This abstract was published in the Proceedings of the Eigth International Conference on Ground Penetrating Radar, GPR2000, Gold Coast, Australia, May 23-26.  This abstract is also available in a pdf-version.

Migration using multi-configuration GPR data

Due to the radiation pattern of the GPR antennas, the amplitude of the reflection is not only dependent on the distance between the target and the antennas, but also on the angle of orientation between the antennas and this target. Alford rotation is applied to this radiation pattern of the antennas, and used to extract the location of the origin of the reflected wavefield. This information is used to improve the migration scheme. In conventional migration schemes, recorded data are migrated to all angles. In this method, instead the recorded data are migrated to certain grid points only. This makes the migration algorithm faster and more accurate. This Alford migration method is applied to synthetic data and is shown to be successful below a noise level of about 1% of the amplitude level of the data. A higher level of noise results in an inaccurate estimate of the angle to the location of the target and the signal to noise level to decrease. The result can be improved by migrating over a limited sweep of angles around the estimated angle. Application of this method to field data collected at a controlled test site has shown poor results, as there was too much noise present in the data and errors might occur due to dispositioning of the antennas.

Radiation pattern

In this study one important aspect of the GPR antenna is used: its directivity. The GPR antenna is a dipole source, which means that the transmitted wavefield has a distinct directivity, which can be used to extract information about the location of the origin of the reflected wavefield. The radiation pattern of a horizontal, electromagnetic dipole along the plane interface of two lossless dielectric, non-magnetic half spaces is described by Engheta et al. (1982). Arcone (1995) shows more numerical and measured results of these radiation patterns. The amount of energy radiated in the plane parallel to the antenna is different from the amount of energy radiated in the plane perpendicular to the antenna. Most of the excited energy is distributed along the plane that is perpendicular to the antenna and crosses the antenna in the middle. Almost no wave is generated in the direction of the endpoints of the antennas. Consequently, the amplitude of the reflected signal is dependent on the angle between the orientation of the antennas and the orientation of the line of data collection. The amplitude of the reflected signal is maximum when the target is located in the plane that is perpendicular to the antenna and crosses the antenna in the middle.

Alford rotation

Collection of multi-configuration GPR data can be compared to collection of multi-component elastic data. By rotation of the transmitter a situation is obtained similar to the two different shearwave sources and by rotation of the receiver the two different reflected electromagnetic components are recorded, which is similar to recording the two different shearwave components. Both in the elastic and in the electromagnetic case the amplitude and the arrival time of the reflections is dependent on the orientation of the source and receiver to the orientation of the axis of anisotropy of the medium (Alford, 1986).

One of the most successful ways of evaluating shearwaves is the use of Alford rotation (Alford, 1986). Alford rotation enables us to find the angle of orientation of the main axis of anisotropy and the average azimuthal anisotropy of the medium (e.g. fractures). After collection of data in just four different configurations, being the yy-, xy-, yx-, and xx-configurations, the response for every angle of orientation can be constructed. This can be achieved for any possible angle of rotation, thereby calculating the response for all four configurations for every different angle between the orientation of the antennas and the orientation of the line of data collection. In seismic applications it is known that the amplitude of the reflection values for the xy- and yx-configurations are minimum when the transmitter or receiver is parallel to the main axis of anisotropy of the medium. By plotting the amplitude response versus angle of rotation and observing where the amplitude of the reflection is minimum for the xy- or yx-configuration, one can find the main orientation of the axis of anisotropy of the medium.

Previous work has shown that Alford rotation can be effectively applied to GPR data to determine the angle of orientation of an object with a distinct orientation (Van Gestel and Stoffa, 1999). They applied this method to synthetic and field data to extract the angle of orientation of a cylinder.

Migration

In several GPR studies, data are migrated using conventional migration methods (e.g. Fisher et al., 1992). Others even implemented the directivity of the GPR antenna in their migration algorithms (Campman and Slob, 1999; Moran et al. 1998; Saintenoy and Tarantola 1998). In this study a migration method is used that implements the radiation pattern in the migration algorithm.

