Orientation domains: A mobile grid clustering algorithm with spherical corrections

Abstract

An algorithm has been designed and tested which was devised as a tool assisting the analysis of geological structures solely from orientation data. More specifically, the algorithm was intended for the analysis of geological structures that can be approached as planar and piecewise features, like many folded strata. Input orientation data is expressed as pairs of angles (azimuth and dip). The algorithm starts by considering the data in Cartesian coordinates. This is followed by a search for an initial clustering solution, which is achieved by comparing the results output from the systematic shift of a regular rigid grid over the data. This initial solution is optimal (achieves minimum square error) once the grid size and the shift increment are fixed. Finally, the algorithm corrects for the variable spread that is generally expected from the data type using a reshaped non-rigid grid. The algorithm is size-oriented, which implies the application of conditions over cluster size through all the process in contrast to density-oriented algorithms, also widely used when dealing with spatial data. Results are derived in few seconds and, when tested over synthetic examples, they were found to be consistent and reliable. This makes the algorithm a valuable alternative to the time-consuming traditional approaches available to geologists.