A general theory for wave field extrapolation in bounded and unbounded homogeneous media

Abstract

In this article wave field extrapolation in bounded and unbounded homogeneous media is studied. A generally applicable description for any type of homogeneous medium with arbitrary boundary conditions is developed. The extrapolation theory is based on the Kirchhoff integral in the frequency domain. In several steps this Kirchhoff integral is transformed into a straightforward extrapolation expression. First, Green’s function is expanded in an infinite series of eigenfunctions belonging to the lateral directions. Second, the wave field extrapolation operation is diagonalized by choosing a base of eigenfunctions for the Hilbert function space. Further facilitation of the extrapolation problem for both bounded and unbounded homogeneous media is achieved by employing one‐way wave equations. These one‐way wave equations decompose a wave field into a downstream and an upstream traveling wave field. The final result is a comprehensive description of both forward and inverse wave field extrapolation, which can easily be applied to quite complicated extrapolation problems in any type of homogeneous medium.