Proceedings Template - WORD€¦ · Web viewMulti-Channel Ground Penetrating Radar. Holger Gerhards1, Ute Wollschläger1, Stefan Schneider, and Kurt Roth1. 1Institute of Environmental

12th International Conference on Ground Penetrating Radar, June 16-19, 2008, Birmingham, UK

Exploring Complex Formations with Multi-Channel Ground Penetrating Radar

Holger Gerhards1, Ute Wollschläger1, Stefan Schneider, and Kurt Roth1

1Institute of Environmental Physics, University of Heidelberg69120 Heidelberg, Germany

email [email protected], ute.wollschlaeger@iup..., kurt.roth@iup...

Abstract – Traditional ground penetrating radar applications for long range measurements use a single monostatic or bistatic setup. Because the travel time of a signal depends on velocity and reflector depth, the data evaluation requires ad-ditional ground truth information and further assumptions concerning the lateral evolution of reflector depth or mean water content distribution along the survey path.

To overcome these difficulties, we use a multi-channel setup, which simultaneously measures the signals of two bistatic ground penetrating radar antennas and their two cross-chan-nels. Herewith, we can perform a moving mini common mid-point measurement over large distances in a time that is marginal longer than a normal common offset measurement. With this, we are able to obtain reflector depth and average water content simultaneously along the survey path.

Here, we applied the method to explore a complex soil for-mation. The required absolute travel time for the multi-channel evaluation and therefore the unknown travel time offsets were calibrated from common midpoint measure-ments conducted at two points. The multi-channel results in reflector depth and average water content for three reflectors are presented. Here, the results indicate the occurrence of side reflections. At two positions, the multi-channel results are validated by normal moveout analysis of the common midpoint measurements.

Keywords – multi-channel GPR, water content, reflector depth.

I. INTRODUCTIONGround penetrating radar (GPR) is used in diverse fields including archaeology, sedimentology, permafrost studies, and hydrology. Its popularity comes from the fast, non-in-vasive, and cheap applicability to scan the near subsurface for either subsurface structure or state variables (e.g. water content) over distances ranging from a several meters to a few kilometers.For surface GPR explorations, there exist different mea-surement techniques, which vary in accuracy, effort and applicability. For instance off-ground GPR is intensively used in engineering areas such as road mapping [4], but also in hydrogeophysics in order to obtain the near subsur-face water content [6]. Its disadvantage is the small pene-tration depth of the electromagnetic signals into the ground.

Another application method is to conduct single common offset measurements, where a transmitter-receiver pair is placed directly on the ground in order to induce a high amount of energy into the subsurface. This technique is commonly used for a fast exploration of subsurface struc-ture, but can also be used for determining subsurface wa-ter content when the reflector depth is known [7].Furthermore, multifold data sets are used, which are mea-surements using different antenna separations along the same survey line. These data sets are sorted into common midpoint (CMP) gathers [1] and evaluated with standard normal moveout analysis [9]. This method is capable of resolving vertical and lateral changes of propagation ve-locities and can therefore be used to infer material proper-ties or water content [2]. However, it is very time consum-ing.A hybrid method is to conduct multi-channel, multi-offset measurements. Here, a small set of transmitters and re-ceivers coupled in a row at fixed distances are used in analogy to single common offset measurements. There-fore, its time effort is marginal larger than a single com-mon offset measurement. The advantage is that it can be regarded as a moving mini-CMP, from which we obtain a fast, simultaneous access to reflector depth and average water content [3]. In this study, we use this multi-channel technique to ex-amine a multi-layered soil formation. At two points, we validated the solutions with a normal moveout analysis from two additional common midpoint measurements.

