Quantitative analysis of water-content estimation errors using ground-penetrating radar data and a low-loss approximation Bernard Giroux 1 and Michel Chouteau 2 ABSTRACT 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 esti- mating water content  . 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 signifi- cant for some hydrogeophysical applications involving cross- hole measurements or low-frequency surface ground-penetrat- ing radar GPR. For instance, when the loss tangent tan  equals 0.5, corresponding to an effective conductivity of 30 mS / m, a di- electric constantof 11, and a frequency of 100 MHz, the relative error on dielectric permittivity is approximately 6%. If the con- ductivity doubles or the frequency is halved, the loss tangent doubles but the error grows to 21%. In addition, considering a sit- uation where the porosity is 20% and tan  0.5, the use of the low-loss approximation leads to a 10% deviation from  . In the context of water-content estimation, we therefore suggest to per- form attenuation tomography, in addition to velocity tomogra- phy 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 to- mography to constrain the borehole GPR amplitude data-pro- cessing steps required by attenuation tomography or to comple- ment the characterization of the survey area and improve the knowledge brought by Q estimates alone. INTRODUCTION Ground-penetrating radar GPR has received increasing atten- tion for hydrogeologic studies during the last 10 – 15 years. Experi- ments using surface and borehole systems have been successful in various ways. For example, Greaves et al. 1996 use multioffset sur- face radar data to map variations in the subsurface volumetric water content. Hubbard et al. 1997 use crosshole velocity tomography to estimate the level of saturation of an aquifer and time-lapse measure- ments to delineate permeable pathways. Gloaguen et al. 2001 use geostatistical analysis of surface GPR measurements together with hydrostratigraphic data to determine the hydraulic conductivity of an aquifer. Binley et al. 2002 use cross-borehole radar and electri- cal resistivity tomography ERT to determine the hydrogeologic parameters of a vadose zone. Tronicke et al. 2004 use cluster analy- sis to correlate and integrate information contained in velocity and attenuation tomograms to build hydrologically meaningful zona- tions of the probed aquifer. Such studies are possible because in the radar regime, the wave velocity is mainly a function of the dielectric permittivity distribu- tion within the ground and because free water has a permittivity well contrasted relative to most geologic materials about 8:1 to 15:1. Experimental and theoretical models exist that relate the dielectric permittivity to the volumetric water content or porosity, depending on the saturation conditions. Hence, mapping the radar-wave veloci- ty field within the ground allows a permittivity distribution map to be inferred for the probed region; consequently, we can image the wa- ter-content distribution within this region at depths typically ranging from a few meters to greater than 50 m. In geophysics, perhaps the most commonly used model to relate dielectric permittivity to water content is the empirical equation of Topp et al. 1980. Another widely used model is the complex refrac- tive index model CRIM, derived from semiempirical mixing mod- els Wharton et al., 1980; Knight and Endres, 1990. Finally, theoret- ical models of effective medium taking into account the responses of mineral grains and pore fluids, such as the Hanai-Bruggeman model Manuscript received by the Editor 7 July 2009; revised manuscript received 14 October 2009; published online 30 September 2010. 1 Institut National de la Recherche Scientifique, Centre Eau Terre Environnement INRS-ETE, Québec, Canada. E-mail: bernard.giroux@ete.inrs.ca. 2 École Polytechnique de Montréal, Montréal, Canada. E-mail: chouteau@geo.polymtl.ca. © 2010 Society of Exploration Geophysicists. All rights reserved. GEOPHYSICS, VOL. 75, NO. 4 JULY-AUGUST 2010; P. WA241–WA249, 4 FIGS., 1 TABLE. 10.1190/1.3464329 WA241 Downloaded 30 Sep 2010 to 198.73.163.28. Redistribution subject to SEG license or copyright; see Terms of Use at http://segdl.org/