A Hamiltonian framework for wavefield depth continuation in seismic imaging

Symplectic algorithms have seen a successful application in astronomy, fluid dynamics, quantum mechanics and many other fields. However, these symplectic algorithms usually refer to evolution of the solution along the time direction, and in seismic imaging wavefield is often continued along the depth direction. A Hamiltonian framework for wavefield depth continuation in seismic imaging is presented in this paper. This framework is established for both two-way and one-way wave equations and provides a new methodology for constructing migration algorithms. The Hamiltonian viewpoint lends itself to applications of promising structure-preserving algorithms to seismic imaging.