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SPECIAL SECTION: SOIL WATER SENSING

Numerical Modeling of GPR to Determine the Direct Ground Wave Sampling Depth

^a Department of Agricultural Engineering, University of Peradeniya, Peradeniya, KY 20400, Sri Lanka
^b Sensors and Software Inc., Mississauga, ON, L4W 3R7, Canada
^c Dep. of Land Resource Science, University of Guelph, ON, N1G 2W1, Canada
^d Dep. of Earth Science, University of Waterloo, Waterloo, ON, N2L 3G1, Canada
^* Corresponding author (gparkin{at}uoguelph.ca)

Received 29 September 2004.

	ABSTRACT

TOP ABSTRACT INTRODUCTION METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
The direct ground wave method of ground penetrating radar (GPR) has been suggested as a cost-effective means of estimating field-scale soil moisture variability for irrigation and water resource management. Knowing the sampling depth of the GPR direct ground wave (GW) is very important because it is critical to know the depth when measuring soil moisture in the field. Few studies have addressed this particular aspect of the GPR method. Numerical simulation of GPR electromagnetic waves using GPRMAX2D was performed for two-layer soil models to estimate the direct GW sampling depth for soil moisture. Dry over wet soil layers and wet over dry soil layers were modeled by using appropriate dielectric permittivity values for each layer. Model runs were conducted for a gradually decreasing upper layer thickness. The GW sampling depth was estimated as the upper dry or wet layer thickness when the modeled GW velocity decreased or increased by 5% as affected by the lower wet or dry layer, respectively. It was found from this modeling exercise that the GW sampling depth changed with the antenna frequency as well as the moisture content of the upper layer. A very strong linear relationship (r² = 0.98) was found between the wavelength and the sampling depth of the GPR direct GW.

Abbreviations: CMP, common mid point • EC, electrical conductivity • FDTD, finite-difference time-domain • GPR, ground penetrating radar • GW, ground wave • TDR, time domain reflectometry

	INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
SOIL MOISTURE content is an important parameter in many field applications, such as irrigation management, contaminant transport, and crop yield. Gravimetric sampling, neutron scattering, capacitance sensors, and time domain reflectometry (TDR) are methods used to measure field soil moisture at small scales (Hillel, 1997). Time domain reflectometry is widely accepted as an accurate method, but it is labor intensive when measuring soil moisture at the field scale (Nielsen et al., 1995; Topp et al., 1980, 1982; Whalley, 1993; Cassel et al., 1994).

Ground penetrating radar methods are showing promise for estimating soil moisture content (Davis and Annan, 2002; Huisman et al., 2003). Specific methods include the direct GW method (Du and Rummel, 1994; Huisman, 2002; Hubbard et al., 2002), the common mid point (CMP) method utilizing subsurface reflection events such as the water table (Greaves et al., 1996; van Overmeeren et al., 1997; Vellidis et al., 1990), the surface reflectivity method (Chanzy et al., 1996; Redman et al., 2002) and the borehole GPR method (Galagedara et al., 2003a; Parkin et al., 2000; Redman et al., 2000; Rucker and Ferré, 2002). The direct GW method, the subject of this paper, may be suitable for cost-effective measurement of soil moisture variability at the field scale, but more information on sampling depth is needed.

The main reason that GPR methods of measuring soil moisture are of interest is that they provide a means to monitor large areas and soil volumes relatively quickly. The methods listed above typically sample volumes much less than 1 m³ and, because they are intrusive, are best suited for monitoring at a single location vs. time. On the other hand, GPR equipment generally samples volumes of 1 m³ or more and can be easily moved from place to place since it is nonintrusive.

With all indirect soil moisture measurement techniques it is important to understand their sampling volume. With the GPR direct GW method, neither the effective sampling area nor sampling depth is easily quantified. The sampling area can be roughly described as the region on the surface between the transmitter and receiver. The sampling depth is more critical since it is important to know that the method is sampling the moisture content in the depth interval of interest. Several authors have concluded experimentally that the direct GW sampling depth, the subject of this paper, is restricted to the near surface, perhaps <0.2 m below the surface. Others have shown that it is also frequency dependent (Chanzy et al., 1996; Du and Rummel, 1994; Galagedara et al., 2003b, 2005; Grote et al., 2003; Hubbard et al., 2002; Huisman et al., 2001).

