沙漠研究 19-1, 121- 124 (2009 )Journal of Arid Land Studies“Desert Technology IX ”
Refereed Paper

Estimating Depth of Influence of GPR Ground Wavein Lysimeter Experiment
Baby PALLAVI1, Hirotaka SAITO1, Makoto KATO1
Abstract: To map the surface soil moisture content with GPR at an intermediate scale, the soil
dielectric constant needs to be determined from the ground wave velocity. However, thedepth of influence of ground wave is still not well defined. In the present study, shallow waterboxes were placed at near surface (0-20 cm) inside the lysimeter to evaluate the effect on theground wave and to compare with the theoretical depth of influence using Sperl and Van
Overmeeren models. Results revealed an increase in dielectric constant with all water box
measurement until 15 cm depth. While at 20 cm depth observed K value was found similar asof background soil. The theoretical prediction of GW depth using both models was foundinsignificant in the present study. Experimentally observed result signifies that the depth of
influence of GW was similar to the quarter of the wavelength.
Keywords: Depth of influence, Dielectric constant, Ground penetrating radar (GPR), Ground wave

1. Introduction
In agricultural management, spatial distribution of soil moisture content is a key parameter for
optimizing crop yields, achieving high irrigation efficiencies, minimizing lost yields due to water logging
and salinization (Hubbard et al., 2002). Available techniques to assess spatial variations of the moisture
content are either suited to measure small-scale or large-scale variations. Ground-penetrating radar (GPR)
allows one to explore the subsurface in a field scale using electromagnetic (EM) energy at frequencies of
10–1200 MHz (Davis and Annan, 1989).
Among different approaches, the ground wave (GW), one of direct waves recorded in GPR
measurements, is of interest in mapping surface soil moistures. Direct waves are those travel directlyfrom the transmitter to the receiver through the air and along the soil surface. GW is the one travels along
the soil surface. The advantage of using GW is that, unlike all reflected or refracted waves, the travel
distances are known. However, the sampling volume of GW is still poorly understood, in other words, thedepth of influence of GW is not well defined. Several authors evaluated the depth of influence bycomparing water content point estimates measured with TDR probes or gravimetric columns with the GPR
measurement (Galagedara et al, 2003; Grote et al., 2003). However comparing with point measured
moisture content values is very questionable because the measurement volume of GPR is clearly bigger
than that of the point measurement.
The main goal of the present study was then to investigate the influence zone of GW using only GPR
information. To estimate the depth of influence of GW, lysimeter experiments were conducted with nearsurface heterogeneity created by placing a large anomaly near the surface.
2. Materials and Methods
2.1. Lysimeter Setup
A wooden lysimeter (180 × 90 × 90 cm) filled with river sand was used to examine the depth of
influence of GW. The textural class of the soil was sand as determined by the grain size analysis.
Different sets of near surface heterogeneity were created by placing shallow plastic boxes filled with waterin the centre of the lysimeter at varying (0-20 cm) depths. Plastic Boxes were used because the dielectric
constant is similar to that of the background sand. Water filled boxes were used because of high contrasts
in the dielectric constant with that of the background soil. As the moisture content in soil increases, theEM velocity decreases. Water boxes in four different dimensions were used (Table 1). The top view ofthe experimental setup with Box-I and GPR antennas is depicted in Figure 1. Similar setups wereachieved for different boxes changing the placement depth only (0, 5, 10, 15 and 20 cm). Boxes were1

United Graduate School of Tokyo University of Agriculture and Technology, 3-5-8 Saiwai-cho, Fuchu, Tokyo
183-8509 Japan.

