Modeling borehole radar by finite-difference time-domain in conductive sandstone

Three-dimensional (3-D) numerical simulations combined with field experiments to study the radar wave responses in a sandstone formation are described. A borehole radar system was used to perform GPR surveys in a conductive sandstone. Finite-difference time-domain (FDTD) modeling is an economical and efficient method to analyze and interpret the experimental results. Using a priori information of the test site and the instrument parameters, a 3-D FDTD code based on perfectly matched layer (PML) boundary conditions was adopted to establish simulation models to study the conductivity impact on the radar response. In the single-hole reflection models, under the condition of sigma /(omega epsilon ) << 1, a borehole radar can detect targets several meters away from the borehole. In this case, the amplitude attenuation of the radar wave changes linearly as the conductivity increases. However, the detecting capability declines rapidly for the two-way attenuation. The cross-hole tomography simulations are in accordance with the result of the tomography survey, which indicates that the conductivity of the site is about 0.015 S/m to 0.02 S/m, and the attenuation coefficient is between 8.9 dB/m and 11.8 dB/m. The reflected wave of the targets, a cliff and another borehole, cannot clearly be identified in the single-hole reflection image. This is supported by the tomographic image, which illustrates that the radar wave attenuation is significant in the sandstone formation. Therefore, the borehole radar system cannot detect the targets in this highly conductive sandstone.