Our main objective in this study was to investigate the effective sampling depth of the GPR direct GW using a two-layer electromagnetic wave numerical model, GPRMAX2D (Giannopoulos, 2002). GPR data sets were generated from this model for a range of frequencies, soil moisture contents and relatively low soil electrical conductivities (EC). High EC soils were not investigated, as Davis and Annan (2002) state that the GPR method is most promising for low EC soils (i.e., <0.02 Sm^–1).

	METHODS

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Ground Wave
When a GPR transmitting antenna is located on the soil surface at the soil–air interface, radar energy is radiated spherically both into the air and ground. This is shown in Fig. 1 for a GPR transmitting antenna that is modeled as an infinite line source. The direct GW, which travels directly from the transmitter antenna to the receiver antenna just below the soil surface is evident as an evanescent wave b in the diagram and the spherical ground wave B below the air–soil interface. A single GW velocity V can be calculated by dividing the travel distance (antenna offset) x by the measured GW travel time (V = x/t). On the other hand, several travel times t₁, t₂,...t_n for the direct GW can be measured by changing the antenna offsets, such as x₁, x₂,... x_n, where n is the number of offsets. Then the average GW velocity is calculated using the inverse slope of the time-offset relationship (Galagedara et al., 2003b). The estimated GW velocity V is converted to the relative dielectric permittivity _r using the speed of light c [_r = (c/V)²]. Volumetric water content can then be estimated using the Topp et al. (1980) empirical relationship or a similar mixing relationship between water content and dielectric permittivity of the soil.

View larger version (8K): [in this window] [in a new window]   Fig. 1. Common GPR wave fronts from a line source (s) kept at the air–soil interface: A and B are spherical waves, C is lateral (head) wave, and b is evanescent wave in air. Direct ground wave (GW) is a combination of B near the interface and b (after Annan, 1973).

The following method was used to determine the effective sampling depth of the GPR GW. The GPR response for a two-layer soil profile was calculated using the GPRMAX2D modeling software for upper layer thicknesses that varied from 0 to 2 m. The GPR response for each model was computed for a set of receiver to transmitter separations to simulate a CMP survey.

The GW velocity was calculated for each of the model runs using an analysis technique that has been applied to field data by Galagedara et al. (2003b). The effective GW sampling depth was then defined as equivalent to the largest modeled upper layer thickness for which the calculated GW velocity differed by an arbitrarily chosen 5% from the velocity of the upper layer as a result of the influence of the lower layer. This modeling process was performed for antenna center frequencies from 100 to 900 MHz and for the cases of a wet soil (large _r) over a dry soil (small _r) and a dry soil over a wet soil.

Two-Layer Model: CMP Method
One of the two-layer soil models used for GPR direct GW penetration depth determination is shown in Fig. 2 . The other model was configured with the same dimensions, but as a wet over dry soil layer system. Common mid point surveys were simulated by starting with a transmitter to receiver antenna separation of 0 m at the middle of the model domain; then the antenna separation was increased by a constant increment. For each antenna offset the numerical modeling was performed to compute the time dependence of the electric field strength at the receiving antenna during and following the transmission of a short pulse from the transmitting antenna. This set of amplitude vs. time data is referred to as a GPR trace.

View larger version (14K): [in this window] [in a new window]   Fig. 2. Schematic diagram of conceptual two-layer model (2 by 4 m domain) for GPR direct ground wave modeling for the dry soil over wet soil model. r is relative dielectric permittivity. The air layer at the top was always 0.2 m thick.

Each simulated CMP survey was used to calculate the direct GW velocity using the inverse slope of the time-offset relationship. Ten different model runs (Models A to J) were performed with different model configurations, frequencies, and soil electrical conductivities as shown in Table 1. For example, the response of Model A for dry soil (_r = 5) over wet soil (_r = 15) layers with zero electrical conductivity was simulated for four frequencies. For Model Runs A to D, an artificial soil was used with arbitrary _r values of 5 and 15 for dry and wet soil conditions, respectively. To investigate GW sampling depths under more realistic wet and dry soil conditions, a sandy loam soil, using water contents equivalent to the wilting point and field capacity was also studied (Model Runs E–J). Wilting point and field capacity of the sandy loam soil were calculated using Campbell's equation:

[1]

where _v (m³ m^–3) is the volumetric moisture content, matric potential (–10 kPa for field capacity and –1500 kPa for wilting point), _s (m³ m^–3) is volumetric moisture content at saturation (equal to porosity) and a (–1.5 kPa) and b (3.7) are Campbell's constants for a sandy loam soil (Roy et al., 2001). According to Eq. [1], volumetric water contents were found to be 0.064 and 0.25 m³ m^–3 for wilting point and field capacity, respectively. Electrical conductivity values were calculated for the partially saturated sandy loam soil using Archie's formula as explained by Reynolds (1997) and Telford et al. (1990).

