Discrimination of Geological Orientation Data with Measurement Errors

Fracture orientation data in structural geology are commonly affected by non-negligible angular uncertainty, which can significantly impact the reliability of classification and interpretation of deformation patterns. In this work, we address the problem of discriminating between two groups of directional observations. To account for measurement uncertainty inherent in field data, we adopt a deconvolution-based circular kernel discriminant rule specifically designed for noisy angular observations. This approach explicitly incorporates the measurement-error mechanism into the estimation process, allowing for more robust classification in the presence of observational noise. The methodology is applied to measurements arising in structural geology, where the discrimination of fracture orientations is relevant to the interpretation of deformation patterns and to applications in rock engineering. Specifically, we consider two datasets from Ordovician turbidites, involving different types of orientation data. The first dataset consists of 𝐿10 axes, representing linear features described by Plunge–Azimuth coordinates, while the second dataset concerns axial-plane cleavage surfaces, expressed in terms of Dip and Dip direction. We assess the performance of the estimator under varying levels of angular uncertainty and alternative error distributions, with a focus on its ability to correctly separate the two geological groups. Results show that explicitly modeling measurement error leads to improved discrimination accuracy and more reliable identification of structural patterns compared to standard methods that neglect noise.