Multi-configuration Ground Penetrating Radar data

Traditionally Ground Penetrating Radar (GPR) measurements are conducted using two co-polarized antennas both oriented perpendicular to the direction of propagation. Configurations where the antennas are held parallel to the direction of propagation or cross-polarized to each other have hardly been used. In this study we show that collection of this kind of data will increase our knowledge of buried objects with a distinct orientation, like cylinders. By recording the electric field in two different orientations using multi-configuration data acquisition, and with the use of Alford rotation we can extract information about the orientation of these objects. Because the reflection of these objects is angle-dependent, we can exactly predict the angle of orientation of the objects. A GPR survey has been conducted at a controlled test-site. The results of this survey show good prediction of the angle of orientation of the buried objects and confirm the expected theoretical results. To obtain a better understanding of the different sources for errors and the underestimate of the angle of orientation an error analysis has been done. Three sources for error have been studied and it has been concluded that with accurate data acquisition and an exact knowledge of the radiation pattern this method should be effective in practice. Having shown this method for elongate cylinders we think that this method can also be applied to other anisotropic features like fractures or dipping layers.

Traditional Ground Penetrating Radar surveys are conducted using two similar antennas. The first one is dedicated as the transmitting antenna, or transmitter, and the second antenna is used as the receiving antenna, or receiver. In traditional recordings the two antennas are held parallel to each other with a fixed distance between them and both antennas are held perpendicular to the direction of propagation. This configuration is called the perpendicular-broadside configuration (Figure 1).

Figure 1: Drawings of the three different configurations that have been used in this study.

The orientation of the polarization of both antennas is identical and the antennas are co-polarized. The transmitter produces an electric field with a polarization parallel to the long axis of the antenna. In the receiver only the component parallel to the long axis of the antenna is recorded. In fact only the y-component of the electric field is transmitted and recorded, therefore we will also refer to this configuration as the yy-configuration. In this study we use two more configurations. In the first we rotate one of the antennas and measure the cross-polarized component of the electric field. This is called the cross-polarized configuration or the xy- or yx-configuration (Figure 1). In theory, due to reciprocity, both configurations should give identical results and only one of two configurations needs to be recorded. In practice we will record both configurations. The second additional configuration we use is the case where both the antennas are parallel to the direction of propagation, or parallel-endfire configuration. This is equal to transmitting and recording the x-component of the electric field, and therefore this is also called the xx-configuration (Figure 1).

These configurations have rarely been used. Tillard (1994) has collected one of the few GPR field surveys with cross-polarized antenna configurations and showed that radargrams could be improved using non-conventional use of the GPR system. Sato et al. (1998) compared co-polarized to cross-polarized borehole measurements to determine a value for the roughness of the surface, which can be related to the amount of fractures in the rock matrix.

Here we want to study multiple configuration GPR data in a more systematic way. Collection of the x and y-components of the reflected field can be compared to multi-component seismic data acquisition and similar work is done in airborne radar collection. In multi-component seismics the Alford rotation has been used to determine the orientation of anisotropies like fractures (Alford, 1986). In electromagnetic airborne radar images a similar technique has been used to enhance the contrast between various areas (Ulaby and Elachi, 1990). We show that application of this method to multi-configuration GPR data will allow us to increase the information about anisotropic features. Here we use this method to determine the angle of orientation of elongate objects, like cylinders. We confirmed this theoretical method with data, which have been collected under controlled circumstances at a test-site in Scheveningen (The Netherlands).

We focus on the determination of the angle of orientation of buried cylinders. We will assume that the length of the cylinders is much larger than its diameter. The diameter again is much smaller than the used wavelength. In practice there are several situations where these conditions will apply, for example when we are looking for metallic or non-metallic pipes, cables, or even elongate storage tanks.

The theoretical electromagnetic reflections of these objects have been studied and are described by Ruck et al. (1970). These reflections show a clear dependence on the angle of the incident wavefield (Figure 2). When the orientation of the electric field is parallel to the orientation of the cylinder the amplitude of the reflection of that cylinder is maximal. Further when the incident electric filed is parallel to the cylinder no cross-polarized reflections will be generated (Figure 2).