View this table: [in this window] [in a new window]   Table 1. Soil physical properties used in the two-layer models of GPR electromagnetic radiation with different frequencies.

The numerical modeling results described below were computed using GPRMAX2D, a finite-difference time-domain (FDTD) two-dimensional algorithm developed by Giannopoulos (1997). A standard Ricker wavelet was used to describe the source pulse shape. The source in this two-dimensional model is an infinite line source that has different spreading characteristics from the finite dipole source used in GPR, resulting in a modified pulse shape and reduced amplitude fall off with distance compared with a dipole source. This has no effect on the travel times computed from the modeling, or the general propagation characteristics, but will affect the amplitude of events observed at the receiver. The model domain (x, y) size is 4.0 by 2.0 m with a spatial discretization of 0.005 and 0.005 m for 200-, 450-, and 900-MHz model runs. For the 100-MHz model runs, the model domain (x, y) size is 6.0 by 3.0 m with a spatial discretization of 0.01 and 0.01 m. The temporal discretization is a function of the spatial discretization (Giannopoulos, 2002). The Higdon-type absorbing boundary condition is used in GPRMAX2D (Giannopoulos, 1997).

	RESULTS AND DISCUSSION

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GPR Wave Fronts in a Two-Layer Soil Model
To understand the EM propagation for a two-layer soil model, it is instructive to view a model of the propagating wave fronts. A snapshot of the electric field strength at suitable delay times after the transmitter pulse was generated is shown for the case of a dry soil over a wet soil in Fig. 3A and for a wet soil over a dry soil in Fig. 3B. It is clear that these two cases produce distinctly different propagation characteristics. These wave fronts are described below.

View larger version (44K): [in this window] [in a new window]   Fig. 3. Simulated wave fronts from a 1000-MHz line source on the soil for a two-layer soil model. The vertical positions of the soil surface and dry or wet layer are 250 and 275 cm, respectively, in the model: (A) dry over wet soil layer case, (B) wet over dry soil layer case.

Wet Soil Over Dry Soil
The spherical airwave is not present because it has moved out of the modeled spatial domain at the larger delay time of 15 ns in Fig. 3B. Wave fronts A¹ and A² are "spherical" airwaves reflected from the subsurface interlayer boundary and emitted into the air. B and B¹ are the direct "spherical" waves in Layer 2. The head or lateral wave that is tied to the "spherical" airwave A¹ is C¹. Waves D and D¹ are the spherical GWs in Layer 1, and critically refracted head wave from Layer 2 in Layer 1, respectively. D² and D³ are "spherical" waves reflected from the subsurface interface and air–soil interface, respectively. Wave front b is the evanescent wave from Layer 1 in air and b¹ is the evanescent wave from the critically refracted wave from Layer 2. The direct GW can be viewed as composed of Layer 1 evanescent combination (D and b) and critically refracted wave from Layer 2, which is also an evanescent combination (D¹ and b¹) in air. Identification and separation of these two components can be very difficult (sometimes impossible) in real field data. The reflected spherical wave from the subsurface interface that has been reflected downward from the air–ground boundary is E.

Synthetic Data Analysis: CMP Survey
Figure 4A and 4B show the simulated CMP data for the cases of the dry over wet layer and wet over dry layer, with the upper layer of sufficient thickness to show no effect of the lower layer on the GW velocity. Each figure shows the direct airwave, direct GW and the reflected wave from the wet–dry or dry–wet layer interface. The velocity of the direct GW was calculated from the inverse slope of the regression line and was found to be 0.134 m ns^–1 (for _r1 = 5) for the dry over wet layer model and 0.077 m ns^–1 (for _r2 = 15) for the wet over dry layer model.

