Introduction

Elsewhere in this report (Claerbout, 1992) a 2-D interpolation scheme based on a mono-planewave assumption is described. To fill in a gap between two traces, a spatial prediction method is used to determine the dip, and the missing traces are constructed by combining the two known traces from either end of the gap, with time shifts and weights appropriate to the estimated dip and the various distances.

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.