EXPERIMENTAL AND STATISTICAL METHODS TO IMPROVE THE RELIABILITY OF SPECTRAL INDUCED POLARIZATION TO INFER LITHO-TEXTURAL PROPERTIES OF ALLUVIAL SEDIMENTS

The characterization of the shallow subsurface constitutes a challenging issue in several applications of science and engineering. Among the other disciplines, hydrogeophysics deals with the use of geophysical methods for the exploration, management, and monitoring of soil and groundwater. One of the main topics is the study of the petrophysical relationships between electrical properties and hydraulic conductivity, mainly through the dependence of such physical parameters on textural properties. The general aim of this work consists in an investigation of porous materials typical of alluvial environments with spectral induced polarization (SIP) method. The driving question of the research is the feasibility of the use of SIP to characterize both the textural assemblage of the sediments and the fluid properties, in presence of interacting effects related to particles’ mineralogy, organic matter, sediments’ fabric, etc. The samples’ set is constituted by 19 unconsolidated materials collected in four sites of the Po plain south of Milano (Orio Litta, Senna Lodigiana, and Landriano) and west of Milano (Lozzolo), and saturated with seven NaCl-water solutions with electrical resistivity varying from 0.9 Ωm to 315 Ωm. The textural composition of the samples varies between slightly-sandy mud and gravelly sand, and the porosity of the repacked samples between 0.26 and 0.63. The measurements are executed with an experimental system designed and realized at the Laboratory of Hydrogeophysics of the Università degli Studi di Milano. The resistivity amplitude and phase spectra are firstly modelled with single-relaxation models (Cole-Cole and generalized Cole-Cole) in a bounded low-frequency interval. Besides a traditional optimization based on the root-mean-square error, an original multi-optimization approach with separated amplitude and phase errors is tested to obtain a set of optimal solutions and an uncertainty interval for each model parameter, in order to avoid the misinterpretation of petrophysical relationships with scarcely reliable parameters. Significant relationships are identified between DC-resistivity and water resistivity, and between chargeability and mud content. The 10-based logarithm of the relaxation time is inversely correlated with a characteristic diameter of the sample. On the other hand, a Debye-decomposition, multi-relaxation model is applied to identify several polarization processes, characterized by different relaxation times, over the whole frequency interval. In order to maintain the whole spectral information also in the search for electrical-textural relationships, a combination of cluster analysis (CA) and principal component analysis (PCA) is adopted. This constitutes a new approach to relate spectral electrical behaviour to litho-textural properties, avoiding the selection of individual parameters or individual investigation frequency. The CA permits to classify the samples on the basis of their electrical behaviour, and the PCA allows to interpret the variability within the database in terms of a series of parameters ordered by importance. A textural characterization (characteristic diameters, gravel and mud contents, uniformity coefficients) is associated to each cluster, based on the characteristics of the corresponding samples. Analogously, a typical range of water resistivity is attributed to each cluster. This association of variability ranges of electrical and sedimentological properties is then used to infer the sediments’ properties of samples external to the input database, with satisfactory results. The high flexibility of the hierarchical clustering also allows evaluating the differences in the inferred properties according to the number of selected clusters. Finally, some preliminary SIP tests are performed in the field; field and laboratory results are not completely comparable, due to the differences in porosity, water content, and scale of investigation. However, some peculiar characters of the laboratory spectra are recognized in the corresponding field spectra, thus supporting a future application of the proposed methodology to interpret the resistivity amplitude and phase distribution in the subsurface.