View larger version (33K): [in this window] [in a new window]   Fig. 4. Some raw data obtained from CMP surveys using GPRMAX2D with 450-MHz frequency: (A) dry (r = 5) soil over wet (r = 15) soil layer model, (B) wet (r = 15) soil over dry (r = 5) soil layer model. The stars give locations of ground wave peaks used to determine the velocity.

Ground Wave Velocity Analysis
Dry Soil Over Wet Soil Layer Model (Nonconducting Case)
Figure 5 shows the GW velocity computed using the CMP method described previously and the calculated soil moisture content dependence on depth to the wet layer for the dry soil over wet soil case and for GPR center frequencies of 100, 200, 450, and 900 MHz. As the upper dry layer thickness decreases (wet layer moves closer to the soil–air interface at the surface), the GW velocity decreases as the influence of the wet layer becomes detectable. The GW sampling depth is assumed to be equivalent to the upper layer thickness when the GW velocity begins to be affected by the lower layer (GW velocity decreases due to the low velocity of the lower wet layer). It is clear in Fig. 5 that the GW sampling depth varies with frequency as the velocity and moisture content start to change at different depths to the wet layer. The sampling depth, as expected, increases as the GPR center frequency decreases. The sampling depths of the GW were found to be 0.85 m for 100 MHz, 0.38 m for 200 MHz, 0.26 m for 450 MHz, and 0.13 m for 900 MHz (Model A in Table 2).

View larger version (23K): [in this window] [in a new window]   Fig. 5. (A, C) Variation of the ground wave velocity and (B, D) the estimated soil moisture for four different frequencies obtained from dry soil over wet soil model.

Wet Soil Over Dry Soil Layer Model (Nonconducting Case)
The velocity variations of GPR direct GW with respect to the thickness of the upper wet layer (depth to the dry layer) for different frequencies and estimated soil moisture contents are shown in Fig. 6 . As seen in Fig. 6A, the GPR ground wave sampling depth for 100 MHz is 0.58 m, while it is about 0.26 m for 200 MHz. On the other hand, the sampling depths of the GW for 450- and 900-MHz frequencies were found to be 0.16 m and <0.09 m, respectively (Model B in Table 2).

View larger version (23K): [in this window] [in a new window]   Fig. 6. (A, C) Variation of the ground wave velocity and (B, D) the estimated soil moisture for four different frequencies obtained from wet soil over dry soil model.

In Fig. 5 and 6 it was not possible to determine GW velocities for some of the modeled cases. When the upper layer thickness decreases to a certain amount, the GW could not be clearly identified due to interference from the reflected wave from the layer interface below. This problem can be avoided by calculating the velocity at larger offsets using the squared antenna offset distance, x², vs. squared travel time, t², relationship of the reflected wave where the GW and reflected wave velocities approach similar values (Reynolds, 1997). However, this approach requires sharp boundaries of moisture content, which are not always available to provide a strong reflected event. Also, using large antennae offsets decreases the spatial resolution of soil moisture measurements and increases the time required to collect the data in the field. It was found that continuous data could be obtained if the contrast was very low between the two layers, such as dielectric permittivities of 14 and 15. Practically in the field, this is difficult to attain if a sharp boundary exists such as a wetting front during an irrigation event.

Penetration Depth and Moisture Content Variation Under Different Dielectric Permittivity
To further investigate the sampling depth of the GPR direct GW, different soil moisture conditions were introduced to the two-layer model by changing the dielectric permittivity values in GPRMAX2D program commands. The GPR direct GW simulations were performed to investigate the moisture content dependence on the GW sampling depth using 200- and 450-MHz center frequencies. For the dry soil over wet soil layer case the upper dry layer dielectric permittivity was increased from 5 to 8 (0.15 m³ m^–3 moisture content) while keeping the lower wet layer values at 15 (Model C in Table 1) for both frequencies. For the wet over dry soil layer case, dielectric permittivity of the upper wet layer was increased to 20 (0.35 m³ m^–3 moisture content) while keeping the lower dry layer dielectric permittivity at 5 for the 450-MHz center frequency (Model D in Table 1). Results for these analyses with different moisture contents are given in Table 2. When comparing dry soil over wet soil layer model results for the 200-MHz frequency with sampling depths for Models A and C, the sampling depth is decreased from 0.38 to 0.34 m when dielectric permittivity increases from 5 (0.08 m³ m^–3) to 8 (0.15 m³ m^–3). The same effect on the sampling depth (reduction from 0.26 to 0.20 m) was found when increasing the soil moisture as seen between Model Results A and C with the 450-MHz frequency. On the other hand, the wet soil over dry soil layer model also shows a reduction in sampling depth when the upper wet layer dielectric permittivity is increased from 15 (0.28 m³ m^–3 moisture) to 20 (0.35 m³ m^–3) with the 450-MHz frequency (Models B and D in Table 2). Data in Table 2 with respect to Models A, B, C, and D show that the GW sampling depth is highly dependent on the GPR frequency, but when a dry layer is present at the surface, the sampling depth is greater than having a wet layer at the surface. Detailed results can be found in Galagedara (2003).

