THE DMO OPERATOR IN THREE DIMENSIONS

As described by Hale 1991, the zero offset rays bouncing off an ellipsoidal reflector of foci S (source) and G (geophone) emerge on the segment [SG]. Therefore, the DMO operator is really a 2-D operator working along the source-geophone line, even in a 3-D space. Consequently, applying the operator in three dimensions is not much different than in two dimensions except that the trace smearing is performed for an irregular spatial sampling according to the azimuth. The technique used in this 3-D DMO code consists of computing the bins affected by the segment [SG]. More precisely, whenever the center of a bin is closer to the [SG] segment than half the bin size, the bin receives an output trace. This operation is repeated for all input traces, gradually filling the output space. This technique is equivalent to the nearest neighbor interpolation in space and linear interpolation in time described by Nichols 1993.

This algorithm requires some evenly distributed data so that the fold over any bin is nearly constant. Dividing the trace amplitude by the fold of the corresponding bin seems an attractive solution, but it may spoil the AVO properties of the data.