Modeling Borehole Radar by Finite-difference Time-domain in ...

19

Modeling Borehole Radar by Finite-difference Time-domain in Conductive Sandstone Chunguang Ma, Qing Zhao, Likai Wang and Shuzhang Liu School of Physical Electronics, University of Electronic Science and Technology of China, No. 4, Section 2, North Jianshe Road, Chengdu 610054, China Email: [email protected]

ABSTRACT 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 s/(ve) ,, 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.

Introduction Borehole radar is a subsurface exploration tool for detecting discontinuities in rock formations. For most geological applications, antenna frequencies of typical borehole radar range from 50 MHz (long range of investigation, up to a few tens of meters) to 500 MHz (short range of investigation, up to a few meters) (Gawthorpe et al., 1993; Slob and Olhoeft, 2010). Borehole radar has been used in a variety of applications; the main ones being subsurface geologic structure imaging and mining (Stevens et al., 1995; Eisenburger and Gundelach, 2000; Fullagar et al., 2000; Mafiri et al., 2008; Kemp et al., 2009), hydrogeology and environmental geology (Olsson et al., 1992; Lane et al., 1994; Grumman and Daniels, 1995; Mansour and Sato, 2012), as well as engineering exploration (Lytle et al., 1976; Nickel et al., 1983; James and Erich, 2005; Takahashi and Sato, 2005; Thierbach et al., 2008). At present, many researchers are devoted to identifying and confirming subsurface anomalies to predict oil or natural gas reservoirs at given locations. The radar wave propagation path, electromagnetic (EM) field intensity, and waveform are influenced by the JEEG, March 2015, Volume 20, Issue 1, pp. 19–29

EM properties and geometrical configuration of the medium. Complete understanding of the EM wave propagation is important for understanding of the performance characteristics of a borehole radar system in a conductive formation, data processing and image interpretation, and extending its potential fields of application. The finite-difference time-domain (FDTD) algorithm (Yee, 1966) is a full-wave, dynamic and powerful numerical method for directly solving Maxwell’s equations in the time domain. Furthermore, the FDTD method is ideal for modeling transient EM fields in inhomogeneous media. Complex geological and antenna structures fit relatively easily into a finite-difference grid, and absorbing boundary conditions can truncate the grid to simulate an infinite region. The smaller the values of the discretization steps, the closer the FDTD model is to a real representation of the problem; however, much more time will be consumed to complete the simulation calculation. Recent advances in computational capability have made it possible to analyze the radiation in realistic borehole conditions by using FDTD analysis (Teixeira and Chew, 2000; Holliger DOI: 10.2113/JEEG20.1.19

20 Journal of Environmental and Engineering Geophysics and Bergman, 2002; Ernst et al., 2006; Irving and Knight, 2006). The complex shape targets can be simply dispersed into a finite-difference grid. Successful modeling attempts of ground penetrating radar (GPR) adopting the FDTD method have been reported by many authors. Giannopoulos (1997, 2005) established a software tool by FDTD, which can be used to model GPR responses from arbitrarily complex targets. A 3-D FDTD method for simulating the GPR response of buried pipes in soils with conductive loss is described in Bourgeois and Smith (1996) and Teixeira et al. (1998). Liu (2006) developed a FDTD forward modeling to simulate the fundamental radar response for fractures filled with conductive and non-conducive materials. Chen and Oristaglio (2002) published a feasibility study of borehole radar for oil field applications in resistive oil reservoirs using a 3-D FDTD code. Muhkopadhyay et al. (2009) implemented a 3-D FDTD code for simulating radar wave propagation in a sedimentary layer, and reflection from a geological reverse fault and potholetype structure in a conductive host rock. The FDTD method is beneficial to observe radar wave propagation in conductive media. However, the above mentioned studies are limited to numerical simulations. Simulations combined with the result of a field experiment would be valuable to better understand the radar response in lossy formations. Ernst et al. (2006) carried out a study of borehole radar antenna radiation properties using realistic FDTD modeling and performed experimental tests in crystalline rock and alluvial sediments. Combined with borehole radar experimental data and 2-D finite difference models, Wang and McMechan (2002) assessed the distribution of velocity and attenuation for a sandstone reservoir. However, both of these studies focused mainly on crosshole surveys. The single-hole reflection is an economical and efficient approach for geophysical application. A transmitting antenna generates an oscillating electric field into the formation. When this field encounters an anomalous body with differing electrical properties (electrical permittivity and conductivity), a wave is reflected back toward a receiving antenna. The reflected wave amplitude and transit time are recorded and used to produce a reflector map in traveltime. Borehole radar reflection data are interpreted to determine the location of the anomalous body, and to estimate the radial extent of such features beyond the borehole. The penetration of the radar signal is dependent on the attenuation during its travel path. Radial penetration in electrically resistive rock (greater than 500 ohm-m) may be more than 9 m, while in a relatively low resistivity sedimentary bedrock (near 100 ohm-m) radial penetration can be less than 3 m (Williams et al., 2002). Ma et al. (2014) used a