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Table 1. Dimensions of water boxes.
XTx

Rx Y

38 cm

90 cm

S = 38 cm

180 cmWater box Dimensions (cm)
[X; Y; Z]
Box-I
24 x 31.5 x 2.5

Area(cm2)
756

Volume(cm3)1,890

Box-II48 x 31.5 x 2.5

1,512

3,780

Box-III

24 x 31.5 x 5

756

3,780

Box-IV12 x 36 x 3.5

432

1,512

Fig. 1. Schematic top view of the lysimeter with
Box-I and antennas placements.

always placed in the same manner as shown in Figure 1. When the boxes were placed at 0 cm depth, theupper surface of the box and the soil surface were kept at the same level. The GPR measurements wereconducted using a pulseEKKO pro 250 system, which has a 250 MHz central frequency.
2.2. Theoretical Background of GPR
In GPR, the transmitter radiates energy spherically both into air and ground. The receiving antenna
subsequently records the modified signals. The wave propagates through the soil is reflected, scatteredand attenuated by subsurface dielectric contrasts (Fig. 2). The first strong signal usually represents
airwave (AW), which travels directly from the transmitter to the receiver through the air at the speed of theEM wave in vacuum. GW travels between the transmitter and the receiver along the soil surface. The
propagation velocity of GW (vgw) depends on the dielectric constant of the soil K (in other words, themoisture content θ). The velocity (vgw) is calculated by dividing the antenna separation (S) by the groundwave travel time (GWTT: tgw);

v gw =S(1)t gw

The dielectric constant K is then calculated by the following equation (Davis and Annan, 1989),⎛ c ⎞K ≈⎜ ⎟⎜v ⎟⎝ gw ⎠2(2)where c is the speed of the EM wave in vaccum (3 × 108 m/s). The volumetric water content is thenobtained from K using one of the empirical models, such as the Topp equation (Topp et al., 1980). Two
different models have been proposed to calculate the depth of influence of GPR ground wave (Dgw). First
model is proposed by van Overmeeren et al. (1997), who adapted the seismic approximation.
1 v gw S(3)Dgw =2fThe second model is proposed by Sperl (Huisman, 2003),v gw(4)
Dgw = 0.145
fAntenna separation (S)where f is the central frequency of GPR (Hz).
Air wave
Rx
Tx
2.3. GPR Survey
Two common GPR acquisition approaches;common midpoint (CMP) and common offset (CO),were used in this study.
2.3.1. Common-midpoint (CMP) Approach
In CMP, the separation distance between twoantennas are increased in a constant step size, while

Ground wave
Reflection
depth (d)Reflectedwave

Transmittedwave
Mid point
Reflecting layer

Fig. 2. Schematic diagram of travel path of waves
at a single offset (Lunt et al., 2005)

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keeping the mid point common (Fig. 2). As the distance between two antennas increases, the EM wave
travel time also increases. The EM wave velocity is then the inverse of the linear slope obtained byplotting GWTT as a function of the antenna separation.
2.3.2. Common-offset (CO) Approach
In CO, two antennas are moved along the survey line by keeping the distance between the transmitterand the receiver constant. This mode is easy to operate, provides rapid measurement and is used widely
in mapping purposes. However, proper time-zero calibration is inevitable. Time-zero is defined as thetime when EM pulse starts and all other arrival times need to be analyzed with respect to this time. Each
GPR system has an inherently defined time zero, but it cannot be directly obtain. Instead, there areapproaches to indirectly estimate time-zero. One approach is to use AW (referred to as AW time-zero
calibration). Since the true AW travel time (AWTT) can be estimated by dividing the antenna separationby the speed of light, we can readily obtain time zero by subtracting AWTT from the AW pick. This may
not be an ideal option as time-zeros for AW and GW are usually different. Another approach, referred toas the CMP time-zero calibration, is then to use the CMP measurement where one can obtain the true GW
velocity. From the true velocity, true GWTT can be calculated, which is then subtracted from the GW
pick to determine the CMP calibrated time-zero.
3. Results and Discussion
The profile of the lysimeter sand without an anomaly obtained with the CMP survey is shown inFigure 3 with AW and GW picked. The estimated GW velocity was 0.16 mns-1, which was converted todielectric constant (K= 3.53) using Eq. (2). Point measurements were also made using the gravimetricmethod and soil moisture sensors to compare with GPR data. All these point measurements gave thevolumetric water content estimates, which were converted to dielectric constants using the Topp equation.
The estimated dielectric constant of 3.17 from reference point measurements showed a small differencewith that obtained from the CMP survey. The moisture content for K= 3.17 corresponds to 0.034 m3m-3
and that for K= 3.53 corresponds to 0.043 m3m-3 based on the Topp equation.
In the next experiment, measurements with water boxes were conducted. The CO survey with a
0.38-m antenna separation was conducted to observe the response of an anomaly on the single trace data.
The single trace data of the sand and the sand with Box-I are given in Figure 4. The first strong trough(minimum amplitude) was picked as AW, while the next minimum for the GW. The amplitude of AWfor the sand and the sand with Box-I was same as expected, but amplitudes were different between the twofor GW and others due to the existence of the anomaly. The GWTT of the sand collected from raw dataof the CO survey was 5.48 ns, whereas that corrected by the AW time zero was 4.09 ns and that correctedby the CMP time zero was 2.38 ns. As the CMP survey gives more accurate information, the CMP
calibrated time zero was used to calculate the velocity and the dielectric constant for all anomaly setups in
the remainder of the paper.
The estimated dielectric constants for all four boxes placed at the depth of 0 to 20 cm inside thelysimeter are shown in Figure 5. For Box-I, a 0.04 ns increase in GWTT from the sand without box wasobserved. This increase led the dielectric constant of the surface soil to 4.85 that corresponds to the30000-6-4

