Combining multi-configuration Ground Penetrating Radar data using a weighted migration approach

Traditionally Ground Penetrating Radar (GPR) measurements are conducted using two co-polarized antennas both oriented perpendicular to the line of data collection. Configurations where the antennas are held at an angle to the line of data collection are rarely used. In this study we show that collection of this kind of data and combination of the different recordings using a weighted migration increases the signal to noise ratio of GPR data.

We show this method to work on synthetic 3D GPR data, by comparing the signal to noise improvement in the images resulting from the different migration algorithms for different combinations of antenna configurations. We also applied this method successfully to a 2D and a 3D field data set that were collected at a controlled test-site.

GPR surveys are conducted using two similar antennas. The first one is dedicated as the transmitter, and the second antenna is used as the 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 line of data collection. We chose the line of data collection to be the x-direction and name configurations after the direction of the orientation of the transmitter and receiver respectively. For example the conventional, co-polarized, perpendicular, broadfire configuration is denoted as the yy-configuration.

In most GPR surveys, data are collected using the yy-configuration only. However, the recorded data are different when we change the angle of orientation of the antennas to the orientation of the line of data collection. We try to better understand the value of collecting data using different configurations and determine how we can use this information to improve the final radargram. In Van Gestel and Stoffa (1999), we show the use of Alford rotation to combine data collected using the yy-, yx-, xy-, and xx- configuration to provide information about the orientation of objects with a distinct orientation. In this study we focus our attention on combining the recorded data of different configurations where both antennas rotate compared to the line of data collection and the target.

The amount of work that is conducted in this field is very limited. Configurations, where the GPR antennas are rotated to the target or the line of data collection, are never studied. Conventional acoustic migration methods are applied to GPR data, for example by Fisher et al. (1992), and several studies even implemented the radiation pattern in the migration (Campman and Slob, 1999; Moran et al. 1998; Saintenoy and Tarantola 1998), but never have different configurations been combined in a stacked radargram.

In this study we present the results of configurations where both antennas are rotated to the line of data collection, but kept parallel to each other. We also studied the results where only one of the antennas was rotated and the second was held at a constant angle to the line of data collection. Although this method has similar results the effect is smaller than the case where both antennas are rotated simultaneously. In our calculations and during the collection of the field data, we keep both antennas on the line of data collection and change from a broadside configuration to an endfire configuration. Alternatively you could keep a broadside configuration and move both antennas around one constant midpoint. However, as our targets are located in the far field, this should give similar results.

In this study we make use of the fact that the GPR antenna is a dipole source, which means that the transmitted wavefield has a distinct directivity. The equations for the radiation of a horizontal electromagnetic dipole along the plane interface of two lossless dielectric, non-magnetic half spaces are given by Engheta et al. (1982).

For the final radiation pattern we need to combine the radiation pattern for the transmitting and the receiving antenna. Figure 1 shows a cross-section of this radiation pattern at a depth of 2.5 m below two antennas in the yy-configuration, with a separation of 30 cm, and are located at the interface of air and a medium with e _r = 5, s = 0 mS/m, and m _r = 1. It can be observed that most of the excited energy is distributed along the plane that is perpendicular to the antenna and crosses the antenna in the middle. Another important aspect is the critical angle, which has a strong effect on the shape of the radiation pattern. By rotation of the antennas this plane rotates simultaneously and a different part of the subsurface becomes the main focus point of the antenna configuration. Combination of these different configurations results in a better data coverage and improves the final radargram as the combined coverage of the subsurface is more uniform.

Figure 1. Theoretical radiation pattern of two GPR antennas in the yy-configuration on the boundary of two homogeneous halfspaces. Cross-section at a depth of 2.5 m, the antenna separation is 30 cm and their midpoint is located at the origin. The main axis of the antennas is pointed towards the y-axis, e _r = 5, s = 0 mS/m, and m _r = 1 in the lower halfspace.