MALA RAMAC borehole radar system to image a limestone cliff formation. With a background material conductivity of about 0.6 mS/m and attenuation of about 0.36 dB/m, the radar system could detect the reflected wave signal of the cliff wall, which was about 10 m from the borehole. To establish a technical basis for developing a borehole radar system for oil and gas reservoir exploration, we carried out a field experiment in a sandstone formation, also using a MALA borehole radar system. One of the most challenging issues in modeling open boundary problems is truncating the computational domain to a finite simulation region. The perfectly matching layer (PML) formulation (Berenger, 1994; Chen et al., 1997) was introduced as an absorbing boundary condition for the lossy media. Hence, we chose to use a 3-D FDTD code based on the PML to simulate the models. In this paper, we describe a borehole radar system and test site, and the image results of single-hole reflection and cross-hole tomography measurements in a sandstone formation. The 3-D FDTD code is used to simulate the models based on the experiment conditions and instrument parameters. We simulate the radar responses in various conductive environments for different models. Finally, we analyze the simulation results and interpret the images obtained during the field experiments. Radar System, Test Site and Field Measurements Borehole Radar System The borehole radar system for the field experiment is a commercial radar from MALA Geosciences Sweden. The ground control section includes a ProEx Control Unit (CU) and a laptop computer. The CU provides the standard time signal, control command, and data acquisition command. The computer is used for storing data and displaying images. The underground detection section consists of an ultra-wideband (UWB) transmit probe and receive probe, which contains a transmitter with a transmitting antenna and a receiver with a receiving antenna. The two sections are linked together by 150-m fiber optic cables. To achieve a far detection range, the 100-MHz half-wave dipole antennas were used for the experiments. A borehole radar system mainly has two operation modes: single-hole reflection and cross-hole tomography surveying. In the single-hole reflection method, the transmitting and receiving antennas are connected together as a logging tool. The antennas are separated by a fixed spacer and moved along the borehole. The greatest strength of single-hole reflection logging is the ability to identify features that do not intercept the

21 Ma et al.: Modeling BHR by FDTD in Conductive Sandstone

Figure 1. Photograph of the test site. The host rock is sandstone and is quite homogeneous. The width and height of the cliff are about 36 m and 14 m, respectively. At the bottom of the steep cliff is a shallow pool. borehole, although there is the challenge of two-way attenuation. A tomography experiment is designed to estimate the EM properties of the medium between two boreholes, which limits the utility of the tomographic mode for target detection. The transmitting and receiving antennas are separated in two different boreholes. The tomography configuration covers the survey area between the boreholes with raypaths. The traveltime and amplitude of the waveform traces are recorded for each raypath. Therefore, the complementary use of both the reflection and tomography survey has advantages to evaluate the effectiveness of the radar system during a test. Test Site To validate the detection range and the resolution of a directional borehole radar system, which was designed for oil and gas resources exploration, we built a test site in an idle quarry in the suburban district of Ziyang City, Sichuan Province, China. The site is located on an open hillside with a sharp cliff on one side of the hill. The host rock is sandstone and is quite homogeneous up to 14 m below ground level. The test site is shown in Fig. 1; the cliff is about 36 m in width and 14 m above the surface of a pool. The small, shallow pool is about 0.8-m deep and was formed from drained stagnant water during quarrying. Figure 2 is the layout of the test field. On the top of the cliff, there is a narrow