Electrical Conductivity Effect on GPR Ground Wave Sampling Depth
For the case of soil water electrical conductivity >0, modeled dielectric permittivities ranged from 4.4 (wilting point of 0.06 m³ m^–3) for the dry soil layer to 13.4 (field capacity of 0.25 m³ m^–3), as shown in Table 1.

Ground penetrating radar GW velocity variations (450 MHz) and the sampling depth variability due to different electrical conductivity values were analyzed (Galagedara, 2003). As shown in Table 1, Models E, F, and G were used to determine the sampling depth dependence for zero, small, and large EC values, respectively, for the case of dry soil over wet soil. Similar EC values were used for wet soil over dry soil layer model when Model Runs H, I, and J were completed (Table 1).

The GPR direct GW sampling depth variability due to different EC values is given in Table 2. As shown, the estimated sampling depths are similar (0.24 m) for all three EC values used for dry soil over wet soil layer model (Model Results E, F, and G). However, the maximum upper dry layer thickness decreases with increasing EC. This could potentially be due to the difficulty in picking the direct GW arrival time in the lower (wet) layer with decreasing wave amplitude (with increasing conductivity). The GPR direct GW sampling depth was found to be in the range of 0.16 to 0.18 m for wet soil over dry soil layer model with three different conductivity values (Model Results H, I, and J in Table 2). The maximum upper wet layer thickness is not consistent for different conductivity values, but ranges between 0.06 to 0.10 m as seen in Table 2. The maximum upper layer thickness (when the GW was traveling entirely through the lower layer) was affected by changing the EC value in the lower layer. Once again, this is mainly due to the difficulty in picking the GW arrival time when high EC severely decreases the signal amplitude.

Dependence of the GPR Ground Wave Sampling Depth on Frequency
Variation of the effective GW sampling depths was compared against the respective frequency for dry over wet layer model (dry layer _r = 5 and V = 0.134 m ns^–1) and wet over dry layer model (wet layer _r = 15 and V = 0.077 m ns^–1). The GW sampling depths closely followed the same pattern for both the dry over wet and wet over dry conditions, with respect to the frequency, with very high correlation (r² = 0.98 for both functions) using a simple power function (data not shown). This function shows greater dependency of GW penetration depth on the wavelength, which itself is a function (inverse power relationship) of the frequency. The best-fit functions to the GW sampling depths with respect to frequency (inversely proportional relationships) are given in Eq. [2] (dry over wet) and [3] (wet over dry), respectively:

[2]

[3]

where D_d is the GW sampling depth for dry over wet layer model, D_w is the GW sampling depth for wet over dry layer model, and f is the frequency.

To compare the results of this study with previous work, an investigation of the relationship between sampling depth and wavelength for dry over wet and wet over dry cases combined was undertaken (Fig. 7) . Linear regression analysis of the data in Fig. 7 gives:

[4]

where D is the GW sampling depth for both layer configurations and is the wavelength. Du (1996) (in Huisman et al., 2003) suggested that the GW sampling depth is approximately one-half of the wavelength, similar to Eq. [4]. In fact, the lower 95% confidence limits on the slope and intercept of Eq. [4] are 0.51 and –0.01, respectively. On the other hand, Sperl (1999) (in Huisman et al., 2003) reported that the depth of sampling is a function of wavelength and from a modeling exercise shows that the sampling depth is 0.145^1/2. A comparison of GW influence depths calculated with the three models (this study; Du, 1996; Sperl, 1999) is given next.

