The study presents a novel approach for fault detection on geological terrains using supervised learning algorithm and careful variable selection. Synthetic faulted terrains are generated using Delaunay triangulation via the Computational Geometry Algorithms Library (CGAL) allowing for adjustments of parameters. We introduce 24 variables, including local geometric features and neighborhood analysis, for classification. Support Vector Machine (SVM) is employed as the classification algorithm, achieving high precision and recall rates for fault-related observations. Application to real borehole data demonstrates the effectiveness of the method in detecting fault orientations, the challenges remain with respect to distinguishing faults with opposite dip directions. The study highlights the need to address 3D fault zone complexities and their identification. Despite limitations, the proposed supervised approach offers significant advancement over clustering-based methods, showing promise in detecting faults of various orientations. Future research directions include exploring more complex geological scenarios and refining fault detection methodologies.