Three-Dimensional Reverse Time Migration of Ground-Penetrating Radar Signals

  • Weiqiang Zhu
  • Qinghua HuangEmail author
  • Lanbo Liu
  • Bowen Ma


Three-dimensional (3D) ground-penetrating radar (GPR) systems and 3D seismic imaging techniques have been developing fast and evolving rapidly in the last decade. Ray-based migration methods have been successfully applied to processing 3D GPR signals based on the similarity between electromagnetic and seismic waves. However, reverse time migration (RTM) of 3D GPR signals has not been well studied in the past. In this paper, we present a 3D RTM based on Maxwell’s equations for 3D GPR surveys. Migration recovers the true subsurface structure from a distorted and unfocused time profile and suppresses common electromagnetic clutter and noise. RTM based on Maxwell’s equations can consider conductivity directly and compensate for the attenuation within a high-conductivity zone. Compared with 2D RTM, 3D RTM back-propagates both in-line and cross-line signals simultaneously and can include complex 3D permittivity and conductivity models. We have integrated a parallel finite-difference time-domain (FDTD) algorithm based on a hybrid MPI and OpenMP scheme to reduce the computational cost of 3D problems. The 3D RTM experiments on an anomaly of “EM” shape and a realistic sand dune model demonstrate the effective recovery of 3D subsurface structures.


Three-dimensional (3D) ground-penetrating radar (GPR) reverse time migration (RTM) 



This work is supported by the National Science Foundation of China (41574104, 41874082). The calculations were performed on a Tianhe-1(A) supercomputer. We are grateful to the three anonymous reviewers for their excellent reviews and constructive suggestions.