II. SITE DESCRIPTION AND DATA AQUISITIONThe GPR survey was conducted in the nature protection area Hirschacker near Schwetzingen, Germany in October 2007. The subsurface consists almost of sandy soil, which is covered with mosses, grass and small plants such as thyme (Figure 1).For the GPR measurements, we used two 250 MHz RA-MAC/GPR antenna systems connected with a rope with the setup shown in Figure 1. We performed a single multi-channel survey (Figure 2), resulting in four common offset measurements with different antenna separations, ==0.36 m, =4.04 m, and =3.32 m. Furthermore, at two positions ( =19.8 m and =42.4 m), we conducted


two common midpoint (CMP) measurements, which result in four CMP radargrams using the cross-channels shown in Figure 1. One for each position is shown in Figure 3.For all measurements, we used a sampling frequency of about 10 samples per nanosecond and a time window of about 110 ns. The spatial trace increment for all measure-ments was 0.1 m.In the upper part of the radargrams displayed in Figure 2, a large number of dipping reflectors are observable. They might origin from ancient dunes. These are underlain by a continuous reflector, which is identifiable in all radar-grams between 10 and 70 m. Beneath this reflector, two further reflectors can be found, one between 33 and 44 m and a third one almost throughout the whole radargram.

III. MULTI-CHANNEL MEASUREMENT AND EVALU-ATION

3.1 Ray Approach Travel TimesIn surface GPR applications, the main observable signals result from direct and reflected waves. Their absolute travel times are described by

(1)

and

. (2)

Here, the direct wave travel time is only a function of antenna separation and relative permittivity of the medium the wave is traveling through. Assuming a hori-zontal reflector, the reflected wave travel time de-pends additionally on the reflector depth .

If a dipping reflector is considered, Equation (2) yields

(3)

where and are the actual measurement position and a reference point, respectively. In contrast to Equation (2), where is assumed to be constant for all measurement positions, the depth of a dipping reflector is a function of spatial position and therefore, we define the depth in Equation (3) as the reflector depth directly at the reference point . For the dipping angle the convention is cho-sen that it is positive for a decreasing reflector and vice versa.

3.2 Multi-Channel Evaluation TechniqueA multi-channel GPR survey is a simultaneous measure-ment with a set of transmitters and receivers at different antenna separations. It can be considered as a moving mini common midpoint measurement (mini-CMP).Using a setup shown in Figure 1, we can obtain four travel times for a common reflector at a single measurement po-sition. Instead of a pointwise normal moveout analysis [1, 2], we follow a different procedure, because of the limited amount of data for a single measurement location.For our approach, we use the fact that a dipping reflector leads to a characteristic trend in travel time for changing measurement positions, Equation (3). Therefore, depend-ing on the measurement setup we can use the travel time information ( ; ) of antenna separations and measurement positions around a reference point . Then, the describing material model ( , , ) at a reference point must fulfill the mini-mization requirement

(4)that the sum over all squared differences between mea-sured and modeled travel times for different antenna sepa-rations and measurement positions around the reference point yield a minimum.The requirement for this minimization procedure is that the reflector beneath all used measurement positions shall follow a linear behavior. Furthermore, the more measure-ment points are used for the evaluation for a single refer-ence point, the more is the averaging volume for the resul-tant relative permittivity, because it is assumed to be con-stant above the reflector in Equation (3). A detailed de-scription of this approach can be found in [3].

Figure 1: Setup of a multi-channel measurement.

Figure 2: Section of measured radargrams from the nature protection area Hirschacker near Schwetzingen with the setup shown in Figure 1 using two 250 MHz RAMAC/GPR antenna systems. The antenna separations are =

=0.36 m, =4.04 m, and =3.32 m. All radargrams are shifted to a common measurement point and a dewow filter was applied to each trace.

Figure 3: Two of four common midpoint measurements obtained from the setup in Figure 1. (a) shows channel 3 () at 19.8 m and (b) channel 3 at 42.4 m. Only a dewow filter was applied on each trace.


3.3 Data Processing and EvaluationThe evaluation of the radargrams shown in Figure 2 starts with some preprocessing steps. First, the logged measure-ment positions of the radargrams were shifted horizontally such that they correspond to each other. Here, we define a measurement position as the midpoint between transmitter and receiver. In a second step, a dewow filter was applied in order to remove low frequencies. From the filtered radargrams, the central extremum of the ground waves in channels 3 and 4 and of the three main

reflectors were picked. The absolute travel times from all waves are obtained by a zero-correction. Here, time zero

for channels 3 and 4 was estimated from two CMP measurements, Figure 3, performed at =19.8 m and =42.4 m. The results for the air and ground wave evaluation for both channels of both CMPs are shown in Table 1. Appar-ently, the error of for channels 3 and 4 is quite signifi-cant. Introducing these errors to the multi-channel evalua-


