Efficient Electromagnetic Imaging of the Vadose Zone Using Cross-Borehole Radar

Abstract

Ground-penetrating radar (GPR) is an effective tool for imaging the spatial distribution of water content. Cross-borehole GPR has been widely used to characterize the shallow subsurface and to monitor hydrogeologic processes. To investigate an infiltration process in the vadose zone, an artificial groundwater infiltration test was conducted in Nagaoka, Japan. Time-lapse cross-borehole GPR data were collected using zero-offset profiling (ZOP) mode. The infiltration process was observed as a variation of GPR traveltimes, which can be transformed into a dielectric constant, and further converted to volumetric water content. Since electromagnetic (EM) wave velocities in the vadose zone are largely controlled by variations in water content, an increase in traveltime is interpreted as an increase in saturation. High-frequency EM wave propagation associated with borehole GPR is a complicated phenomenon. To improve the understanding of the governing physical processes, we employ a finite-difference time-domain (FDTD) solution of Maxwell’s equations in cylindrical coordinates. This approach allows us to model the full EM wavefield associated with crosshole GPR surveys. Furthermore, the use of cylindrical coordinates is computationally efficient, correctly emulates the three-dimensional (3D) geometrical spreading characteristics of the wavefield, and is an effective way to discretise explicitly small-diameter boreholes. Numerical experiments show that the existence of a water-filled borehole can give rise to a strong waveguide effect which affects the transmitted waveform, and that excitation of this waveguide effect depends on the diameter of the borehole and the length of the antenna. In the test zone, the infiltrated water penetrated downward with an average velocity of about 2.7 m/h. The FDTD method using 2D cylindrical coordinates is applied to simulate radargrams associated with the advancing wetting front and to quantify the effects of critical refraction. A standard ZOP mode for which all first-arrivals are assumed to be direct waves results in an underestimation of water content in the transition zone above the wetting front. As a result, correct velocity analysis requires identification of first-arriving critically refracted waves from the traveltime profile to accurately determine a water content profile. The standard ZOP analysis results in an underestimation of the dielectric constant because of the existence of critically refracted waves. We present an efficient algorithm using the maximum first-cycle amplitude to approximately determine the traveltime of direct arrival, deriving a dielectric constant model more accurately than the standard ZOP analysis from ZOP data. Tests on synthetic and real field data show that the proposed approach is effective in building accurate water content profile without iterative calculations as in the standard ZOP analysis. We further present an approach to extract accurate information about the hydrogeologic process in the vadose zone from ZOP data. This approach is based on a least-squares inversion method using singular-value decomposition, in which the FDTD forward modeling is used for computing EM wave fields on 2D cylindrical coordinates. The inversion approach is validated using a synthetic example and applied to the field data. We can successfully estimate the variation of soil water content during infiltration in the Nagaoka site from the reconstructed dielectric constant models. The inversion results show that the saturation information is useful to assess hydrogeologic properties of the test soil zone.