Numerical limitations of the attainment of the orientation of geological planes

Abstract

The paper discusses limitations of analytical attainment of the attitude of a geological plane by using three non-collinear points. We present problems that arise during computing the orientation of a plane generated by almost collinear points. We referred these errors to floating-point arithmetic inaccuracies. To demonstrate the problem, we examined a surface of constant orientation. We used Delaunay triangulation to calculate its local orientation parameters. We introduced a new measure of collinearity applicable for collecting attitude of planar triangles. Using this measure we showed that certain planes generated by the triangulation cannot be treated as a reliable source of measurement. To examine the relationship between collinearity and orientation, we used a combinatorial algorithm to obtain all possible planes from the given set of points. A statistical criterion of rejecting almost collinear planes was suggested.