Quantitative analysis of water-content estimation errors using ground-penetrating radar data and a low-loss approximation

Expressions are derived to quantify the error when estimating permittivity that results from using the low-loss approximation under lossy conditions and to examine the repercussions on estimating water content [Formula: see text]. Values are computed under a range of porosity, clay-content, water-quality, and frequency conditions. Although in most cases the error is negligible, it can be significant for some hydrogeophysical applications involving cross-hole measurements or low-frequency surface ground-penetrating radar (GPR). For instance, when the loss tangent [Formula: see text] equals 0.5, corresponding to an effective conductivity of [Formula: see text], a dielectric constantof 11, and a frequency of [Formula: see text], the relative error on dielectric permittivity is approximately 6%. If the conductivity doubles or the frequency is halved, the loss tangentdoubles but the error grows to 21%. In addition, considering a situation where the porosity is 20% and [Formula: see text], the use of the low-loss approximation leads to a 10% deviation from [Formula: see text]. In the context of water-content estimation, we therefore suggest to perform attenuation tomography, in addition to velocity tomography for crosshole data, or estimate the quality factor [Formula: see text] for surface GPR data to compute the loss tangent over the probed area. If proven necessary, the parameters sought can then be determined more accurately using a lossy formulation. We also propose to supplement GPR measurements with electrical-resistivity tomography to constrain the borehole GPR amplitude data-processing steps required by attenuation tomography or to complement the characterization of the survey area and improve the knowledge brought by [Formula: see text] estimates alone.