12th International Conference on Ground Penetrating Radar, June 16-19, 2008, Birmingham, UK
Simulating Commercial GPR antennas: How close can we get? Craig Warren, and Dr Antonis Giannopoulos Institute for Infrastructure and Environment, School of Engineering and Electronics, University of Edinburgh Edinburgh, Scotland
[email protected] [email protected] Abstract – This paper presents three-dimensional (3D) numerical models of commercially used Ground-Penetrating Radar (GPR) antennas from Mala Geoscience and Geophysical Survey Systems, Inc. (GSSI). GprMax, an electromagnetic simulator based on the Finite-Difference Time-Domain (FDTD) technique, is used along with ParaView (an opensource visualisation application) to create, visualise and validate the models. Comparisons of modelled and real A-scans of antenna free-space responses (crosstalk) have shown good agreement, and further validation using experimental data from buried pipes has corroborated these findings. Accurate antenna models of real GPR antennas allow the direct comparison of modelled and real GPR signals, providing an investigative tool for future research in areas such as material property and geometry information from GPR wavelets, and optimisation of antenna designs. Keywords – Commercial antennas, Antenna modelling, Ground-Penetrating Radar (GPR), Finite-Difference TimeDomain (FDTD)
I. INTRODUCTION Ground-Penetrating Radar (GPR) systems are being used for a wide range of different applications across the fields of both engineering and geophysics. This is placing increasing importance on the development of accurate GPR models that can enable better interpretation of GPR signals. In turn this should lead to more rapid development in research areas such as, object detection and identification, material property identification, and also antenna design. However, this relies on GPR simulations including models of real antennas, and often this is not the case. The GPR antenna is instead represented by a theoretical source such as a Hertzian dipole [1]-[2]. By omitting a model of the antenna from the simulation, no direct comparison, which is especially important for close range targets, can be made between the model output and data from a real GPR system. Therefore, a GPR simulation should include accurate models of the ground/structure, objects/targets, and the GPR antennas. This paper begins with an overview of the tools and methods used to create the antenna models. Section III describes in detail the antenna models, including the spatial discretisation, excitation, material properties, and computational requirements. In Section IV, free-space response (crosstalk)
results from the models are validated against data from real GPR systems. Finally, further validation results are presented from the comparison of B-scans of buried pipes. II. MODEL CREATION: COMPUTATIONAL TOOLS A range of the most commonly used antennas from leading GPR manufacturers – Geophysical Survey Systems, Inc. (GSSI), Mala Geoscience, and Utsi Electronics – have been studied. This paper focuses on models of a Mala 1.2GHz antenna and GSSI 1.5GHz antenna. Both of these antennas are high frequency and high resolution, and are in common use for applications such as concrete evaluation, reinforcement location, and road layer mapping. An accurate, and preferably fast, electromagnetic (EM) solver is an important tool in any GPR simulation. Additionally, for antenna modelling, good visualisation software is required to create numerical models that include all the fine geometrical features of real GPR antennas. GprMax3D and ParaView are the tools being used for these tasks in this research. GprMax3D is part of a suite of electromagnetic wave simulators [3] based on the Finite-Difference Time-Domain (FDTD) method. GprMax has been used for a variety of different GPR simulations by a number of researchers [4]-[6]. It includes features such as: Perfectly Matched Layer (PML) boundaries; user-specified excitation; 1D transmission line feeding; frequency dependent materials; and parallelisation using OpenMP. ParaView [7] is an open-source parallel application that utilises the Visualisation Toolkit (VTK) format to enable visualisation of scientific data. III. MODEL DETAIL: PARAMETERS AND PROPERTIES A key factor when creating accurate models of real GPR antennas is the availability of information on the antenna’s internals. Whilst most geometrical information was readily obtained, assumptions had to be made in areas such as the antenna feeding circuitry, and material properties such as that of the EM absorbing material being used. A full parametric study was beyond the scope of this research because of the number of different parameters, and the range of potential values each could take. Therefore, unknown parameters were refined by trial-and-error procedure from an initial assumption.
12th International Conference on Ground Penetrating Radar, June 16-19, 2008, Birmingham, UK The main physical features in the antenna models are: the bowtie transmitting and receiving elements, encapsulated in a printed circuit board (PCB); the transmitter and receiver surface mount (SMT) loading resistors; the antenna shielding and enclosure; the EM absorbing material. Figure 1 shows an example of the modelled geometry for the Mala 1.2GHz antenna.