and step-shaped platform with 1.5-m height and 2-m width. Two boreholes were placed at the site. BH-1 extends 40 m into the ground with 130-mm diameter and 7-m distance from the cliff. BH-2 has a total depth of 20 m with a diameter of 200 mm, and is 5 m from the cliff. The two boreholes are about 3-m apart and the top of each borehole is at the same elevation. The original expectations of the site layout are: 1) A borehole radar moving along BH-1 can detect the reflection signal from the cliff and shallow pool, 2) BH-2 can be used for the detection of targets at a shorter detection range, and 3) because BH-2 has a larger diameter, it can be filled with different materials, such as air, fresh water, and saline water, and used for validating the resolution of the borehole radar system. To determine the EM properties of the sandstone, core samples were taken from BH-1 between 5 m and 14 m depth. Each core had a length of 10 mm and diameter of 50 mm. We adopted a microwave resonator method (Kobayashi and Katoh, 1985) to measure the cores. At a test frequency of 1.17 GHz, the relative dielectric permittivity and loss angle tangent are about 7.29 and 0.031, respectively. In this study, the main concern is reproducing the observed traveltime behavior of the reflections along with approximate amplitudes. The waveform changes and details such as dispersion are of less interest. Experimental evidence from GPR surveys (Davis and

22 Journal of Environmental and Engineering Geophysics and the receiver probe was lowered down BH-1 at a near uniform speed. Though there was one-way attenuation between the antennas, a short semi-hyperbola could be seen only from 4.6 m to 9.4 m in the tomographic image (Fig. 3(b)). When the receiving antenna was at the same position as the transmitting antenna, the received signal had the shortest transmission distance and the signal appeared at about 30 ns, where the amplitude was at a maximum. It shows that the conductivity of the site is quite high. Thus, the energy of the reflected wave may be completely exhausted during the reflection measurement for the two-way attenuation. According to the environment of the test site and the testing patterns of the borehole radar system, we established the following simulation models to study the impact of conductivity on radar wave responses. 3-D FDTD Numerical Simulation

Figure 2. Layout of the test site showing the two boreholes locations (BH-1 and BH-2) and their geometry related to the cliff. Dimensions are shown as used in the simulated models. Annan, 1989) demonstrates that if the loss tangent is ,, 1, the velocity of propagation of the EM waves does not depend strongly on frequency. Therefore, we take the relative dielectric permittivity of sandstone to be 7.29 in the simulation models. Test Results We carried out a single-hole reflection measurement in BH-1 to image both the cliff and BH-2. As the radar moved from the bottom of the borehole to the top, the data were processed using MALA’s Ground-Vision 1.4.5 software. We can easily distinguish the direct wave signal in the image (Fig. 3(a)), the waveform of which is steady and coincident from the top of BH-1 to 14 m. It can be inferred that uniform strata is surrounding the borehole in this interval. However, some oscillating signals exist and we cannot distinguish the reflected wave from BH-2 and the cliff. The direct wave from 14 m to 30 m is instable and inconsistent, which may be caused by the inhomogeneity of the layers. The water table is about 30 m below ground level, and the interface between air and water is clearly seen at that depth. Considering the radar wave’s two-way attenuation in the medium, we took a cross-hole tomography measurement, which was used to estimate EM properties in the plane between the two boreholes. The transmit probe was fixed at 7-m depth inside BH-2,

