Estimation and scaling of hydrostratigraphic units: application of unsupervised machine learning and multivariate statistical techniques to hydrogeophysical data

Abstract

Numerical models provide a way to evaluate groundwater systems, but determining the hydrostratigraphic units (HSUs) used in constructing these models remains subjective, nonunique, and uncertain. A three-step machine-learning approach is proposed in which fusion, estimation, and clustering operations are performed on different data sets to arrive at HSUs at different scales. In step one, data fusion is performed by training a self-organizing map (SOM) with sparse borehole hydrogeologic (lithology, hydraulic conductivity, aqueous field parameters, dissolved constituents) and geophysical (gamma, spontaneous potential, and resistivity) measurements. Estimation is handled by iterative least-squares minimization of the SOM quantization and topographical errors. Application of the Davies-Bouldin criteria to k-means clustering of SOM nodes is used to determine the number and location of discontinuous borehole HSUs with low lateral density (based on borehole spacing at 100 s m) and high vertical density (based on cm-scale logging). In step two, a scaling network is trained using the estimated borehole HSUs, airborne electromagnetic measurements, and numerically inverted resistivity profiles. In step three, independent airborne electromagnetic measurements are applied to the scaling network, and the estimation performed to arrive at a set of continuous HSUs with high lateral density (based on sounding locations at meter (m) spacing) and medium vertical density (based on m-layer modeled structure). Performance metrics are used to evaluate each step of the approach. Efficacy of the proposed approach is demonstrated to map local-to-regional scale HSUs using hydrogeophysical data collected at a heterogeneous surficial aquifer in northwestern Nebraska, USA.