In three dimensions, the location of a trace to be filled
in by interpolation will not always lie on a line drawn
between some pair of input traces. Thus while it was
sufficient in 2-D interpolation to find the *apparent*
dip between two traces, in 3-D interpolation we need to find
the *true* dip. A pair of traces is insufficient
for finding the true 3-D dip. At least three traces must be used,
since three points are required to define a plane.

Given this realization, a simple 3-D analog to Claerbout's 2-D mono-planewave scheme can be proposed. To construct a trace at a location, examine the three nearest traces. Use the spatial predictor described in Claerbout's paper to find the dip between one pair of traces, then another pair (with a different source-receiver azimuth). From these two apparent dip measurements, the true dip can be recovered and used for interpolation, following Claerbout.

We develop a slightly more general alternative to this simple approach, one that uses an arbitrary number of neighboring traces and is less susceptible to problems that might be caused by a single bad trace.

11/18/1997