Assessing error in the 3D discontinuity-orientation distribution estimated by the Fouché method

Realistic discontinuity network modelling of rocks requires the accurate input of the three-dimensional discontinuity orientation distribution (3DDOD), but in practice, access to such three-dimensional information is limited. Fouché recently developed a method for estimating the 3DDOD from one-dimensional scanline-mapping observations. However, little is known about the error in such 3DDOD estimates. This study focuses on (1) the error and its possible contributors, (2) error prediction, and (3) error mitigation. An error investigation based on synthetic discontinuity geometry data reveals that the 3DDOD estimates are not always accurate. The error is significantly impacted by three factors: the Fisher constant (к), the angle between the major discontinuity plane and the mapping scanline (θ), and the discontinuity sample size (n), with larger к, θ, or n values contributing to lower errors. This к-, θ-, and n-dependent error appears to be inherently related to the sample density, which is defined as the pole number per unit cell (1° × 1°) in the Fouché method. Additionally, a predictor of the error based on an error-and-factors empirical relationship is developed to provide precise error prediction and optimize the scanline sampling for error mitigation. The weakness of the developed predictor is also disclosed.