Data and codes for " A Unified Hybrid Deterministic-Stochastic Inversion Methodology" submitted to Jounal of Hydrology.

Accurate characterization of spatial heterogeneity in hydraulic properties is crucial for reliable groundwater modeling. Conventional studies either employ deterministic zonation inversion, which is computationally efficient but oversimplifies subsurface variability, or adopt fully stochastic or stochastic zonation inversions, which capture heterogeneity in detail but can be computationally intensive and even prohibitive for large-scale inverse problems. To balance inversion accuracy and computational efficiency, a mixed homogeneity-heterogeneity parameterization configuration is introduced to parameterize the subsurface field. This configuration delineates the model domain into multiple homogeneous and heterogeneous zones, encompassing diverse heterogeneity patterns: zonation homogeneity, global heterogeneity, and zonation heterogeneity. Accordingly, a unified hybrid deterministic–stochastic (HDS) inversion methodology is proposed within a geostatistical inversion framework to flexibly support three conventional inversion strategies: deterministic zonation inversion, fully stochastic inversion, and stochastic zonation inversion. When integrated with the Reduced-Order Successive Linear Estimator (ROSLE), the HDS-ROSLE approach achieves dimensionality reduction both conceptually and mathematically. A representative mixed configuration is considered—a leaky aquifer system consisting of two homogeneous aquifers separated by a discontinuous, window-punctuated aquitard. A synthetic hydraulic tomography survey is performed for identifying the aquitard window. Four inversion strategies are implemented via the HDS-ROSLE approach. Comparative analysis reveals that the HDS inversion delivers data-fitting performance comparable to those of fully stochastic and stochastic zonation inversions. Most significantly, the HDS inversion resolves the localized heterogeneity with higher accuracy and lower uncertainty, and substantially reduced computational cost. The inherent structure of the mixed parameterization provides a feasible foundation for the HDS inversion methodology to effectively characterize non-Gaussian fields.