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

摘要

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 theta. 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 crosshole measurements or low-frequency surface ground-penetrating radar (GPR). For instance, when the loss tangent tan delta equals 0.5, corresponding to an effective conductivity of 30 mS/m, a dielectric constantof 11, and a frequency of 100 MHz, the relative error on dielectric permittivity is approximately 6%. If the conductivity doubles or the frequency is halved, the loss tangent doubles but the error grows to 21%. In addition, considering a situation where the porosity is 20% and tan delta = 0.5, the use of the low-loss approximation leads to a 10% deviation from theta. 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 Q 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 Q estimates alone.