Investigating Scale Effects on Petrophysical Relationships: Comparison between Laboratory and Field Approaches to estimate Soil Water Content from Electrical Resistivity

The application of geophysical tools provides soil information without disturbing the soil. For the analysis of hydrological properties, one of the most commonly used geophysical methods is electrical resistivity tomography (ERT). The electrical resistivity measures the soil ability to counteract the passage of an electrical current. Since liquid water is the conductive phase of a soil (i.e., where ions act as charge carriers), its measure can be employed as an estimation of soil water content. However, such quantification demands the use of a petrophysical relationship. Petrophysical calibration is crucial and requires a good knowledge of the soil, numerous measurements of both electrical resistivity and water content on the studied soil. Considering the current state of the art, two methods are commonly employed for this calibration. The first method, at the sample scale, is made in laboratory with cylindrical undisturbed soil samples with four electrodes and tracks the changes in water content by the variation in sample weight during desiccation. The second approach, at the field scale, is made in-situ and consists of installing Time-Domain Reflectometry (TDR) probes in different soil horizons below a profile of electrodes used to make electrical resistivity tomography. This study examines the effect of scale on petrophysical relationships due to investigated volumes by comparing the petrophysical relationship calibrated from three different methods with three different footprints on the same soil profile. This research is developed on the Hydrogeological Experimental Site of the University of Poitiers, on an unsaturated soil (Cambisol (Luvic)) developed on Tertiary and Quaternary sedimentary formations. The soil at the site is composed of silt and clays, with sandier soil lenses and a high proportion of flints, up to 50% in the first 90 cm. The field acquisition set-up consists of 48 electrodes on the soil surface spaced of 0.5 m to perform time-lapse ERT (the largest footprint), of four trenches equipped with TDR probes and quadrupole of electrodes at 30, 60, 90, 120, 150 and 180 cm depth (the intermediate footprint), and of 20 undisturbed soil samples collected in 9.5 cm diameter and 5 cm thickness cylinders analyzed in the laboratory at 25°C (the smaller footprint). In-situ measurements are affected by weather conditions and soil water content, meaning that deeper soil horizons show a limited variation in water content. Our laboratory characterization allows us to explore a larger range of soil moisture and to calibrate the petrophysical relation with more accurate precision. However, the sample may not be spatially representative. Our first results demonstrate that the three methods show similar trends with a notable difference in the amplitude of the values obtained for electrical resistivity. These findings enable a deeper comprehension of scale effects in the configuration of petrophysical relationships with the aim of improving accuracy of models to estimate soil water content from ERT measurements.