzed and found to belong to a family of mappings called contact or symplectic transformations. The transformations are found explicitly for the case of constant velocity media, so that their structure and properties can be analytically developed. Both geometrical and dynamical aspects of the transformations are discussed. The analysis provides a powerful insight into the nature of seismic imaging and migration.