Sequential Gaussian Mixtures for Transient Hydraulic Tomography Inversion in Fractured Aquifers

Fractured aquifer parameters are expected to have complex non-Gaussian spatial distributions. Gaussian Mixture Models, known for their effectiveness in representing non-Gaussian distributions, present a promising alternative for capturing the complex heterogeneity of fractured geologic settings however their usage in the fractured geologic settings is unexplored. In this study we extended the application of Gaussian mixtures to transient hydraulic tomography on laboratory-based fractured geologic settings using sequential Gaussian Mixture Model (GMM). We further examined the impact of the number of Gaussian components, sampling strategies and the amount of pumping data on the performance of the sequential GMM. Results demonstrate that GMM with an optimal number of Gaussian components effectively identifies high and low conductivity regions, fracture connectivity, and reasonably predicts drawdowns (R² = 0.61) pumping from validation ports. Stratified sampling of GMM parameters (R² = 0.74, average RMSE_median= 9.89 mm) outperforms other sampling strategies like random (R² = 0.61, average RMSE_median= 20.64 mm ), uniform (R² = 0.64, average RMSE_median= 11.70 mm) and quasi-random sampling (R² = 0.67, average RMSE_median= 11.40 mm) techniques in mapping the fracture connectivity and parameter distribution. Stratified sampling with reduced and information-based pumping data maintains commensurable accuracy (R² = 0.75, average RMSE_median= 11.34 mm). Overall, our findings suggest that the sequential GMM combined with stratified sampling technique effectively captures the spatial variability of aquifer parameters in fractured media.