Bayesian Integration Using Resistivity and Lithology for Improving Estimation of Hydraulic Conductivity

Abstract

The characterization of spatially heterogeneous hydraulic conductivity (K) is important in groundwater resources management. We propose a Bayesian statistical method that integrates multiple secondary data (continuous and category data) with primary data (K) to improve regional K field characterization. Considering the disparity of the data scale, spatial scarcity of primary and secondary data, and need for regional-scale site characterization, the aquifer thickness is used as the scale for data integration. We transform the high-resolution secondary data to the scale of K and perform linear/ nonlinear regression analyses for the transformed secondary data and primary data. A Bayesian approach using Metropolis-within-Gibbs sampling is developed for jointly integrating the primary and transformed secondary data without a limitation on the type of data attribute and the number of data set. A synthetic example is first presented to demonstrate the capability of the proposed method. Results show that the correlation strength, not the relation type, is the primary factor for improving the estimates. The Bayesian method is applied to Choushui River alluvial fan in Taiwan. Resistivity logs and a lithological description are first upscaled and then simultaneously integrated in the K estimation. Results indicate that the improvement of the K estimate obtained using resistivity data is higher in the proximal and mid fans but lower in the distal fan compared to that obtained using lithofacies data. Jointly integrating two-attribute data outperforms using one or no secondary data set for K estimates. The proposed Bayesian integration method is thus versatile and suitable for large-scale aquifer characterization.

Determination of hydraulic conductivity for granular filters based on constriction size and shape parameters

“…Boadu (2000) concluded the measurement of hydraulic conductivity by the laboratory and field methods as costly and time consuming, and insufficient field data of aquifers and hydraulic boundaries add to the limitation (Freeze & Cherry 1979;Todd & Mays 2005). These limitations have led researchers to shift to analytical approaches for the study of groundwater and the porous media (Salmasi & Azamathulla 2013;Cheng & Hsu 2021). Hazen (1893), Carman (1939), Sherard et al (1984), Vukovic & Soro (1992), Indraratna et al (1996) and Ishaku et al (2011) conducted investigations to suggest empirical equations for the hydraulic conductivity determination based on particle sizes of granular soils.…”

Effects of grain size, solution salinity and pH on the electrical response of oil‐bearing carbonate sands

“…Verdet et al (2020) carried out true 3D ERT measurements on a karstic site and revealed the undercover karst features by combining 3D ERT with geomorphological and geological data. Cheng and Hsu (2021) fused resistivity logs and lithology description through Bayesian integration to improve the estimation of hydraulic conductivity for large-scale aquifer.…”