Figure 2: Theorectical reflection of a cylinder for co- and cross-polarized configuration. Also the actual measured response for the co-polarized component is shown.

For GPR measurements with two parallel antennas this means that the amplitude of the received signal will be maximal when both antennas are parallel to the cylinder. For cross-polarized antenna configurations the reflection will be zero when one of the antennas is parallel and the other is perpendicular to the cylinder. We can use this angle-dependence of the reflections to determine the orientation of the cylinder.

Therefore the Alford rotation can be used, developed in shear wave seismics to determine the orientation of anisotropy (Alford, 1986). Using basic goniometric relations we can determine the reflection for every single angle out of the recording of the yy-, xy-, yx- and xx-configurations. After the reflected field has been determined for every different angle we can observe where the amplitude of the reflection is maximal. In this case the angle of the electric field is equal to the angle of the orientation of the cylinder.

In the spring of 1998 several lines of GPR data were collected in a test-site at Scheveningen (The Netherlands). At this location a test-site has been built, which makes it possible to collect GPR data under perfectly controlled conditions. The test-site consisted of a dry sandpit of 10 m by 10 m, and is 3 m deep. In the test-site several cylinders were buried at a depth of 1 m. For our measurements we focused on one cylinder that is made of iron, a length of 1.012 m, and a diameter of 22.3 cm.

For the measurements the pulse EKKO system 1000 was used, which has shielded GPR antennas. All measurements were done using the 450 MHz antenna and an antenna separation of 30 cm. The relative permittivity of the sand has been measured and is 4.59. This leads to an electromagnetic wavefield velocity of 0.14 m/ns and a wavelength of 31 cm, which is bigger than the diameter of the cylinder.

Four GPR lines were collected in a straight line over the middle of the cylinder with a shotpoint separation of 10 cm. The four lines have a different angle between the direction of propagation and the orientation of the transmitter. This angle was respectively 0, 15, 30 and 45 degrees. For every shotpoint four different configurations were recorded, as we rotated the transmitter and receiver. In this way we recorded both the x- and the y-component of the reflected field for the case when the transmitted field is in the y-direction and the case this transmitted field is in the x-direction.

A 3D grid was also collected which covered the whole cylinder and was collected under a 30-degree angle to this cylinder. The 3D grid consisted of 13 lines with 25 cm spacing between them. Shotpoint spacing was 10 cm and again the four different configurations were recorded.

A simple, standard data processing sequence has been applied to the data, which consists of trace-editing, filtering, spherical gain correction, resampling and a constant velocity migration. We compare results both before and after migration.

Now we use Alford rotation to calculate the reflections for all the different angles of the transmitter. These calculated reflections are used to determine the angle where the amplitude of the reflection is maximal. This corresponds to the angle of orientation of the cylinder.

Figure 3: Calculated results for the 2D lines.

Table 1 and Figures 3 and 4 show the results of the calculated angles. Figure 3 shows the results for the four lines crossing the cylinder. The cylinder is at trace number 12. For every trace on the line we have picked the reflection of the cylinder and calculated the angle of orientation of this cylinder, which is displayed in the four subplots at every trace. The mean of the 12 traces around the middle of the cylinder is posted as well.

Figure 4: Topview of the cylinder, showing the calculated results for the 3D grid.

Figure 4 shows the results of the 3D grid. We look at a topview of the cylinder, which is shown in light gray in between line number 4 and line number 7. For every sample on every shotpoint in this 3D grid we have calculated the angle of orientation. Again we used a window of about the length of a wavelength around that sample. Then we have drawn a line in the direction of this calculated angle of orientation. The length of this line is as long as the amplitude of the reflection at that sample of that trace.

We can observe that for most traces the amplitude of the reflection is small and the calculated angle is random. However where the amplitudes are higher, and we look at the reflection of the cylinder the calculated angle of orientation of the cylinder is similar to the real angle of orientation.

Table 1: Results of the 2D lines and three lines of the 3D grid.