The radiation pattern is also affected by the construction of the shields of the antennas, which are different for every GPR set. Exact knowledge of the radiation pattern is necessary for accurate data interpretation. However, even measurement of the radiation pattern under controlled circumstances does not guarantee exact knowledge of this pattern, as the radiation pattern is dependent on the permittivity, permeability and conductivity of the surrounding media and accordingly changes due to changes in terrain. In this study we use the theoretical radiation pattern of the antennas, but we keep in mind, that the results can be improved if accurate measurements of the radiation profile are recorded.

For this study, we first generated synthetic data for the reflection of one scatter point in a homogenous background. The generated 3D grid consists of 51 x 51 shotpoints, with a sample spacing of 10 cm in both directions. A scatter point was located in the middle of the grid at a depth of 2.5 m. We generated synthetic data for 12 different configurations for every shotpoint. The angle of orientation between the antennas, with a separation of 30 cm, and the line of data collection changed from -90 to +75 degrees, with a 15-degree increase between every configuration. We generated the radiation pattern using the theoretical equations (Enghata et al., 1982) and combined the radiation patterns of both antennas in the final radargram.

Figure 2. Results of imaging of the 3D synthetic data. A. Using the weighted migration B. Using the regular migration.

The synthetic data are migrated using both a regular migration technique and the weighted migration method. For the regular migration technique we apply a standard Kirchhoff migration (Yilmaz, 1987). For the weighted migration we calculate the strength of the radiation pattern for the specific image grid point and multiply the recorded signal with this factor before migrating the signal to this grid point. In this way, the strongest reflections have the highest multiplication factors, and as a result the signal to noise ratio of the final image improves. Results of both the regular and the weighted migration are shown in Figure 2. As we multiply with a weighted function during the weighted migration, the final amplitude of the signal is scaled and the true amplitudes of the final images can not be compared. Therefore, we added random noise to all generated synthetic data before the migrations were applied and we studied the ratio between the signal and noise in the final images resulting from both methods.

Table 1. Signal to noise ratios of the images for five different numbers of configurations and five different migrations of the synthetic data. See text for explanation of migration methods.

Table one shows the signal to noise ratio for five different migrations and five different number of configurations, ranging from 1 to 12. The first migration that is applied, is the weighted migration. The second migration is the regular Kirchhoff migration. The third column is added to compare the migration results to the conventional data collection method. Only the data in yy-configuration are migrated to generate this image, but we combined the same amount of measurements as in the first two migration methods. Due to the radiation pattern, the signal to noise ratio of the final image is dependent on its location compared to the line of data collection. The reflection of the target is stronger when it is located along the axis perpendicular to both antennas than when it is located along the axis parallel to both antennas. The resulting range is given in column four and five, with the highest signal to noise ratio in column four and the lowest in column five.

We can observe that the weighted migration leads to the best signal to noise ratio, significantly stronger than the signal to noise ratio of the image resulting from the regular migration. Collecting data in all configurations leads to a slight increase in signal to noise ratio, but especially to a much more uniform result, where the signal to noise ratio is more consistent and less dependent on the location of the target.

In the spring of 1998 several lines of GPR data were collected at a GPR testing site in Scheveningen, The Netherlands. The GPR testing site is 10 m by 10 m and filled with dry sand, with known permittivity, permeability, and conductivity values. The relative permittivity of the sand was measured and is e _r= 4.59. For the measurements the pulse EKKO system 1000 was used, which has shielded GPR antennas. All measurements were done using the 450 MHz antennas, and an antenna separation of 30 cm. In the GPR testing site several objects are buried at a depth of 1 m. For our measurements we focused on one cylinder that is made of iron, has a length of 1.012 m, and a diameter of 22.3 cm.

Seven GPR 2D lines were collected in a straight line over the middle of the cylinder with a trace separation of 10 cm. The seven lines have a different angle between the orientation of the line of data collection and the orientation of the transmitting and receiving antennas. This angle was respectively 0, 15, 30, 45, 60, 75 and 90 degrees, resulting in configurations ranging from the yy- to the xx-configuration. We also collected a 3D grid that 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. Trace spacing was 10 cm and data were collected for every trace in the yy-, yx-, xy-, and the xx-configuration.

Figure 3. Results of imaging of the 2D field data. A. Using the weighted migration B. Using the regular migration.

