Characterizing Roughness and Connectivity Properties of Aquifer Conductivity Using the Method of Anchored Distributions (MAD)

The conductivity of aquifers is usually hard to represent in a precise manner due to having a high degree of spatial variability combined with a scarcity of information. As a result, such conductivity fields are commonly modeled as a random field, defined by its expectation value and the variogram function. This variogram is usually parametrized by fitting a model functions to an experimental variogram derived from point measurements of said conductivity. In this study, we investigate properties of such conductivity fields, that are hard to detect using such classic characterization schemes. The first property is roughness, which can be modeled by the flexible Matern function. The second property is connectivity, which has a strong impact on flow and transport behavior. These two properties are hard to characterize from point measurements alone. As a result, it is necessary to use additional data. Therefore, we use the Method of Anchored Distributions (MAD), which is a novel Bayesian tool for the inverse characterization of random fields. MAD is versatile with respect to the used data and does not assume any formal relationship between the target variable, i.e. the log hydraulic conductivity, and the data used for the inversion process, e.g. head measurements, drawdown from pumping tests or break-through curves of a tracer. With respect to the characterization of the aforementioned properties, we investigate the impact of several factors on their identifiability, including alternative and complementary data types, the necessary amount of data, where to collect this data or how to assimilate it.