The 3-D FDTD code is implemented in a Cartesian coordinate system to simulate radar responses in a conductive medium, and the simulation material is considered to be homogeneous, isotropic and nondispersive. The PML is added at the outer boundary to truncate the simulation region. In addition, the simulations use a vertical electric dipole with infinitesimal length as the radar source. The source wavelet is the first derivative of a Gaussian pulse; the amplitude spectrum of the source has a nominal frequency of 100 MHz. The source function is added to the Ez component at the source position at each time step. The EM field of the echo signal is recorded by the receiving antenna. As the 3-D FDTD code uses a rectangular grid, the cylindrical borehole surface is discretized by an averaged staircase approximation. The grid dimensions used in the simulation models in both the horizontal and vertical coordinates is 3 cm, which, assuming a maximum usable frequency of 150 MHz, is approximately 66 grid points per wavelength in air, which, with a time step of 57.8 ps, satisfies the stability condition (Taflove, 1995). Single-hole Reflection Mode Simulation The cliff and BH-2 are two known reflection targets at the site, so the simulation models were built according to the information about 14 m underground. In addition, we are mainly interested in the EM parameters of the sandstone, therefore, the assumption is that the conductivity and relative permittivity of the surface soil are s 5 0.01 S/m and er 5 15. Figure 4 shows the side and top views of a single-hole reflection model with a dimension of (x, y, z) 5 (9.0, 4.3, 15.0) m. BH-1 (diameter 130 mm) and BH-2 (diameter 200 mm) were placed along the Z-axis at (x, y) 5 (1.0, 3.24) m


Figure 3. GPR B-scan of the test result by the MALA borehole radar system. a) Radargram of a single-hole reflection image; b) radargram of a cross-hole transmission. and (x, y) 5 (3.0, 1.0) m at a distance of 7 m and 5 m from the cliff, respectively. The host rock is sandstone (s 5 0.0001 S/m, er 5 7.29); on top of the host rock is a half-meter thick soil layer, and the boreholes are filled with air (s 5 0 S/m, er 5 1). The arrow and dot represent the dipole source and receiving antenna, respectively, in the figure. The initial position of the transmitting and receiving antennas were placed at (x, y, z) 5 (1.0, 3.24, 0.5) m and (x, y, z) 5 (1.0, 3.24, 3.25) m,

respectively. The antennas had a fixed spacing of 2.75 m and moved along the central axis of BH-1 by a step of 0.6 m. Figure 5 shows the received radar traces for the antennas at different locations. Seven different types of waveforms are clearly visible in the synthetic traces. The direct wave is very strong for the little attenuation in the borehole filled with air. The amplitude of the reflected wave from the BH-2 is weaker than that from the cliff,

24 Journal of Environmental and Engineering Geophysics

Figure 5. The simulated waveforms for the model shown in Fig. 4.

Figure 4. The single-hole reflection simulation model: a) side view, b) top view. which is only inferior to the direct wave. In theory, the speed of the radar wave in the sandstone is approximately 1.1 3 108 m/s. Knowing that BH-1 is a horizontal distance of about 3 m and 7 m from BH-2 and the cliff, respectively, the time delay is about 34.7 ns between the BH-2 reflection wave and direct wave, and 103.6 ns between the cliff reflection wave and direct wave. Waveform A is caused by the reflection from the ground. Because the host rock has low conductivity and the energy attenuation is relatively weak in this simulation, the radar wave travels a relatively long way and the ground reflection waveform is still clearly visible. The time delay of the waveform gradually decreases as the antennas move upward toward the soil layer; the reflection waves from the step-shaped platform (see Fig. 2) and the surface become more

