A method of reconstructing complex stratigraphic surfaces with multitype fault constraints

The construction of complex stratigraphic surfaces is widely employed in many fields, such as petroleum exploration, geological modeling, and geological structure analysis. It also serves as an important foundation for data visualization and visual analysis in these fields. The existing surface construction methods have several deficiencies and face various difficulties, such as the presence of multitype faults and roughness of resulting surfaces. In this paper, a surface modeling method that uses geometric partial differential equations (PDEs) is introduced for the construction of stratigraphic surfaces. It effectively solves the problem of surface roughness caused by the irregularity of stratigraphic data distribution. To cope with the presence of multitype complex faults, a two-way projection algorithm between threedimensional space and a two-dimensional plane is proposed. Using this algorithm, a unified method based on geometric PDEs is developed for dealing with multitype faults. Moreover, the corresponding geometric PDE is derived, and an algorithm based on an evolutionary solution is developed. The algorithm proposed for constructing spatial surfaces with real data verifies its computational efficiency and its ability to handle irregular data distribution. In particular, it can reconstruct faulty surfaces, especially those with overthrust faults.