Figure 2. Relative error for different spatial discretisations (0.25mm model baseline reference)
Figure 1. Mala 1.2GHz antenna: Model geometry
3.1 Spatial discretisation A study into the effects of ‘staircasing’ of the antenna bowtie elements was conducted to find a level of spatial discretisation for the models that minimised computational requirements but retained an acceptable level of accuracy. Staircasing is a commonly accepted source of error when using uniform orthogonal grids to model non-conformal features. A simple model consisting of a single bowtie with a 45˚ flare angle (to give maximum potential staircasing error) was used to investigate the errors. Five models were run with different spatial discretisations - 0.25mm, 0.5mm, 1mm, 2mm, and 4mm* - and the relative errors were calculated. The equation in (1) was used as a metric to calculate a relative error for each spatial discretisation, taking the 0.25mm model as a baseline reference. Figure 2 shows the errors when the standard FDTD Yee algorithm is used, and Figure 3 shows CPU time and RAM utilisation. (1) (N.B. N is the number of iterations, and all models are sampled at the coarsest spatial discretisation.)
*
Spatial discretisation was the same for x, y, and z-directions, the models were excited using a 2GHz centre frequency Gaussian pulse, and the electric field measured at a fixed distance from the bowtie.
Figure 3. Computational requirements for different spatial discretisations
A spatial discretisation of 1mm (in x, y, and z-directions) was chosen as an acceptable compromise between computational requirements and model accuracy, whilst also providing sufficient resolution of antenna features. 3.2 Computational requirements Initial models were of the antennas in free-space. A freespace 1mm model of the Mala 1.2GHz antenna was 284x209x155 (9.2 million) cells, utilising 593MB of RAM. A typical 6ns trace required 25mins to run on a 4 x 2-core machine (2.6GHz AMD Opteron processors, 4GB RAM per core). GprMax3D has been benchmarked on both AMD (Linux cluster) and Intel (Apple Mac Pro workstation) architectures, and the results are presented in Figure 4.
12th International Conference on Ground Penetrating Radar, June 16-19, 2008, Birmingham, UK Table 1. Model material properties
Antenna feature
Material
εr
ρ
Bowtie elements
Copper
-
59.6x106S
EM absorber
Carbon-loaded, open-cell foam
12
0.33S
Skid plate
Polycarbonate
4
-
PCB
Glass epoxy
4
-
IV. MODEL VALIDATION
Figure 4. GprMax3D benchmarking
3.3 Excitation The exact shape and frequency content of the pulses used by Mala and GSSI to excite the antennas being studied were unknown. However, many GPR simulations use a Gaussian shaped pulse with a centre frequency around that specified for the antenna [1],[8]-[11]. Therefore, a Gaussian pulse of the form given in (2) was used with a centre frequency of 950MHz for the Mala 1.2GHz antenna, and 1050MHz for the GSSI 1.5GHz antenna. These values were deduced by trial-and-error improvement of initial 1.2GHz and 1.5GHz assumptions.
4.1 Free-space responses (crosstalk) The antenna models were initially validated by comparing their free-space responses with that from the real GPR systems. The following unknown parameters were improved by trial-and-error procedure from initial assumptions to achieve the best fit between modelled and real data: centre frequency of voltage source feed; internal resistance of the voltage source feed; EM absorber permittivity and conductivity; and additionally for the GSSI model the loading resistors on the transmitter and receiver bowties.
(2)
Two feed models were available and potentially applicable to the antenna models. Firstly, a voltage source could be introduced in the position of an electric field component as either a hard source, i.e. replacing the electric field component value, or having lumped internal resistance. Secondly, it was possible to define a 1D two-wire transmission line to used as a feed. Both feed models were investigated but it was found that using a voltage source with internal resistance produced results that more accurately matched data from the real GPR systems. 3.4 Material properties Most of the materials used by the manufacturers to design and build the antennas were easily identifiable, and their properties (most importantly permittivity and conductivity) readily obtained, or calculated in the case of discrete circuit components. Both Mala and GSSI use EM absorbing material in their antennas whose exact properties are not known. Once again initial assumptions from data available for similar products such as Eccosorb [12] were improved by trialand-error procedure. Table 1 lists the main properties for the key materials used in the models.