  1. Baysal, E., Kosloff, D. D., & Sherwood, J. W. C. (1983). Reverse time migration. Geophysics, 48(11), 1514–1524.CrossRefGoogle Scholar
  2. Benson, A. K. (1995). Applications of ground penetrating radar in assessing some geological hazards: examples of groundwater contamination, faults, cavities. Journal of Applied Geophysics, 33(1), 177–193.CrossRefGoogle Scholar
  3. Biondi, B. (2007). Concepts and Applications in 3D Seismic Imaging. Society of Exploration Geophysicists and European Association of Geoscientists and Engineers.Google Scholar
  4. Bourgeois, J. M., & Smith, G. S. (1996). A fully three-dimensional simulation of a ground-penetrating radar: FDTD theory compared with experiment. IEEE Transactions on Geoscience and Remote Sensing, 34(1), 36–44.CrossRefGoogle Scholar
  5. Bristow, C. S., Bailey, S. D., & Lancaster, N. (2000). The sedimentary structure of linear sand dunes. Nature, 406(6791), 56–59.CrossRefGoogle Scholar
  6. Bristow, C. S., Porat, N., Duller, G., Armitage, S. J., Roberts, H. M., Clarke, B. M., et al. (2003). Evidence for dune reactivation from GPR profiles on the Maputaland coastal plain, South Africa. Geological Society, London, Special Publications, 211, 29–46.CrossRefGoogle Scholar
  7. Claerbout, J. F. (1971). Toward a unified theory of reflector mapping. Geophysics, 36(3), 467–481.CrossRefGoogle Scholar
  8. Daniels, D. J. (2005). Ground Penetrating Radar. Hoboken: Wiley.Google Scholar
  9. Ernst, J. R., Maurer, H., Green, A. G., & Holliger, K. (2007). Full-waveform inversion of crosshole radar data based on 2-D finite-difference time-domain solutions of Maxwell’s equations. IEEE Transactions on Geoscience and Remote Sensing, 45(9), 2807–2828.CrossRefGoogle Scholar
  10. Feng, X., Wang, Q., Lu, Q., Liu, C., Liang, W., Li, H., Yu, Y., Ren, Q. (July 2012). Subsurface imaging by modified migration for irregular GPR data. In: 2012 IEEE International Geoscience and Remote Sensing Symposium (IGARSS). pp. 3194–3197.Google Scholar
  11. Fisher, E., McMechan, G. A., Annan, A. P., & Cosway, S. W. (1992). Examples of reverse-time migration of single-channel, ground-penetrating radar profiles. Geophysics, 57(4), 577–586.CrossRefGoogle Scholar
  12. Fu, L., Liu, S., Liu, L., & Wu, J. (2014). Airborne ground penetrating radar numerical simulation and reverse time migration. Chinese Journal of Geophysics-Chinese Edition, 57(5), 1636–1646.Google Scholar
  13. Green, A., Gross, R., Holliger, K., Horstmeyer, H., & Baldwin, J. (2003). Results of 3-D georadar surveying and trenching the San Andreas fault near its northern landward limit. Tectonophysics, 368(1), 7–23.CrossRefGoogle Scholar
  14. Gross, R., Green, A., Horstmeyer, H., Holliger, K., & Baldwin, J. (2003). 3-D georadar images of an active fault: efficient data acquisition, processing and interpretation strategies. Subsurface Sensing Technologies and Applications, 4(1), 19–40.CrossRefGoogle Scholar
  15. Herrmann, F. J., & Hennenfent, G. (2008). Non-parametric seismic data recovery with curvelet frames. Geophysical Journal International, 173(1), 233–248.CrossRefGoogle Scholar
  16. Huang, Q., Li, Z., & Wang, Y. (2010). A parallel 3-D staggered grid pseudospectral time domain method for ground-penetrating radar wave simulation. Journal of Geophysical Research, 115(B12), B12101.CrossRefGoogle Scholar
  17. Jakubowicz, H., & Levin, S. (1983). A simple exact method of 3-D migration-theory. Geophysical Prospecting, 31(1), 34–56.CrossRefGoogle Scholar
  18. Jol, H. M. (2008). Ground penetrating radar theory and applications. Amsterdam: Elsevier.Google Scholar
  19. Klokov, A., Sato, M. (July 2011). Application of 3-D migration algorithm to GPR on an irregular ground surface. In: 2011 IEEE International Geoscience and Remote Sensing Symposium (IGARSS). pp. 870–873.Google Scholar
  20. Knight, R. (2001). Ground penetrating radar for environmental applications. Annual Review of Earth and Planetary Sciences, 29(1), 229–255.CrossRefGoogle Scholar
  21. Leuschen, C., & Plumb, R. (2001). A matched-filter-based reverse-time migration algorithm for ground-penetrating radar data. IEEE Transactions on Geoscience and Remote Sensing, 39(5), 929–936.CrossRefGoogle Scholar
  22. Levander, A. R. (1988). Fourth-order finite-difference P-SV seismograms. Geophysics, 53(11), 1425–1436.CrossRefGoogle Scholar
  23. Liu, S., Lei, L., Fu, L., & Wu, J. (2014). Application of pre-stack reverse time migration based on FWI velocity estimation to ground penetrating radar data. Journal of Applied Geophysics, 107, 1–7.CrossRefGoogle Scholar
