Probabilistic constraints on structural lineament best fit plane precision obtained through numerical analysis

Understanding the orientation distribution of structural discontinuities using the limited information afforded by their trace in outcrop has considerable application, with such analysis often providing the basis for geological modelling. However, eigen analysis of 3D structural lineaments mapped at decimetre to regional scales indicates that discontinuity best fit plane estimates from such datasets tend to be unreliable. Here, the relationship between digitised lineament vertex geometry (coplanarity/collinearity) and the reliability of their estimated best fitting plane is investigated using Monte Carlo experiments. Lineaments are modelled as the intersection curve between two orthonormally oriented fractional Brownian surfaces representing the outcrop and discontinuity plane. Commensurate to increasing lineament vertex collinearity (K), systematic decay in estimated pole vector precision is observed from these experiments. Pole vector distributions are circumferentially constrained around the axis of rotation set by the end nodes of the synthetic lineaments, reducing the rotational degrees of freedom of the vertex set from three to one. Vectors on the unit circle formed perpendicular to this arbitrary axis of rotation conform to von Mises (circular normal) distributions tending towards uniform at extreme values of K. This latter observation suggests that whilst intrinsically unreliable, confidence limits can be placed upon orientation estimates from 3D structural lineaments digitised from remotely sensed data. A probabilistic framework is introduced which draws upon the statistical constraints obtained from our experiments to provide robust best fit plane estimates from digitised 3D structural lineaments.