It was shown that the reflection is maximum when the object is located in the plane perpendicular to the main axis of the two antennas. By rotation of the antennas the location of the target can be found by plotting the recorded amplitude of the reflected field versus angle of orientation of the GPR set. Alford rotation allows one to extract all these amplitudes and the location of the target from four configurations only. By recording the electric field in the yy-, yx-, xy-, and xx-configurations and applying Alford rotation one can extract the vertical plane in which the origin of the reflection is located. This is equivalent to defining the horizontal angle of orientation of the origin of the reflection. This information can be used for example to find the dipping direction of a dipping plane as the reflection is maximum when the antennas are parallel to the dip of the plane.

In this study it is shown that this information can be used to improve migration schemes. Instead of migration of the recorded data to all directions, the migration scheme is limited to a small range of angles, which results in a faster, cheaper and more accurate migration algorithm. A regular Kirchhoff migration (Yilmaz, 1987) is modified, as the migration is limited to those paths that are within the predicted angle of orientation extracted using Alford rotation.

Synthetic data were generated for the reflection of one scatter point in a homogenous background. A simple travelpath, reflection amplitude method was used to generate the results. A 3D grid was generated that 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. Synthetic data were generated for the four configurations being the yy-, yx-, xy-, and xx-configurations. The radiation pattern was generated using the theoretical equations (Enghata et al., 1982). The radiation patterns of both antennas are combined in the final radargram.

The images resulting from the Alford migration and the regular migration are compared. In the Alford migration the location of the target is calculated using Alford rotation for every samplepoint on every trace and the data are migrated in that direction only. The regular migration consists of a conventional Kirchhoff migration of the yy-configuration only. Results of both the Alford and the regular migration are shown in Figure 1 for two different noise levels. The Alford migration (Figure 1B) results in a more focused image than the regular migration (Figure 1A), when no noise is present in the data. The angle of orientation can be exactly determined and the data are only migrated to the correct angle. As a result almost no migration artifacts are present in the final image. However, the result decreases when noise is added to the synthetic data. The regular imaging method is hardly influenced by the noise (Figure 1C), but the Alford migration method shows considerate distortion (Figure 1D).

Figure 1 Results of the imaging of the synthetic data for the regular migration method and the Alford migration method. Results are shown for two different levels of noise. A. Regular migration method without noise. B. Alford migration method without noise. C. Regular migration method with 10 % noise. D. Alford migration method with 10 % noise.

As the amplitude of the signal is scaled, the true amplitudes of the final images can not be compared. Therefore, random noise is added to the synthetic data before the migrations were applied and the ratio between the signal and noise in the final images resulting from both methods is compared. These signal to noise ratios are only valuable to make comparisons between the various methods. They are dependent on too many variables to justify qualitative significance.

To improve the results of Alford migration the data are migrated to a range of angles around the calculated angle instead of migration to the calculated angle only. When noise is added to the synthetic data, the calculation of the angle is incorrect. By sweeping through a range of angles the exact angle of orientation of the target is covered, but the method is still faster and more accurate method than the regular migration to all angles.

Table 1 and Figure 2 show the signal to noise ratios for seven different migrations and four different noise levels i.e. 0 %, 0.1 %, 1% and 10 %. The first six migration methods that are applied, are Alford migrations with different kind of ranges of angles. The last method is the

Figure 2 Plot of the various signal to noise ratios of the images resulting from the different migration methods for different levels of noise. Dashed line is the result of the regular migration method. Six solid lines are the results of the Alford migration method for six different ranges.

regular migration. For low noise levels the Alford migration results in a better signal to noise ratio than the regular migration. However, when more than about 1 % of noise is added to the synthetic data, the regular migration has a higher signal to noise ratio. Further, for low noise levels in the synthetic data the Alford migration to a small range of angles is better than Alford migration to a wider range of angles. However, when the noise level in the synthetic data increases the results get closer and finally the Alford migration with wider ranges has better results than the Alford migration with smaller ranges.

In Table 1 the necessary time to run the migration can be found. These numbers are only valuable to make comparisons between the various methods. One can see that the Alford migration is 29 times faster than the regular migration. However, by applying the method where you migrate the data to a sweep of angles instead of one angle, the method slows down significantly, with the Alford migration over a range of 20 degrees already being slower than the regular migration.