significant. The cliff reflection is caused by the horizontal plane of the platform (waveform B). The reflection from the vertical plane is reflected by the interfaces between sandstone–soil and soil–air, which form waveforms C and D, respectively. As the transmitting and receiving antennas move upward to the soil layer, the propagation distance of the reflection from the sandstone–soil interface decreases gradually. The energy of the reflection has a relatively weaker attenuation in the sandstone, so the amplitude of waveform C is enhanced. However, the amplitude of waveform D decreases as the antennas move up the borehole; the increasing propagation distance in the soil leads to greater energy attenuation. A small time delay is observed as a result of the lower layer propagation speed (about 0.77 3 108 m/s) in the soil. To study the impact of variable conductivities on the radar response in sandstone, especially for the reflection from BH-2 and the cliff, the above model was modified. The modified simulation model has a dimension of (x, y, z) 5 (9.0, 4.3, 12.5) m, with varying sandstone layer conductivities; all other settings remain unchanged except for adding the PML on the top boundary. Figure 6 shows one radar trace of each model with different conductivities. There are three main waves (direct wave and reflection waves from BH-2 and the cliff) and secondary reflection waves (some scattered waves of BH-2 were reflected by the cliff) apparent on each trace. The waveform amplitude diminishes as the conductivity increases from 0.000001 S/m to 0.004 S/m. In addition, the radar traces are basically unchanged when the conductivity is between 0.000001 S/m and 0.00001 S/m, because the conductivity is quite low.


Figure 6. Influence of different sandstone conductivities on the radar wave responses. The dotted line represents the radar wave response of the model without BH-2. When the conductivity is above 0.004 S/m, only the direct waves can be seen in the traces. The dotted line is a trace of the model without BH-2 at 0.000001 S/m, therefore, there is no BH-2 reflection or secondary reflection wave in the trace. Cross-hole Tomography Mode Simulation Figure 7 shows the side and top views of a crosshole tomography model with a dimension of (x, y, z) 5 (5.0, 2.4, 14.0) m. BH-1 and BH-2 are placed along the Z-axis at (x, y) 5 (1.0, 1.2) m and (x, y) 5 (4.0, 1.2) m, respectively, and the boreholes are filled with air (s 5 0 S/m, er 5 1). The transmitting antenna is placed at (x, y, z) 5 (1.0, 1.2, 7.0) m, and the initial position of the receiving antenna is at (x, y, z) 5 (4.0, 1.2, 1.6) m. The source function is added to the Ez component at the source position. The receiving antenna moved along BH-1 by a step of 0.6 m. The relative dielectric permittivity of sandstone is 7.29, while the conductivity is variable for each simulation. Figure 8 shows the direct wave between the transmitting and receiving antennas in a homogeneous sandstone with different conductivities of 0.005 S/m, 0.01 S/m, 0.015 S/m and 0.02 S/m. When the receiving antenna moved to 7.0 m, which is directly opposite of the transmitting antenna, the arrival traveltime is the shortest and the arrival amplitude is the largest. The traveltime and the amplitude of direct waves above and below the location of the transmitting antenna are symmetric and appear as a semi-hyperbola form, which is most obvious in the medium with a conductivity of 0.005 S/m. As the conductivity increases, the signal

Figure 7. The cross-hole tomography simulation model: a) side view, b) top view. amplitude reduces significantly and the semi-hyperbola is only faintly visible at 0.02 S/m. Discussion In the single-hole reflection simulation, we can obtain information on waveforms produced by different stratum structure and identify different types of waveforms present at lower conductivities. The reflection amplitude of BH-2 is much smaller than that of the cliff, although the raypath of the cliff is more than twice as that of BH-2. Because of the curved surface and small diameter of BH-2, most of the energy is scattered. While the effective scattering cross section of the cliff is large, most of the reflected energy can be captured by the receiver. Figure 6 demonstrated that the radar wave amplitude is dependent on the conductivity of the transmission medium at a fixed frequency. The attenuation of the direct wave in sandstone is about 3.0 dB at a conductivity of 0.005 S/m when compared with that in air. The amplitude attenuation of a waveform changes linearly as the conductivity increases from 0.000001 S/m to 0.06 S/m, and the relation curve between the amplitude attenuation and conductivity is shown in Fig. 9. The energy loss of the reflected wave from the