Figure 5. Mala 1.2GHz antenna: Real vs. modelled crosstalk
Figure 6. GSSI 1.5GHz antenna: Real vs. modelled crosstalk
12th International Conference on Ground Penetrating Radar, June 16-19, 2008, Birmingham, UK Figure 5 and Figure 6 show that the modelled responses for the Mala and GSSI antennas compare well with the responses recorded from the real systems. A trade-off exists between achieving good matches for the different wavelets that make up the overall modelled signal. After setting the known parameters in the model, the values for permittivity and conductivity of the EM absorber material were found to have the most significant impact on the amplitude and phase values of the signal. For example varying the permittivity of the absorber changed the amplitudes of the second and third positive peaks and the second negative trough in the signal. Generally the amplitudes increased or decreased by a similar amount for each peak/trough. The conductivity of the absorber affected the amplitude and phase of the third positive peak, and second negative trough. It was also found that the permittivity of the PCB affected the late-time (tail) amplitudes of the signal. 4.2 B-scans from sandbox experiments Once a satisfactory match was achieved between modelled and real free-space responses, further validation was conducted in the form of B-scans of “realistic” environments. A sandbox experiment was setup using dry sand (with a relative permittivity of 3) and a selection of pipes of different materials and diameters. The rationale behind this setup was two-fold: firstly to allow more comprehensive validation of the antenna models, and secondly for future investigation of the correlation between material properties/geometry, and wavelets in the GPR signal. The results from one the experiments are presented here. A 15mm diameter copper pipe was buried at a depth of 100mm, and directly below it, at a depth of 250mm, a water-filled plastic pipe of diameter 38mm was also buried. Figure 7 shows A-scans from the actual GPR system, the full antenna model, and also from a model where a Hertzian dipole source was used instead of the antenna model. There is excellent agreement between the real GPR signal and the modelled one, and the differences between the real GPR signal and the modelled signal with the simple theoretical source are clearly shown. This reinforces the need for incorporating a model of the actual antenna in GPR simulations. Figure 8 and Figure 9 show B-scans for the buried pipes, and further demonstrate the good agreement between the real and modelled data.
Figure 7. Mala 1.2GHz antenna: Real vs. modelled A-scan of copper and plastic pipes buried in sand
Figure 8. Mala 1.2GHz antenna: Real B-scan of copper and plastic pipes buried in sand
Figure 9. Mala 1.2GHz antenna: Modelled B-scan of copper and plastic pipes buried in sand
12th International Conference on Ground Penetrating Radar, June 16-19, 2008, Birmingham, UK V. CONCLUSIONS A toolset has been put together that allows the creation, visualisation, and validation of detailed three-dimensional GPR antenna models. GprMax is an EM simulator based on the FDTD method, and is used along with ParaView, a parallel visualisation application, for this process. Initial models of commonly used commercial antennas (Mala 1.2GHz and GSSI 1.5GHz) have shown good agreement with data from the actual GPR systems. The validation process has composed comparison of free-space responses followed by comparison of B-scans of more realistic environments i.e. buried pipe detection. These models have been built without any intimate knowledge of the internals of the antennas. Trial-and-error refinement of estimates for parameters in areas such as material properties and antenna excitation were employed. Accurate models of realistic GPR antennas will permit investigation into areas such as the correlation of ground/structure material properties, and target/scatterer geometry with the wavelets that compose the actual GPR signal. The models will also enable research into antenna coupling effects with different ground/structural materials. VI. FURTHER WORK The authors hope for communication with GPR system manufacturers so that the antenna models can be further improved. Alternatively, optimisation techniques such as Taguchi’s method [13] are being considered to help improve the models in terms of refinement of key parameters. This could be extended to investigating different antenna designs. It is hoped that the computational requirements of the models can be reduced by using an FDTD-ADI algorithm. This permits relaxation of the standard FDTD CourantFrederichs-Levy stability condition [14], and hence a larger time-step maybe used. VII. ACKNOWLEDGMENTS The authors would like to thank William Hall and Laura Scott for their contribution of experimental validation data to this research. VIII. REFERENCES [1] Gurel, L. and Oguz, U. (2000). Three-dimensional FDTD modeling of a ground-penetrating radar. Geoscience and Remote Sensing, IEEE Transactions on, 38(4), 15131521. [2] Teixeira, F. L., Chew, W. C., Straka, M., Oristaglio, M. L., and Wang, T. (Nov 1998). Finite-difference timedomain simulation of ground penetrating radar on dispersive, inhomogeneous, and conductive soils. Geoscience and Remote Sensing, IEEE Transactions on, 36(6), 19281937.
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