View larger version (15K): [in this window] [in a new window]   Fig. 7. Variation of the GPR ground wave influence depth with respect to the wavelength in both the dry over wet and wet over dry layer cases.

View larger version (25K): [in this window] [in a new window]   Fig. 8. Variation of GPR ground wave sampling depth (predicted using Eq. [4]) with respect to soil moisture content for four different frequencies. Predicted sampling depths by Du (1996) and Sperl (1999) are also included for comparison.

View this table: [in this window] [in a new window]   Table 3. The predicted ground wave sampling depth with respect to low and high soil moisture contents for four different frequencies.

Evaluation of Apparent Moisture Content Estimated with the Model Calculated Ground Wave Velocity with Respect to True Moisture Content in Two-Layer Models
In this study, the GW velocities were calculated from inverse slopes of time–offset CMP relationships by picking the peak arrival time of the GW. This analysis was performed for each model run for both dry soil over wet soil and wet soil over dry soil layer models using the dielectric permittivities of 5 and 15 for dry and wet layers, respectively (Model Runs A and B, Table 1). Estimated (apparent) radar wave velocities V_app were converted to apparent volumetric soil moisture contents (_app) using the Topp et al. (1980) method. As explained in the methods section, changing the depth to the wet or dry layer produced the different two-layer model runs. This variable layer thickness allowed for dielectric permittivity variability (i.e., changing moisture content) with depth. The GPR ground wave sampling depth with respect to the wavelength can be calculated using Eq. [4] in which the wavelengths were estimated using the V_app and the respective frequency, f (wavelength = V_app/f).

The true _r (depth-weighted arithmetic average of the two _r values within the GPR GW sampling depth calculated with Eq. [4]) was calculated and converted to true average soil moisture content (_true) for each GW sampling depth. The estimated apparent moisture contents (_app) are compared with true moisture contents (_true) in Fig. 9 . As seen in Fig. 9, the apparent and true moisture contents scattered around a 1:1 line for both the wet over dry and dry over wet cases. Regression using both wet over dry and dry over wet conditions shows that the slope is equal to 1, and the intercept is equal to 0 at the 99% confidence level with an r² of 0.96. It is well known that TDR probes measure true arithmetic average soil moisture content weighted equally along the entire depth range of the waveguides; however, a linear weighting function has never been shown for the GPR direct GW method. Nonlinear weighting function(s) for GPR could be the reason for the data scatter in Fig. 9 and will be the subject of future modeling work.

View larger version (15K): [in this window] [in a new window]   Fig. 9. Comparison of apparent moisture content estimated using the calculated ground wave velocity and true average moisture content. Overall RMSE = 0.017 m3 m–3.

	CONCLUSIONS

TOP ABSTRACT INTRODUCTION METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 
Ground penetrating radar direct GW penetration depth was analyzed numerically with GPRMAX2D, which solves Maxwell's equation using a FDTD method. It was found from the CMP analysis that the GW sampling depth changes according to the two modeling approaches used in this study. The GW sampling depth was negatively correlated with GPR frequency. Also, the GW sampling depth was found to be deeper for the dry over wet layer model compared with the wet over dry layer model. However, no significant effect was found for the GW sampling depth with different electrical conductivities used in the models with the 450-MHz frequency. Also, it was found that when increasing the upper layer moisture content in both models of dry over wet soil and wet over dry soil, the GPR direct GW sampling depth decreased. A strong positive linear relationship with very high correlation coefficient was found between the GW sampling depth and the wavelength. The estimated sampling depths were greater than those calculated with two other methods, possibly due to the way in which the GPR sampling depth was defined in this study. Apparent moisture content estimated using the GW velocity and the true linear average moisture content from the model are scattered around the 1:1 line, where the slope is statistically equal to 1 and the intercept is equal to 0.

	ACKNOWLEDGMENTS

 
The authors wish to acknowledge Ontario Ministry of Agriculture and Food (OMAF) and Natural Science and Engineering Research Council of Canada (NSERC) for providing the financial support. Very special thanks are given to Dr. A. Giannopoulos of the University of Edinburgh, Scotland, UK for providing the GPRMAX2D model free of charge. Kevin Kingdon of Sensors and Software Inc. gave excellent support in GPR simulation.

	REFERENCES

TOP ABSTRACT INTRODUCTION METHODS RESULTS AND DISCUSSION CONCLUSIONS REFERENCES

 

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