26 Journal of Environmental and Engineering Geophysics

Figure 8. The direct wave for different sandstone conductivities in the tomography models. The conductivity of the sandstone in each model is 0.005 S/m (a), 0.01 S/m (b), 0.015 S/m (c) and 0.02 S/m (d). farther target is greater as the conductivity increases, and its corresponding waveform disappears earlier on the radar trace. The reflected wave from the closer reflector surrounding the borehole cannot be received because of the two-way attenuation at a higher conductivity. In the cross-hole tomography simulation, the distance between the antennas changes from 3.8 m to 3 m then back to 3.8 m as the receiving antenna is moved along the borehole. The direct wave signals are distinctly seen at 0.005 S/m (Fig. 8(a)). However, only the direct wave can be seen in the single-hole reflection

mode modeling the same background material (Fig. 6), as the reflected wave energy virtually runs out because of the two-way attenuation. The amplitude of the direct wave decreases with increasing conductivity from 0.005 S/m to 0.02 S/m. The attenuation coefficient of the sandstone increased about 4 times, from 3.0 dB/m to 11.8 dB/m. The direct waves are faintly visible at 0.015 S/m when the receiving antenna is positioned at 4.6 m and 9.4 m on the Z axis, but they disappear at 0.02 S/m. The tomographic image (Fig. 3(b)) only shows a short semi-hyperbola between 4.6 m and 9.4 m, and the change of signal amplitude is very distinct. When the


Figure 9. The relation curve between the amplitude attenuation and conductivity. receiver antenna moved out of this section, the transmission signal is attenuated and it could not be effectively detected. Therefore, the conductivity of the test site should be between 0.015 S/m and 0.02 S/m. This means that the amplitude of the radar wave will decay quickly with attenuation between 8.9 dB/m and 11.8 dB/ m. Most borehole radar antennas experience ringing as a result of radiating a UWB signal, and this ringing tends to obscure later time signals. There appears to be some periodic oscillator signals after the direct wave 14 m underground (Fig. 3(a)), which may be caused by the ringing effect. Therefore, we cannot obtain the reflected wave signal from BH-2 in the single-hole reflection measurement, and it is impossible for the cliff reflected wave to be detected at this high conductivity. Conclusions Our models show that the FDTD method is beneficial to observe radar wave responses in a conductive media, and the simulation results can be used for objective analysis and interpretation for the data and images of field measurements. The depth of penetration of the radar waves varies inversely with the frequency of the waves and conductivity of the formation; thus, for a fixed frequency (e.g., 100 MHz), the radial penetration is primarily dependent on the conductivity. For a higher conductivity formation, the radial penetration is lower. Simulations with a 3-D FDTD code demonstrate that, under the condition of s/ (ve) ,, 1, a borehole radar can detect targets several meters away from the borehole in single-hole reflection mode, and the amplitude attenuation of the radar wave changes linearly as the conductivity increases. Accord-

ing to the cross-hole tomography simulation results, the sandstone conductivity is between 0.015 S/m and 0.02 S/ m. This corresponds to an amplitude attenuation of the radar wave of 8.9 to 11.8 dB/m. The simulation is in accordance with the results of the cross-hole tomography survey. The tomographic image illustrates that the radar wave attenuation is significant in the sandstone formation because the radar wave can only be collected effectively within 3.8 m for a single-way travel. Thus, the two-way attenuation is more serious in the single reflection survey. Hence, the borehole radar cannot capture the reflection signal from BH-2 and the cliff in the high conductivity formation. The oscillating signal in the image may be caused by the ringing effect, which is not the reflection of the borehole BH-2 or the cliff. Thus, this site is not suitable for standardizing a borehole radar system because of the high loss in the formation, and it is not beneficial for studying radar wave propagation characteristics. Acknowledgments The authors gratefully acknowledge financial support from the China Scholarship Council.

