I propose a filter technique that yields a dip estimation for data volumes that consists mostly of a set of parallel planes (plane layer volume). The filter is based on the cross product of vector algebra and improves and clarifies Claerbout's earlier Lomoplan formulation Claerbout (1994). I developed the dip estimation technique for the computation of coherency attributes of seismic images Schwab et al. (1996). The method may also be useful in the estimation of seismic data quality, the optimization of migration velocities, or in general inversion theory.
In this article, I first argue that a seismic image almost everywhere resembles a simple plane layer volume. Next, I suggest a simple cross product expression to detect and estimate the dip of a plane layer volume. I attempt an interpretation of the filter output. Finally, I clarify and enhance Claerbout's original Lomoplan idea and discuss the advantages to extend the technique to PE filters.
In summary, I have not tested the reliability of the dip estimation. The scheme's extension to PEF has failed to yield convincing results in the calculation of coherency attributes (partially since PEF are more powerful in removing events than the simple Finite Difference filter of the cross product formulation). Alternative approaches, such as direct estimate of coherency or estimates of a normed gradient, exist. I hope to apply the method to dip estimation, e.g., for migration velocity estimation. Coherency attributes could possibly use the dip estimation. But the simple filter approach to removing the plane layer volume contribution seems to fail.