Dip misfit by crossproduct residual

The residual of the least-squares estimation (12)

indicates how well the seismic volume is approximated by a plane wave. The computation does not explicitly involve the plane-wave waveform f(s), but is the cross-product of the the local gradient and the patch's best-fitting plane-wave gradient ${\bf p}$.For a three-dimensional input volume, the residual of the cross-product operator expression yields a three-dimensional vector at each output location of the three-dimensional image volume.