Cross product operator detects plane reflectors

Matthias Schwab

matt@sep.stanford.edu

ABSTRACT

I propose an estimation of the dip of a plane layer volume by minimizing the output of a cross product differential expression. This rather peculiar expression allows reliable estimates in small expectation volumes and it is easily extended to Prediction Error (PE) filters. I believe the method yields reasonable dip estimates even for cases that only approximate a plane layer volume (e.g., after the addition of noise). However, the approach does not yield a straightforward technique for subtracting the dominant plane-layered contribution from the original image. The cross product expression yields a vectorial, not a scalar output. The back-projection of the vectorial output by the adjoint operation results in a scalar function which does not have a simple, meaningful interpretation. The usefulness of the cross product expression is uncertain.