References Berenger, J.P., 1994, A perfectly matched layer for the absorption of electromagnetic waves: Journal of Computational Physics, 114, 185–200. Bourgeois, J.M., and Smith, G.S., 1996, A fully threedimensional simulation of a ground-penetrating radar: FDTD theory compared with experiment: IEEE Transactions on Geoscience and Remote Sensing, 34, 36–44. Chen, Y.H., Chew, W.C., and Oristaglio, M.L., 1997, Application of PML to the transient modeling of subsurface EM problems: Geophysics, 62, 1730–1736. Chen, Y.H., and Oristaglio, M.L., 2002, A modeling study of borehole radar for oil-field applications: Geophysics, 67, 1486–1494. Davis, J.L., and Annan, A.P., 1989, Ground-penetrating radar for high-resolution mapping of soil and rock stratigraphy: Geophysical Prospecting, 37, 531–551. Eisenburger, D., and Gundelach, V., 2000, Borehole radar measurements in complex geological structures: Proceedings of the 8th International Conference on Ground Penetrating Radar, SPIE, 121–125. Ernst, J.R., Holliger, K., Maurer, H., and Green, A.G., 2006, Realistic FDTD modeling of borehole georadar antenna radiation: Methodology and application: Near Surface Geophysics, 4, 19–30. Ernst, J.R., Maurer, H., Green, A.G., and Holliger, K., 2007, Full-waveform inversion of crosshole radar data based on 2-D finite-difference time-domain solutions of Maxwell’s equations: IEEE Transactions on Geoscience and Remote Sensing, 45, 2807–2828.

28 Journal of Environmental and Engineering Geophysics Fullagar, P.K., Livelybrooks, D.W., Zhang, P., Calvert, A.J., and Wu, Y.R., 2000, Radio tomography and borehole radar delineation of the McConnell nickel sulfide deposit, Sudbury, Ontario, Canada: Geophysics, 65, 1920–1930. Gawthorpe, R.L., Collier, R.E.Li., Alexander, J., Bridge, J.S., and Leeder, M.R., 1993, Ground penetrating radar: Application to sand body geometry and heterogeneity studies: Geological Society, London, Special Publications, 73, 421–432. Giannopoulos, A., 1997. The investigation of transmission-line matrix and finite-difference time-domain methods for the forward problem of ground penetrating radar, Ph.D. thesis, University of York, York, England. Giannopoulos, A., 2005, Modeling ground penetrating radar by GprMax: Constructions and Buildings Materials, 19, 755–762. Grumman, D. Jr., and Daniels, J., 1995, Experiments on the detection of organic contaminants in the vadose zone: Journal of Environmental and Engineering Geophysics, 1, 31–38. Holliger, K., and Bergmann, T., 2002, Numerical modeling of borehole georadar data: Geophysics, 67, 1249–1257. Irving, J., and Knight, R., 2006, Numerical simulation of antenna transmission and reception for crosshole ground-penetrating radar: Geophysics, 71, 37–45. James, P.C., and Erich, D.G., 2005, Borehole tomography and surface 3D radar for coal mine subsidence detection: Electronic Journal of Geotechnical Engineering, 10, 1–20. Kemp, C., Smith, K., Bray, A., Mason, I., and Sindle, T., 2009. Imaging an orebody ahead of mining using borehole radar at the snap lake diamond mine, Northwest Territories, Canada, Seventh International Mining Geology Conference, Perth, WA, 17–19. Kobayashi, Y., and Katoh, M., 1985, Microwave measurement of dielectric properties of low-loss materials by the dielectric rod resonator method: IEEE Transactions on Microwave Theory and Techniques, 33, 586–592. Lane, J.W. Jr., Haeni, F.P., and Williams, J.H., 1994, Detection of bedrock fractures and lithologic changes using borehole radar at selected sites: in Proceedings of the Fifth International Conference on Ground Penetrating Radar, Kitchener, Ontario, Canada, 1994, Waterloo, Ontario, Waterloo Center for Groundwater Research, 557–592. Liu, L.B., 2006, Fracture characterization using borehole radar: Numerical modeling: Water, Air, and Soil Pollution: Focus, 6, 17–34. Lytle, R.J., Lager, D.L., Laine, E.F., and Davis, D.T., 1976, Using cross-borehole electromagnetic probing to locate a tunnel: Prepared for U.S. Energy and Research & Development Administration under contract No. W7450-Eng-48, Lawrence Livermore Laboratory, University of California. Ma, C.G., Zhao, Q., Ran, L.M., and Chang, X.H., 2014, Numerical study of borehole radar for cliff imaging: Journal of Environmental and Engineering Geophysics, 19(4), 269–276.

