Geostatistical inference using crosshole ground-penetrating radar

High-resolution tomographic images obtained from crosshole geophysical measurements have the potential to provide valuable information about the geostatistical properties of unsaturated-zone hydrologic-state variables such as moisture content. Under drained or quasi-steady-state conditions, the moisture content will reflect the variation of the physical properties of the subsurface, which determine the flow patterns in the unsaturated zone. Deterministic least-squares inversion of crosshole groundpenetrating-radar GPR traveltimes result in smooth, minimumvariance estimates of the subsurface radar wave velocity structure, which may diminish the utility of these images for geostatistical inference. We have used a linearized stochastic inversion technique to infer the geostatistical properties of the subsurface radar wave velocity distribution using crosshole GPR traveltimes directly. Expanding on a previous study, we have determined that it is possible to obtain estimates of global variance and mean velocity values of the subsurface as well as the correlation lengths describing the subsurface velocity structures. Accurate estimation of the global variance is crucial if stochastic realizations of the subsurface are used to evaluate the uncertainty of the inversion estimate. We have explored the full potential of the geostatistical inference method using several synthetic models of varying correlation structures and have tested the influence of different assumptions concerning the choice of covariance function and data noise level. In addition, we have tested the methodology on traveltime data collected at a field site in Denmark. There, inferred correlation structures indicate that structural differences exist between two areas located approximately 10 m apart, an observation confirmed by a GPR reflection profile. Furthermore, the inferred values of the subsurface global variance and the mean velocity have been corroborated with moisturecontent measurements, obtained gravimetrically from samples collected at the field site. INTRODUCTION Crosshole ground-penetrating-radar GPR tomography has the potential to produce high-spatial-resolution images of the electromagnetic EM wave velocity distribution of the subsurface e.g., Hubbard et al., 1997; Eppstein and Dougherty, 1998; Binley et al., 2001; Alumbaugh et al., 2002 . The EM wave velocity is directly related to the relative permittivity of a material; in the unsaturated zone, the relative permittivity is strongly influenced by the moisture content of the porous media Topp et al., 1980 . Crosshole GPR therefore enables an indirect estimate of the subsurface moisture content. As a result, crosshole GPR methods have been used extensively for hydrologic applications Annan, 2005 . The high-resolution 2D tomographic images obtained from crosshole GPR data provide information regarding the spatial correlation structures of the subsurface that could otherwise be obtained only through extensive invasive sampling. Under drained or quasisteady-state conditions where the hydrologic-state variables can be expected to represent the physical properties of the subsurface, the geostatistical information i.e., correlation lengths and variability may serve as input to stochastic hydrologic models that provide more reliable predictions of water flow and therefore also contaminant transport Hubbard et al., 1999; Binley et al., 2004 . However, the quantitative estimation of 2D moisture-content images from crosshole GPR traveltimes is still subject to uncertainties, mainly associated with the assumed petrophysical relationships used to compute moisture content from relative permittivity , data uncertainty, and assumptions inherent in the applied inversion algorithms. SimManuscript received by the Editor 22 December 2009; revised manuscript received 29 June 2010; published online 29 October 2010. University of Copenhagen, Department of Geography and Geology, Copenhagen, Denmark. E-mail: [email protected]; [email protected]; [email protected]. Formerly University of Copenhagen; presently Technical University of Denmark, Center for Energy Resources Engineering, Lyngby, Denmark. E-mail: [email protected]. Lancaster University, Lancaster Environment Centre, Lancaster, U. K. E-mail: [email protected]. © 2010 Society of Exploration Geophysicists.All rights reserved. GEOPHYSICS, VOL. 75, NO. 6 NOVEMBER-DECEMBER 2010 ; P. J29–J41, 13 FIGS., 4 TABLES. 10.1190/1.3496001