csugeo3d/AdaHRBF: AdaHRBF

Three-dimensional (3D) stratigraphic modelling is capable of modeling the shape, topology, and other properties of strata in a digitalized manner. The implicit modeling approach is becoming the mainstream approach for 3D stratigraphic modelling, which incorporates both the off-contact attitudes and the on-contact occurrence information of stratigraphic interface to estimate the stratigraphic potential field (SPF) to represent the 3D architectures of strata. However, the magnitudes of SPF gradient controlling variation trend of SPF values cannot be directly derived from the known stratigraphic attribute or attitude data. In this paper, we propose an Hermite-Birkhoff radial basis function (HRBF) formulation, AdaHRBF, with an adaptive gradient magnitude for continuous 3D SPF modeling of multiple stratigraphic interfaces. In the linear system of HRBF interpolant constrained by the scattered on-contact attribute points and off-contact attitude points of a set of strata in 3D space, we add a novel optimizing term to iteratively obtain the true gradient magnitude. The case study shows that the HRBF interpolants can consistently establish accurate multiple stratigraphic interfaces and fully express the internal stratigraphic attribute and attitude. To ensure harmony of the variation of stratigraphic thickness, we adopt the relative burial depth of stratigraphic interface to the Quaternary as the SPF attribute value and propose a new stratigraphical thickness index (STI) to represent the variation trend of stratigraphic thickness in SPF. In addition, the proposed stratigraphic potential field modeling by HRBF interpolants can provide a suitable basic model for subsequent geosciences numerical simulation