Summary
The radio imaging method (RIM) employs the propagation of radio-frequency EM waves (100 kHz to 10 MHz) to image the conductivity distribution between the boreholes. We studied the wave propagation using the finite-elementmodeling (FEM) algorithm implemented in the Comsol RF module. Appropriate element sizes are quantified by comparing the Comsol modeling results of 6 types of element sizes at 4 frequencies with analytical solutions for the homogeneous whole-space model. The comparison reveals that modeled data with 5 elements per wavelength have errors less than 5%; 7 to 8 elements per wavelength provide errors around 1%; and when there are 10 elements per wavelength, the errors are less than 1%. We also compared the solutions for spherical models, which shows the Comsol solutions are consistent with the analytical solutions and the solutions from a finite-difference timedomain algorithm. To illustrate the flexibility of Comsol package, we provide an example with two moderately conductive bodies between boreholes. The EM wave attenuation and reflection by the conductive bodies can be observed on the relative variation map. We used the synthetic data to reconstruct a tomographic image with the SIRT algorithm. The image shows that the location of the conductive anomalies are reconstructed fairly successfully, although, there are some artifacts. From our work, we conclude that Comsol modeling is helpful to study the radio wave propagation and tomographic imaging methods.
Introduction
Radio imaging method (RIM), also known as radiofrequency tomography, is a cross-hole exploration method, which employs radio-frequency electromagnetic (EM) waves to image the distribution of electric properties between boreholes. RIM can be applied to the prediction of coal-seam hazards (Hill, 1984), delineation of ore bodies (Thomson and Hinde, 1993; Zhou et al., 1998; Mutton, 2000) and site selection for underground disposal of nuclear waste (Korpisalo and Heikkinen, 2014). Figure 1 is a schematic diagram of a RIM survey: we place a transmitter at one borehole (BH_1), and a receiver in another borehole (BH_2) and move each to a series of positions where the EM field is measured. The amplitude profiles in Figure 1 are based on a simplfied geometrical optics model, in which EM waves propagate as straight rays, but, the situation is, in reality, more complex. The purpose of RIM is to use the variation in the EM fields to tomographically reconstruct an image of the electrical properties (primarily conductivity) on the cross-hole plane. EM tomography has been successfully applied to explore the earth using high-frequency (typically 10 – 1500 MHz) EM waves (Holliger et al., 2001). However, rapid attenuation of the high-frequency EM waves results in short propagation distances (usually meters to tens of meters). In order to obtain a longer exploration range, it is necessary to lower the frequency to the medium frequency range (100 kHz to 10 MHz). However, the characteristics of EM fields in this range are more complicated. Both radiation and induction exist, and both conductivity and dielectric permittivity need to be considered (Wilkinson, 2005).
