Three-Dimensional Modeling of Geological Bodies Using Radial Basis Function with External Drift Function

Three-dimensional (3D) geological modeling is a vital tool for visualizing subsurface geometries and understanding associated uncertainties, crucial for applications ranging from resource exploration to environmental management. Among the various modeling techniques, implicit methods have gained prominence due to their computational efficiency and ability to integrate diverse geological datasets. However, while methods such as dual kriging have successfully incorporated drift terms to enhance model accuracy, radial basis function (RBF) methods have traditionally not utilized this feature, limiting their adaptability in complex geological settings. This study addresses this gap by proposing an innovative approach that integrates geometrical external drift functions into the RBF framework. This enhancement allows the RBF models to converge to the geological expert’s conceptual geometries, significantly improving their ability to accurately model various geological structures such as planar strata, folded formations, and salt domes. The proposed methodology is demonstrated through two case studies on a synthetic fold model and real salt dome model, where its effectiveness is compared against traditional methods, showing notable improvements in both accuracy and computational efficiency. 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, particularly if the general subsurface geometrical configuration is understood.