Amplitude (μv) (02Time (ns)SandBox-I

20000-2vaw ~ 0.30 m/ns

46vgw ~ 0.16 m/ns

8101210000
0-10000 -2-20000-30000

1416
0.38

0.47

0.56

0.65

0.74
0.83
Position (m)

0.92

1.01

1.10

Fig. 3. Wiggle trace of the sand profile with AW &GW velocity.

-40000024

68101214

Ground wave
Airwave
Time (ns)Fig. 4. Early time (-2 to 10 ns) single wavelets
acquired for sand and sand with water Box-I.

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Box-I
Box-II
Box-III
Box-IV

10864
2030
Theoretical depth (cm) )Dielectric constant (12Overmerrern model
Sperl model

2520151050-505
101520
Water box position inside lysimeter (cm)25

Fig. 5. Measured dielectric constant with water box
placement (0-20 cm) inside lysimeter.

3691215
Dielectric constant

1821Fig. 6. Theoretical depth of influence of GW formaterial (K= 3 to 20) using 250 MHz antenna.

moisture content of 0.075 m3 m-3 based on the Topp equation. Then a slight increase in K value wasfound for the 15 cm placement. Similarly, for the Box-II, estimated K values were smaller for 0 and 5 cmplacement (K= 4.85) than those for 10 and 15 cm placements (K= 9.92). For Box-III, the K values werelarger than those obtained for Box-I and Box-II experiments when boxes were placed in shallow depth.
The K value decreased for the 15-cm placement. Comparison between Box-II and Box-III reveal thatboxes with the same volume but with the different surface areas resulted in different K values. The K
value is larger for the box with a larger surface area. The K values were almost constant for Box-IV
regardless of its placement depth. This might be due to the small surface area of the water box (Table 1).
It is therefore clear that the GW is influenced not only by the volume of water but also by the surface areaof the box. Overall, it can be said that, except for Box-IV, boxes were imaged by GW until 15 cm depth.
At the depth of 20 cm, the estimated dielectric constants are all similar to that of the background sand for
all four boxes. This result suggests that the depth of influence of GW in this study was smaller than 20 cm.
The theoretical depths of influence of GW were then calculated using van Overmeeren (1997) andSperl (Huisman, 2003) models. Predicted depths for the materials (K= 3 to 20) using 250 MHz GPR
antenna by both models were given in Figure 6. In general, the van Overmeeren model predicts larger
depths than the Sperl model (Fig. 6). The depth of influence of GW for the background sand wascalculated 25 and 12 cm (shown by arrows in Fig. 6), respectively. In this study, all observed depths ofinfluence were less than 20 cm but greater than 15 cm. The theoretical prediction of GW depth using
both models does not match with experimental results. The depth of influence was found similar to thequarter of wavelength 16 cm (e.g., Dgw= (λ/4); where, λ = (vgw/f) = (16 cmns-1/250×106) = 64 cm) in thisstudy. In conclusion, the study signifies that when working with GW of GPR, the CO survey followed bytime zero calibration by the CMP survey would provide precise travel time information. Accordingly, theGW velocity can be used to map surface soil moisture contents with the known sampling volume.
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