Table 1 summarizes the results for the four different lines across the middle of the cylinder and for three of the lines out of the 3D grid. Results are shown for two methods. In the first method we did not migrate the data, but calculated the angle of orientation of the cylinder for every single trace. After the angle of orientation was calculated we take the mean of the 12 traces closest to the cylinder. In the second method we migrated the data first and then calculated the angle of the orientation of the cylinder. The difference between the two methods is that in the first method we calculate the angle of orientation first and then average over all the traces. In the second method we take the average first and then calculate the angle of orientation.

The results appear to be in close agreement with the actual angle of orientation of the cylinder. However, all the calculated angles of orientation underestimate the actual angles. In the next section we will discuss the origin of this underestimate. Further we consider the method where the angles are determined before migration, as it is easier to identify and eliminate some erroneous values.

To get a better understanding of the effects of the various sources of errors and understand where the overall angle underestimate originates from we conducted an error-analysis using theoretical data. We studied three different sources for miss estimation of the angles of orientation.

First we study the general background noise. When we look at the collected data it appears as if there is a high noise level, especially for the cross-polarized configurations. The actual reflection coming from the cylinder seems to be buried in the background noise. We applied different amounts of background noise to theoretical data and calculated the angle of orientation. We observed that this noise-effect only generates a small error and moreover that the final mean angle of orientation for several traces will still be correct.

Secondly we studied the effect of shifting the data. During data acquisition the antennas were placed by hand, estimating the distance and angle between the two antennas. Besides the data were collected in loose sand which has small elevation differences. These two effects will generate a time shift of the reflection of the cylinder in the data. The reflections will not exactly align in the four different configurations. Again we studied this effect using theoretical data. We concluded that this shift effect can result in considerable errors and the angle of orientation will be underestimated. However when we shift the data back by picking the reflections and realigning them, this error can be removed. By making our data acquisition technique more accurate we can remove this source of error.

The third source of error turned out to be the most significant. This is the radiation pattern of the antennas. GPR dipole antennas are constructed to collect co-polarized data. As a result the co-polarized configurations will be more amplified than the cross-polarized ones. This can be shown by comparing the actual measured electric field at a specific angle of the receiver to the electric field reconstructed from its x- and y-components. When this is done it becomes clear that the reconstructed field is stronger in amplitude than the actual field, while they are supposed to be similar. This difference indicates that the antennas amplify the signal more when they are polarized. When we study this effect in theoretical data we conclude that this effect will also cause an underestimate of the data. Amplifying the traces collected in the cross-polarized configurations leads to better calculations of the angle of orientation. To apply this amplification correctly we need an accurate measurement of the radiation profile of the antennas.

Collecting multi-configuration GPR data provides additional information about buried objects. By collecting data in three configurations at every shotpoint, and using Alford rotation we can extract the orientation of buried elongate objects, like cylinders. This was shown to work in theory and in real data.

Background noise should not be a problem for this method, however accurate data acquisition and a good knowledge of the radiation pattern of the GPR antennas is required to apply this method with good results.

As this method has shown good results for cylinders it should also be applied to other situations where we have distinct anisotropies, with angle dependent reflection or transmission coefficients, like vertical fractures, dipping planes, or anisotropic media, like coalbeds and schists.

We would like to thank the Delft University of Technology and TNO-FEL for providing the equipment and the availability of their test-site. Also we would like to thank Dr. J.J. Fokkema, Dr. E.C. Slob, Dr. J.L. Simmons, Dr. M.M. Backus, and Dr. M.K. Sen for their input and discussions and E.J.B. van der Holst who assisted in the field.

Alford, R.M., 1986, Shear data in the presence of azimuthal anisotropy, 56^th SEG meeting, Houston, Texas, Expanded Abstracts, p. 476-479.

Ruck, G.T., Barrick, D.E., Stuart, W.D., and Kirchbaum, C.K., 1970, Radar Cross Section Handbook, Vol. 1: Plenum Press, New York, NY, 472 p.

Sato, M., M. Takeshita, T. Miwa, and H. Niitsuma, 1998, Polarimetric Borehole Radar applied to geophysical exploration, GPR 1998 Proceedings, Lawrence, Kansas, p. 7-12.

Tillard, S., 1994, Radar experiments in isotropic and anisotropic geological formations (granite and schists), Geophysical Prospecting, p. 615-636.

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