Born theory of wave‐equation dip moveout

Abstract

Wave‐equation dip moveout (DMO) addresses the DMO amplitude problem of finding an algorithm which faithfully preserves angular reflectivity while processing data to zero offset. Only three fundamentally different theoretical approaches to the DMO amplitude problem have been proposed: (1) mathematical decomposition of a prestack migration operator; (2) intuitively accounting for specific amplitude factors; and (3) cascading operators for prestack migration (or inversion) and zero‐offset forward modeling. Pursuing the cascaded operator method, wave‐equation DMO for shot profiles has been developed. In this approach, a prestack common‐shot inversion operator is combined with a zero‐offset modeling operator. Both integral operators are theoretically based on the Born asymptotic solution to the point‐source, scalar wave equation. This total process, termed Born DMO, simultaneously accomplishes geometric spreading corrections, NMO, and DMO in an amplitude‐preserving manner. The theory is for constant velocity and density, but variable velocity can be approximately incorporated. Common‐shot Born DMO can be analytically verified by using Kirchhoff scattering data for a horizontal plane. In this analytic test, Born DMO yields the correct zero‐offset reflector with amplitude proportional to the angular reflection coefficient. Numerical tests of common‐shot Born DMO on synthetic data suggest that angular reflectivity is successfully preserved. In those situations where amplitude preservation is important, Born DMO is an alternative to conventional NMO + DMO processing.