Sergey Fomel![[*]](icons/footnote.png)
and Norman Bleistein
Offset continuation (OC) is the operator that transforms common-offset
seismic reflection data from one offset to another. Earlier
papers by the first author presented a partial differential
equation in midpoint and offset to achieve this transformation.
The equation was derived from the kinematics of the continuation
process with no reference to amplitudes. We present here a proof
that the solution of the OC partial differential equation does
propagate amplitude properly at all offsets, at least to the same
order of accuracy as the Kirchhoff approximation. That is, the
OC equation provides a solution with the correct traveltime and
correct leading-order amplitude. ``Correct amplitude'' in this
case means that the transformed amplitude exhibits the right
geometrical spreading and reflection-surface-curvature effects
for the new offset. The reflection coefficient of the original
offset is preserved in this transformation. This result is more
general than the earlier results in that it does not rely on the
two-and-one-half dimensional assumption.
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