The shapes of geological boundaries such as contacts and faults play a crucial role in the transportation, deposition and preservation of metals in magmatic and hydrothermal systems. Analyzing the shapes of geological boundaries, in particular those associated with mineralization, is an important step in 3D mineral prospectivity modeling. However, existing methods of shape analysis are limited in the adaptation of various shapes, scales and topologies of geological boundaries. This paper presents a general method of shape analysis based on mathematical morphology (MM), which is a generalization of the original MM method for shape analysis. The generalization extends the applicability of the original MM method from closed surfaces to general surfaces, while inheriting the real 3D and multi-scale analysis capabilities of the original method. This is achieved by regarding MM operations on 3D sphere structural elements as their equivalent operations, and redefining the operations to general surfaces. The generalized MM method enables us to handle complex 3D shapes such as overturned and/or recumbent geological boundaries as well as incomplete shapes due to weathering processes and data unavailability. The proposed method was applied to analyze the shape of an intrusive contact in the Fenghuangshan Cu ore field, Eastern China, whose shape was in the form of a non-closed surface. This analysis revealed a stronger spatial association between the large concave parts of the contact zone and the mineralization. Due to its enhanced adaptability to different shapes, the generalized MM method, compared with the original MM method, allows us to capture shape features that are more plausible for the geological setting.
