Analysis of heterogeneity in a sedimentary aquifer using Generalized sub-Gaussian model based on logging resistivity

It is critical to recognize and reproduce aquifer heterogeneity properly in groundwater modeling and management due to its impacts in groundwater flow, transport, mixing and reaction. It is widely reported that attributes of geologic formations often exhibit statistical scaling with probability distribution of non-Gaussian type. To capture those features in a unified and self-consistent manner, a general geostatistical model termed Generalized sub-Gaussian (GSG) model was proposed by Riva et al. (Water Resour Res 51:4623–4634, 2015. https://doi.org/10.1002/2015WR016998 ). One may wonder whether GSG also works on a broader variety of environmental systems having attributes of different types. Geophysical data are playing growingly significant role in aquifer characterization mainly due to its ease of implementation and low cost. This study focuses on assessing the applicability and transferability of GSG model via a dataset of electrical resistivity collected in three deep boreholes in the northern Ordos Basin in China. By analyzing statistical scaling behaviors, frequency distributions and model fittings of resistivity data, it is found that resistivity data from each borehole indeed can be characterized by GSG model. Though three neighboring boreholes are in a same formation and bear similar geological texture, their corresponding GSG models seem distinct. Cross-validation results further suggest that GSG model calibrated using two boreholes are different from that based on the remaining borehole, though large-lag increments exhibit similar frequency distributions. It is found that GSG is able to characterize well log resistivity in three boreholes but with distinct parameters. Attention should be paid when transferring a calibrated GSG model to the vicinity even within a single sedimentary structure.