Geodesic Distance Integration in Analytical Frameworks for Aquifer Hydraulic Modeling

Traditional analytical models in groundwater studies often simplify the complexities arising from spatial variations in aquifer geometry and anisotropy, limiting their ability to capture the full theoretical nuances of groundwater flow. In this study, we present a novel methodology that integrates geodesic distances within the intrinsic geometry of confined, constant-thickness aquifers, while also accounting for directional anisotropy in hydraulic properties. This approach provides a rigorous mathematical framework for accurately capturing the true distances along the aquifer geometry between pumping and observation wells, in contrast to traditional Euclidean distances. Our methodology is compatible with various analytical solutions, including the Theis (1935, https://doi.org/10.1111/jawr.1965.1.3.9) and Papadopulos and Cooper (1967, https://doi.org/10.1029/wr003i001p00241) solutions, extending their theoretical applicability to more complex aquifer geometries and anisotropic conditions. Numerical simulations of synthetic examples illustrate the theoretical consistency of the proposed approach, aligning drawdown patterns within this advanced framework. While primarily focused on enhancing existing analytical models, this methodology sets the stage for future theoretical advances in groundwater modeling, offering a conceptual expansion of analytical solutions to better address geometric and anisotropic complexities.