An omnidirectional seismic image extension

Abstract

This paper introduces an operator, which extends the Born operator for the linearized variable density acoustic wave equation. Inspired by angle dependent scattering, I will define it as acting on distributions depending on space and angle coordinates. I will show that it can be written as a weighted integral of space-shift extended operators associated to arbitrary directions after a suitable coordinate transform. I will also formulate conditions under which its normal operator is a pseudo-differential operator. These will be seen to be less restrictive than the ones imposed on horizontal space-shift extended operators in the sense that they allow diving wave paths.