Geometric Analysis of Seismic Imaging Operators and Continuation Operators

In this paper we provide an overview of some concepts and results by S.V.Goldin in the field of geometric theory of seismic imaging. Then we present some recent results on velocity continuation of seismic images developing his ideas. We will provide a few examples of Hamiltonians describing propagation of singularities during a velocity continuation of seismic (extended) images and propagation of isochrones in the framework of constant-offset migration.