Flexible Geological Modeling with Radial Basis Functions Integrating External Drift

Abstract Three-dimensional geological modeling is a vital tool for visualizing subsurface geometries and understanding associated uncertainties. As such, it is an elementary component of applications ranging from resource exploration to environmental management. Among the various modeling techniques, implicit methods have gained prominence because of their efficiency and ability to integrate diverse geological data. Covariance-based methods such as kriging and kernel-based methods such as radial basis functions (RBFs) are widely used to obtain the interpolation of implicit fields. Whereas kriging facilitates the incorporation of auxiliary covariates into spatial prediction by modeling the trend component of a stochastic random field with a drift function, traditional RBF interpolation treats spatial variation as a purely deterministic function and lacks a principled approach for embedding prior geological knowledge. This study proposes a hybrid extension of RBF interpolation with external drift, enabling the flexible integration of structured geological priors within a deterministic, yet spatially informed, interpolation framework. This enhancement allows RBF models to be purposefully biased toward desired geometric configurations such as planar strata, folded formations, or dome structures. The proposed methodology is demonstrated through two case studies on a synthetic fold model and a real salt dome model, where notable improvements in both accuracy and computational efficiency are shown in comparison to traditional methods. The findings suggest that incorporating external drift into RBF not only broadens the applicability of this method, but also provides a more robust tool for subsurface modeling, balancing prior information and available data, particularly in scenarios where the general shape of the geometric setting is known.