We migrated the data and combined the different configurations into a new image. We applied and compared the following four migrations: 1) the weighted migration, 2) the regular migration, 3) the migration of just the yy-configuration and 4) the migration of just the xx-configuration. Figure 3 shows the images of the first two migrations for the 2D field data case.

Table 2. Signal to noise ratios of the images for four different migrations of the field data. See text for explanation of migration methods.

Table 2 shows that again the weighted migration leads to the best signal to noise ratio. In the field data case, migration of just the yy-configuration results in a better signal to noise ratio than the regular migration of all configurations, although you have three configurations less to construct the image. This is probably due to location inaccuracies due to manual positioning of the antennas. Further, we notice a larger difference in between the migration of the data in the least and in the most preferred direction than was present in the synthetic data. This is due to the difference in reflection amplitude of the elongate cylinder, which has a higher reflection amplitude in the case when both antennas are parallel to the main axis of the cylinder.

Implementation of the radiation pattern using a weighted migration significantly increases the signal to noise ratio of the final image. This is shown both in a synthetic case and in the field data. Creating a GPR antenna set with a more focused radiation pattern would strengthen this effect. The more focused the radiated energy, the better one knows where the signal originates from and the better this knowledge can be used to improve the signal to noise ratio of the final image.

For the weighted migration we need accurate knowledge of the radiation pattern. This can be difficult as the exact radiation pattern of the antennas is only known in theory and varies with different subsurface parameters. We recommend accurate measurement of this pattern to improve the method. However, it is encouraging that even with the theoretical radiation pattern we obtain good results in our field data example. Conversely, this method could be applied to find the radiation pattern. Therefore we need measurements of several configurations over a localized reflection point, which forms a distinct hyperbola. We can implement a focusing analysis in which we compare the images of various migrations using different radiation patterns. Thereby, we can find the radiation pattern that results in the best image.

Combination of different configurations makes the final image more uniform and less dependent on the location of the target. Signal to noise ratio can be improved when the target is located in the plane parallel to the main axis of the two antennas. We also want to note that if we use GPR measurements for object localization and collect data using one configuration only, it is better to collect data using the xx-configuration than the commonly used yy-configuration. Using the xx-configuration sends most of the radiated signal into the plane perpendicular to the line of data collection instead of into the plane of the line of data collection, which is already covered by other shotpoints. As a result, using the xx-configuration covers a larger part of the subsurface than would be covered when using the yy-configuration.

We would like to thank the Section of Applied Geophysics and Petrophysics of Delft University of Technology and TNO-FEL for providing the equipment and the availability of their test-site. Also we would like to thank Jakob J. Fokkema, Evert C. Slob, and Xander H. Campman for their input and discussions and Edwin J.B. van der Holst who assisted in the field.

Campman, X. H., E. C. Slob, 1999, Radiation consistent GPR imaging, Expanded Abstract NSG 5.7, S.E.G. Annual Meeting, Houston, Texas

Enghata, N., C. H. Pappas, and C. Elachi, 1982, Radiation patterns of interfacial dipole antennas, Radio Science, vol. 17, p. 1557-1566.

Fisher, E., G. A. McMechan, A. P. Annan, and S. W. Cosway, 1992, Examples of reverse-time migration of single-channel, ground-penetrating radar profiles, Geophysics, vol. 57, p. 577-586.

Moran, M., S. A. Arcone, A. J. Delaney, R. Greenfield, 1998, 3-D Migration/array processing using GPR data, Proceedings of the 7^th International Conference on Ground-Penetrating Radar, Lawrence, KS, p. 225-231.

Saintenoy, A., and Tarantola, A., 1998, Getting ready for GPR data inversion, Proceedings of the 7^th International Conference on Ground-Penetrating Radar, Lawrence, KS, p. 491-496.

Van Gestel, J., P. L. Stoffa, 1999, Multi-configuration Ground Penetrating Radar data, Expanded Abstract NSG 5.1, S.E.G. Annual Meeting, Houston, Texas.

Yilmaz, O., 1987, Seismic data processing, Society of Exploration Geophysicists, Tulsa, OK.

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