Conclusions

I have introduced a partial differential equation (1) and proved that the process described by it provides for a kinematically and dynamically equivalent offset continuation transform. Kinematic equivalence means that in constant velocity media the reflection traveltimes are transformed to their true locations on different offsets. Dynamic equivalence means that the geometric spreading term in the amplitudes of reflected waves transforms in accordance with the geometric seismics laws, while the angle-dependent reflection coefficient stays the same in the OC process. The amplitude properties of amplitude-preserving OC may find an important application in the seismic data processing connected with AVO interpretation .

The offset continuation equation can be applied directly to design OC operators of the finite-difference type. Other types of operators are related to different forms of the solutions of the OC equation. Part 2 of this paper will describe integral-type offset continuation operators based on the initial value problem associated with equation (1). Other important topics in the theory of offset continuation include

• Connection between OC and amplitude-preserving frequency-domain DMO
• Connection between OC and true-amplitude prestack migration
• Generalizing the OC concept to 3-D azimuth moveout (AMO)