Predicting hydrofacies and hydraulic conductivity from direct‐push data using a data‐driven relevance vector machine approach: Motivations, algorithms, and application

The spatial heterogeneity of hydraulic conductivity ( K ) exerts a major control on groundwater flow and solute transport. The heterogeneous spatial distribution of K can be imaged using indirect geophysical data as long as reliable relations exist to link geophysical data to K . This paper presents a nonparametric learning machine approach to predict aquifer K from cone penetrometer tests (CPT) coupled with a soil moisture and resistivity probe (SMR) using relevance vector machines (RVMs). The learning machine approach is demonstrated with an application to a heterogeneous unconsolidated littoral aquifer in a 12 km 2 subwatershed, where relations between K and multiparameters CPT/SMR soundings appear complex. Our approach involved fuzzy clustering to define hydrofacies (HF) on the basis of CPT/SMR and K data prior to the training of RVMs for HFs recognition and K prediction on the basis of CPT/SMR data alone. The learning machine was built from a colocated training data set representative of the study area that includes K data from slug tests and CPT/SMR data up‐scaled at a common vertical resolution of 15 cm with K data. After training, the predictive capabilities of the learning machine were assessed through cross validation with data withheld from the training data set and with K data from flowmeter tests not used during the training process. Results show that HF and K predictions from the learning machine are consistent with hydraulic tests. The combined use of CPT/SMR data and RVM‐based learning machine proved to be powerful and efficient for the characterization of high‐resolution K heterogeneity for unconsolidated aquifers.