Offset continuation (OC) is a process that transforms common-offset seismic data from one constant offset to another. Introduced initially by Deregowski and Rocca 1981 and Bolondi et al. 1982, the OC concept stimulated the early stages of dip moveout (DMO). However, its direct implementation for interpolating and regularizing seismic data was not as successful as that of DMO by Fourier transform Hale (1984) and other versions of DMO Hale (1991b). One of the reasons was the approximate nature of Bolondi's OC algorithm, limiting the range of its application to small offsets and reflector dips. Biondi and Chemingui 1994a and Bagaini et al. 1994 recently derived an improved integral version of offset continuation, which provides a correct kinematics of offset continuation in the constant velocity media.
In Part One of this paper Fomel (1995), I introduced a revised partial differential equation that describes the offset continuation process in time-offset-midpoint space. Under a constant velocity assumption, the equation was proven to provide correct geometry and meaningful amplitudes of the continued reflection events.
This part of the paper starts with an initial value (Cauchy-type) problem for the OC equation. I solve this problem to obtain explicit integral-type operators of offset continuation in the time-space domain. In the rest of the paper, I consider DMO as a special case of offset continuation for the output offset equal to zero and compare the new OC operators with those of the canonical DMO: Hale's Fourier-domain DMO Hale (1984) and Liner's log-stretch DMO Liner (1990).
Here I do not focus specifically on the amplitude preservation properties of offset continuation, assuming that the asymptotic analysis of the OC amplitudes Fomel (1995) applies both to the OC equation and to its solutions.