


 Theory of differential offset continuation  

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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,
in the OC process, the geometric spreading term in the amplitudes of
reflected waves transforms in accordance with the laws of geometric
seismics, while the angledependent reflection coefficient stays the
same.
The offset continuation equation can be applied directly to design OC
operators of the finitedifference type. To construct integral OC
operators, an initial value problem is solved for the
offset continuation equation (1). For the special
cases of continuation to zero offset (DMO) and continuation from zero
offset (inverse DMO), the OC operators are related to the known forms
of DMO operators: Hale's Fourier DMO, Born DMO, and Liner's ``exact
log DMO.'' The discovery of these relations sheds additional light on
the problem of amplitude preservation in DMO.



 Theory of differential offset continuation  

Next: Acknowledgments
Up: Theory of differential offset
Previous: Discussion
20140326