Mafiri, M.T., Nyareli, T., Ngwenya, B., and Vogt, D., 2008, Borehole radar as a tool to optimize mine layouts and production: 2nd CSIR Biennial Conference, CSIR International Convention Centre Pretoria, 1–9. Mansour, K., and Sato, M., 2012, Subsurface fracture characterization using full polarimetric borehole radar data analysis with numerical simulation validation: Exploration Geophysics, 43, 125–135. Mukhopadhyay, P.K., Inggs, M.R., and Wilkinson, A.J., 2005, FDTD modelling of a borehole radar wave propagation: A 3-D simulation study in conductive media: in Proceedings of Geoscience and Remote Sensing Symposium (IGARSS), 2, 1353–1356. Muhkopadhyay, P.K., Wilkinson, A.J., Bennett, T., and Inggs, M.R., 2009, Modeling borehole radar electromagnetic wave propagation in conductive media by implementation of parallel three-dimensional finitedifference time domain technique: Geohorizons, 17–26. Nickel, H., Sender, F., Thierbach, R., and Weichart, H., 1983, Exploring the interior of salt domes from boreholes: Geophys. Prospect., 31, 131–148. Olsson, O., Falk, L., Forslund, O., Lundmark, L., and Sandberg, E., 1992, Borehole radar applied to the characterization of hydraulically conductive fracture zones in crystalline rock: Geophys. Prospect., 40, 109–142. Slob, E., Sato, M., and Olhoeft, G., 2010, Surface and borehole ground-penetrating-radar developments: Geophysics, 75, 103–120. Stevens, K.M., Lodha, G.S., Holloway, A.L., and Soonawala, N.M., 1995, The application of ground penetrating radar for mapping fractures in plutonic rocks within the Whiteshell Research Area, Pinawa, Manitoba, Canada: Journal of Applied Geophysics, 33, 125–141. Taflove, A., 1995. Computational electrodynamics: The finitedifference time-domain method, Artech House, Norwood, MA, 1–30. Takahashi, K., and Sato, M., 2005, Estimation of a buried pipe location by borehole radar: in Proceedings: Geoscience and Remote Sensing Symposium (IGARSS), 1, 304–307. Teixeira, F.L., Chew, W.C., Straka, M., Oristaglio, M.L., and Wang, T., 1998, Finite-difference time-domain simulation of ground-penetrating radar in dispersive, inhomogeneous, and conductive soils: IEEE Transactions on Geoscience and Remote Sensing, 36, 1928–1937. Teixeira, F.L., and Chew, W.C., 2000, Finite-difference computation of transient electromagnetic waves for cylindrical geometries in complex media: IEEE Transactions on Geoscience and Remote Sensing, 38, 1530–1543. Thierbach, R., Eisenburger, D., Sato, M., and Kim, J.H., 2008, Development of ground penetrating radar in the Geocenter Hannover, Germany – A review: Proceedings of the 2008 IEEE International Conference on UltraWideband, 3, 171–174. Wang, D., and McMechan, G.A., 2002, Finite-difference modeling of borehole ground penetrating radar data: Journal of Applied Geophysics, 49, 111–127. Williams, J.H., Lane, J.W. Jr., Singha, K., and Haeni, F.P., 2002, Application of advanced geophysical logging

29 Ma et al.: Modeling BHR by FDTD in Conductive Sandstone methods in the characterization of a fractured-sedimentary bedrock aquifer, Ventura County, California: U.S. Geological Survey, Report No. WRIR 00-4083, 1–28.

Yee, K.S., 1966, Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media: IEEE Trans. Antennas and Propagat. AP- 14, 302–307.