Ground-penetrating radar (GPR) is a non-invasive prospecting technique based on the electromagnetic waves sampling of the near surface. Building quantitative images through these waves requires the reconstruction of both

electrical permittivity and conductivity. This multi-parameter reconstruction is performed through the minimization of a misfit function measuring the discrepancy between observed and synthetic data. The minimization is achieved with a local descent method based on the Newton equation. Both the gradient and the product of the

Hessian matrix with a model vector are necessary for avoiding any trade-off between parameter classes, especially when high contrasts are encountered by electromagnetic waves. This presentation is devoted to the design

of these two key ingredients needed when updating the model, based on efficient first- and second-order adjoint methods. We formulate the problem in the frequency domain and we show that we need two forward modeling for the gradient and two additional forward modeling for the product of the Hessian matrix and a model vector. Our

formulation is such that these quantities are obtained through solution fields, regardless of the numerical scheme used to obtain them.


Article metrics loading...

Loading full text...

Full text loading...


  1. Deeds, J. and Bradford, J.
    [2002] Characterization of an aquitard and direct detection of LNAPL at Hill Air Force base using GPR AVO and migration velocity analyses. In: 9th International Conference on Ground Penetrating Radar (GPR 2002), Santa Barbara, California (USA), SPIE proceedings series, 4758. 323–329.
    [Google Scholar]
  2. Deparis, J. and Garambois, S.
    [2009] On the use of dispersive APVO GPR curves for thin-bed properties estimation: Theory and application to fracture characterization. Geophysics, 74(1), J1–J12.
    [Google Scholar]
  3. Fischer, E., McMechan, G.A. and Annan, A.P.
    [1992a] Acquisition and processing of wide-aperture ground-penetrating radar data. Geophysics, 57(3), 495–504.
    [Google Scholar]
  4. Fischer, E., McMechan, G.A., Annan, A.P. and Cosway, S.W.
    [1992b] Examples of reverse-time migration of single-channel, ground-penetrating radar profiles. Geophysics, 57(4), 577–586.
    [Google Scholar]
  5. Gloaguen, E., Marcotte, D., Chouteau, M. and Perroud, H.
    [2005] Borehole radar velocity inversion using cokrig-ing and cosimulation. Journal of Applied Geophysics, 57, 242–259.
    [Google Scholar]
  6. Hustedt, B., Operto, S. and Virieux, J.
    [2004] Mixed-grid and staggered-grid finite difference methods for frequency domain acoustic wave modelling. Geophysical Journal International, 157, 1269–1296.
    [Google Scholar]
  7. Lavoué, F., Brossier, R., Métivier, L., Garambois, S. and Virieux, J.
    [2014] Two-dimensional permittivity and conductivity imaging by full waveform inversion of multioffset GPR data: a frequency-domain quasi-Newton approach. Geophysical Journal International, 197(1), 248–268.
    [Google Scholar]
  8. Meles, G.A., Greenhalgh, S., van der Kruk, J., Green, A.G. and Maurer, H.
    [2011] Taming the non-linearity problem in GPR full-waveform inversion for high contrast media. Journal of Applied Geophysics, 73, 174–186.
    [Google Scholar]
  9. Meles, G.A., van der Kruk, J., Greenhalgh, S.A., Ernst, J.R., Maurer, H. and 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, 3391–3407.
    [Google Scholar]
  10. Métivier, L., Bretaudeau, F., Brossier, R., Operto, S. and Virieux, J.
    [2014] Full waveform inversion and the truncated Newton method: quantitative imaging of complex subsurface structures. Geophysical Prospecting, 62, 1353–1375.
    [Google Scholar]
  11. MUMPS-team
    [2009] MUMPS - MUltifrontal Massively Parallel Solver users’ guide - version 4.9.2 (November 5, 2009). ENSEEIHT-ENS Lyon, http://www.enseeiht.fr/apo/MUMPS/ or http://graal.ens-lyon.fr/MUMPS.
    [Google Scholar]
  12. Musil, M., Maurer, H., Holliger, K. and Green, A.G.
    [2006] Internal structure of an alpine rock glacier based on crosshole georadar traveltimes and amplitudes. Geophysical Prospecting, 54, 273–285.
    [Google Scholar]
  13. Plessix, R.E.
    [2006] A review of the adjoint-state method for computing the gradient of a functional with geophysical applications. Geophysical Journal International, 167(2), 495–503.
    [Google Scholar]

Data & Media loading...

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error