tion, its results would spread widely [3]. For the following evaluations we fix time zero for channels 3 and 4 to = 11.9 ns and = 13.4 ns, which are the time zero val-ues from the ground waves of the first CMP measurement ( =19.8 m). In contrast to the air wave values, the errors of these ground waves are smaller. Furthermore, we do not use time zero from the ground wave of channel 3 of the second CMP measurement ( =42.4 m), because here the ground wave is only pickable in small sections. For channels 1 and 2, we picked the air-ground wave cen-tral extremum and averaged it. This averaged value is as-sumed to mainly stem from the air wave, which here does not propagate in air but in the medium in the antenna box. The relative permittivity of this material was set to 2.9, which was determined by a ringing analysis of a measure-ment that is not presented here. This ringing

analysis determines the main wavelengths, which leads to resonances within the box. Therefore, these wavelengths are functions of the relative permittivity within the box. From this pick procedure, we obtained the time zero val-ues = 16.9 ns and = 12.7 ns for channels 1 and 2.With the estimated time zero values for each channel, we obtain the absolute travel time values for all reflectors

(Figure 4). The additional ground waves were evaluated using Equa-tion (1) in order to obtain near sur-face relative permittivity and thereof, the water content.For the multi-channel evaluation, Equation (4), we used all for chan-nels ( ). Furthermore, we chose for each evaluation position

in each radargram five neighboring traces on each side. This means that at each position positions are available for the multi-channel evaluation.The results of the multi-channel evaluation four reflector depth and water content for all three reflectors are pre-sented in Figure 5, where the water content is calculated from the composite relative permittivity with the com-plex refractive index model (CRIM)

. (5)

We chose porosity , relative permittivity of the soil matrix and a relative permittivity of water

at the temperature = 15 , calculated from the static relative permittivity of water given [5]. The same conversion was applied for the composite rela-tive permittivity of the ground wave evaluation. The estimated reflector depth displayed in Figure 5 shows that reflectors 2 and 3 are at the same depth between a dis-tance of 32 and 36 m. Here, the average water content val-ues above the reflectors differ by about 0.02 volume per-cent. We presume that at least one reflection might be a side reflection, but with our measured data and with this setup and evaluation method, we cannot extract the dip-ping of the reflectors perpendicular to the survey direc-tion.

IV. NORMAL MOVEOUT ANALYSISIn order to validate the multi-channel solutions, we evalu-ated the CMP measurements presented in Figure 3 apply-ing a normal moveout analysis.

4.1 Evaluation ProcedureIn a first step of the normal moveout analysis, a zero-cor-rection must be applied on the CMP radargrams. After-wards, the travel time and the antenna separation are squared, because of the linear relationship of a reflector under this representation, given by

with . (6)

Figure 4: The absolute travel times obtained from Figure (2) for ground wave (g) and all reflected waves (r1, r2, r3), which can be identified in all radargrams. The two lines for the ground wave stem from channels 3 and 4. For the reflectors, 4 lines for each channel are drawn, where the absolute travel time of channels 1 and 2 overlap.

Table 1: Air and ground wave evaluation of common midpoint measurements to obtain time zero ( ) using linear regression to fit Equation (1). The error is the standard deviation of the parameteres.

position channel 3 channel 4

[m] [-] [ns] [-] [ns]

19.8 air wave 1.3 ± 0.4 12.4 ± 1.5 1.4 ± 0.2 12.7 ± 0.8 ground wave 5.6 ± 0.3 11.9 ± 0.7 5.5 ± 0.2 13.4 ± 0.4

42.4 air wave 1.2 ± 0.2 12.6 ± 1.0 1.1 ± 0.2 13.5 ± 0.6 ground wave 4.5 ± 0.4 11.4 ± 0.6 no data. no data

Figure 5: Results of the multi-channel evaluation for reflector depth and average water content for all reflectors (r1, r2, r3). Additionally, the water content of the ground wave (g) for channels 3 and 4 is presented. The plot for the water content values was split for a better overview.


