Abstract

In this study, the combined application of geodesic kernel and Gaussian process regression was investigated to estimate nonstationary hydraulic conductivity fields in two-dimensional hydrogeological systems. Particularly, a semi-analytical form of the geodesic distance based on the intrinsic geometry of the manifold was derived and used to define positive definite geodesic covariance matrices that are employed for Gaussian process regression. Furthermore, the proposed approach was applied to a series of synthetic hydraulic conductivity estimation problems and the results show that the incorporation of secondary information, such as geophysical or geological interpretations, can considerably improve the estimation accuracy, especially in nonstationary fields. Moreover, groundwater flow and solute transport simulations based on the estimated hydraulic conductivity fields revealed that the accuracy of the simulations was strongly affected by the inclusion of secondary information. These results suggest that incorporating secondary information into manifold geometry can remarkably improve the estimation accuracy and provide new insights on the underlying structure of geological data. This proposed approach has crucial implications for hydrogeological applications, such as groundwater resource management, safety assessments, and risk management strategies related to groundwater contamination.