  24. Loewenthal, D., Lu, L., Roberson, R., & Sherwood, J. (1976). The wave equation applied to migration. Geophysical Prospecting, 24(2), 380–399.CrossRefGoogle Scholar
  25. Mansour, H., Herrmann, F., & Yılmaz, O. (2013). Improved wavefield reconstruction from randomized sampling via weighted one-norm minimization. Geophysics, 78(5), V193–V206.CrossRefGoogle Scholar
  26. McClymont, A. F., Green, A. G., Villamor, P., Horstmeyer, H., Grass, C., & Nobes, D. C. (2008). Characterization of the shallow structures of active fault zones using 3-D ground-penetrating radar data. Journal of Geophysical Research, 113(B10), B10315.CrossRefGoogle Scholar
  27. McMechan, G. A. (1983). Migration by extrapolation of time-dependent boundary values. Geophysical Prospecting, 31(3), 413–420.CrossRefGoogle Scholar
  28. Meles, G. A., Van Der Kruk, J., Greenhalgh, S. A., Ernst, J. R., Maurer, H., & Green, A. G. (2010). A new vector waveform inversion algorithm for simultaneous updating of conductivity and permittivity parameters from combination crosshole/borehole-to- surface GPR data. IEEE Transactions on Geoscience and Remote Sensing, 48(9), 3391–3407.CrossRefGoogle Scholar
  29. Moran, M. L., Greenfield, R. J., Arcone, S. A., & Delaney, A. J. (2000). Multidimensional GPR array processing using Kirchhoff migration. Journal of Applied Geophysics, 43(2), 281–295.CrossRefGoogle Scholar
  30. Naghizadeh, M., & Sacchi, M. (2010). Beyond alias hierarchical scale curvelet interpolation of regularly and irregularly sampled seismic data. Geophysics, 75(6), WB189–WB202.CrossRefGoogle Scholar
  31. Neal, A. (2004). Ground-penetrating radar and its use in sedimentology: principles, problems and progress. Earth-Science Reviews, 66(3–4), 261–330.CrossRefGoogle Scholar
  32. Olhoeft, G. R. (1998). Electrical, magnetic, and geometric properties that determine ground penetrating radar performance. In: Proceedings of GPR ‘98, Seventh International Conference on Ground Penetrating Radar. University of Kansas, Lawrence, KS. Vol. 98. pp. 177–182.Google Scholar
  33. Qian, R., & Liu, L. (2016). Internal structure of sand dunes in the Badain Jaran desert revealed by GPR. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 9(1), 159–166.CrossRefGoogle Scholar
  34. Radzevicius, S. (2008). Practical 3-D migration and visualization for accurate imaging of complex geometries with GPR. Journal of Environmental & Engineering Geophysics, 13(2), 99–112.CrossRefGoogle Scholar
  35. Roden, J. A., & Gedney, S. D. (2000). Convolutional PML (CPML): an efficient FDTD implementation of the CFS-PML for arbitrary media. Microwave and Optical Technology Letters, 27(5), 334–338.CrossRefGoogle Scholar
  36. Song, J., Liu, Q. H., Torrione, P., & Collins, L. (2006). Two-dimensional and three-dimensional NUFFT migration method for landmine detection using ground-penetrating radar. IEEE Transactions on Geoscience and Remote Sensing, 44(6), 1462–1469.CrossRefGoogle Scholar
  37. Su, M., El-Kady, I., Bader, D., Lin, S. (Aug 2004). A novel FDTD application featuring OpenMP-MPI hybrid parallelization. In: ICPP 2004 International Conference on Parallel Processing. Vol. 1. pp. 373–379.Google Scholar
  38. Whitmore, N. D. (1983). Iterative depth migration by backward time propagation. SEG Technical Program Expanded Abstracts, 1983, 382–385.Google Scholar
  39. Yang, X., Klotzsche, A., Meles, G., Vereecken, H., & Van Der Kruk, J. (2013). Improvements in crosshole GPR full-waveform inversion and application on data measured at the Boise hydrogeophysics research site. Journal of Applied Geophysics, 99, 114–124.CrossRefGoogle Scholar
  40. Yoon, K., Shin, C., Suh, S., Lines, L. R., & Hong, S. (2003). 3D reverse-time migration using the acoustic wave equation: an experience with the SEG/EAGE data set. The Leading Edge, 22(1), 38–41.CrossRefGoogle Scholar
  41. Zhu, T., Harris, J., & Biondi, B. (2014). Q-compensated reverse-time migration. Geophysics, 79(3), S77–S87.CrossRefGoogle Scholar
  42. Zhu, W., & Huang, Q. (2016). Attenuation compensated reverse time migration method of ground penetrating radar signals. Chinese Journal of Geophysics, 59(10), 3909.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Geophysics, School of Earth and Space SciencesPeking UniversityBeijingChina
  2. 2.Department of Civil and Environmental EngineeringUniversity of ConnecticutStorrsUSA
  3. 3.Department of GeophysicsStanford UniversityStanfordUSA

Personalised recommendations