Comparing the Orientation of Geological Planes: Motivation for Introducing New Perspectives

Abstract

This article discusses the problem of comparing the orientation of geological planes. We suggest two alternative approaches based on an analytical model using the coordinates of three non-collinear points to document a stratigraphic horizon. The methodological portion of this paper addresses selected topological conditions that should be satisfied such that the introduced tools are compatible with certain basic expectations and intuitions. The authors note that use of the suggested models must be preceded by adequate mathematical proofs. Because this research paper uses preliminary results, we briefly describe different methods of proving the desirable properties of the suggested functions and also present a counterexample associated with a function that is less computationally expensive. Selected basic calculations connected with measuring the angular distance between two investigated planes are also performed, and basic applications of the introduced tools are also described. The applications include assessment of the degree of nonconformities between stratigraphic horizons and the consequent detection of selected palaeo-environmental events of an erosive nature. We also discuss certain hydrogeological applications focused on detection of specific perturbations in unconfined aquifers. Because we offer two alternative approaches, we also present a comparison of the efficiency of the two models in different geological situations.