Here, and denote the reflector depth and the average velocity above the reflector. It is assumed that all reflec-tors are horizontal.Now, using a predefined velocity all squared travel times are shifted upwards by

(7)

according to the antenna separation . After applying the transformation

(8)

on a single trace , these transformed traces were stacked. This transformation was applied to reduce the contrast between reflections with large amplitudes, which occur earlier in the radargram, and reflections with much lower amplitudes later in radargram. Within this stacked traces an extremal value indicates a reflector with an average velocity between surface and this reflector. Because within a CMP measurement multiple reflections can be observed, this procedure of shifting and stacking the radargram must be repeated for a set of reasonable ve-locities or relative permittivity values, which leads to a set of stacked traces. This procedure is different to normal moveout analysis presented by [9] for seismic applications and [8] for GPR applications, because it acts directly on the squared travel times. The advantage of this approach is that there is no expansion and approximation of a square root term in Equation (2).

4.2 Data Processing and EvaluationUsing the radargrams in Figure 3, the zero-correction is done with the time zero values used in the multi-channel evaluation. Furthermore, the CMP radargrams were only dewow filtered.The results of the normal moveout method described above are shown in Figure 6, where the stacked traces for

different velocities are presented in a contour plot. Here, we additionally converted the velocity axis into water con-tent values by recalculating the relative permittivity values

and applying the CRIM model (Equation (5)) using the parameters described earlier to obtain water content val-ues. They also represent an average water content between surface and reflector analogous to the multi-channel eval-uation. Furthermore, we translated the stacked travel times

to reflector depth values using

. (9)

Although this translation is not generally valid, because of refraction effects, we observed only little velocity changes in the measurement. Therefore, we assumed that refraction has no significant influence on the travel time data.

In a last step, we inserted the multi-channel results at =19.8 m and =42.4 m into Figure 6. For both positions, we observe that they are close to predicted reflections from the normal moveout analysis, but there are still devi-ations. A reason for these deviations might be the restric-tion that normal moveout analysis only assumes flat re-flectors, which is not valid within this test site.

Figure 6: Normal moveout analysis for offset corrected common midpoint measurements shown in Figure 3 using the stacked trace method. For the measurement point at 19.8 m (a) and 42.4 m (b) the travel times of the shifted and stacked radargram for different velocities and its conversion to reflector depth and water content are pre-sented. Furthermore, the results of the multi-channel evaluation for both measurement points are inserted as white framed dots.


V. SUMMARY AND CONCLUSIONSIn this study, we demonstrated the application of multi-channel, multi-offset GPR to a test site with multi-layered soil formations. The observed dune structures above the first main reflector indicate a significant influence of a 3D-subsurface structure. The comparison of the multi-channel solutions with a normal moveout analysis of two common midpoint measurements shows that there are some differences in both methods. They can be traced back to the fact that the normal moveout analysis only as-sumes flat reflectors. Furthermore, the multi-channel solu-tions indicate that some reflections might occur from side-reflections, because two reflectors are estimated in the same depth but with different average water content val-ues between surface and this reflector.

ACKNOWLEDGMENTSDeutsche Forschungsgesellschaft (DFG) provided the funding for this research through project RO 1080/10-2.

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[3] Gerhards, H. et al., Continuous and simultaneous measurement of reflector depth and average soil water


content with multi-channel ground penetrating radar, Geophysics, accepted.

[4] Hugenschmidt, J. et al., GPR inspection of mountain motorway in Switzerland, Journal of Applied Geo-physics, 40: 95-104 (1998).

[5] Kaatze, U., Complex Permittivity of Water as a func-tion of Frequency and Temperature. J. Chem. Eng. Data, 34: 371-374 (1998).

[6] Lambot, S. et al., Analysis of air-launched ground-penetrating radar techniques to measure the soil sur-

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[7] Lunt, I. A. et. al., Soil moisture content estimation us-ing ground-penetrating radar reflection data, Journal of Hydrology, 307 : 254-269 (2005).

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Proceedings Template - WORD€¦ · Web viewMulti-Channel Ground Penetrating Radar. Holger Gerhards1, Ute Wollschläger1, Stefan Schneider, and Kurt Roth1. 1Institute of Environmental