AdaHRBF v1.0: gradient-adaptive Hermite–Birkhoff radial basis function interpolants for three-dimensional stratigraphic implicit modeling

Abstract

Abstract. Three-dimensional (3D) stratigraphic modeling 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 modeling, which incorporates both the off-contact strike and dip directions 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 the SPF gradient controlling the variation trend of SPF values cannot be directly derived from the known stratigraphic attribute or strike and dip data. In this paper, we propose a 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 interpolants constrained by the scattered on-contact attribute points and off-contact strike and dip points of a set of strata in 3D space, we add a novel optimizing term to iteratively obtain the optimized gradient magnitude. The case study shows that the HRBF interpolants can consistently and accurately establish multiple stratigraphic interfaces and fully express the internal stratigraphic attribute and orientation. To ensure harmony of the variation in stratigraphic thickness, we adopt the relative burial depth of the stratigraphic interface to the Quaternary as the SPF attribute value. In addition, the proposed stratigraphic-potential-field modeling by HRBF interpolants can provide a suitable basic model for subsequent geosciences' numerical simulation.