Amplitude preserving offset continuation
in theory
Part 1: The offset continuation equation

Sergey Fomel

sergey@sep.stanford.edu

ABSTRACT

This paper concerns amplitude-preserving kinematically equivalent offset continuation (OC) operators. I introduce a revised partial differential OC equation as a tool to build OC operators that preserve offset-dependent reflectivity in prestack processing. The method of characteristics is applied to reveal the geometric laws of the OC process. With the help of geometric (kinematic) constructions, the equation is proved to be kinematically valid for all offsets and reflector dips in constant velocity media. In the OC process, the angle-dependent reflection coefficient is preserved, and the geometric spreading factor is transformed in accordance with the laws of geometric seismics independently of the reflector curvature.