1887
  1. Home
  2. A-Z Publications
  3. Near Surface Geophysics
  4. Volume 10, Issue 6
  5. Article
Volume 10 Number 6
  • ISSN: 1569-4445
  • E-ISSN: 1873-0604

Abstract

ABSTRACT

Ground‐penetrating radar (GPR) data affected by waveguide dispersion are not straightforward to analyse. Therefore, waveguide dispersed common midpoint measurements are typically interpreted using so‐called dispersion curves, which describe the phase velocity as a function of frequency. These dispersion curves are typically evaluated with deterministic optimization algorithms that derive the dielectric properties of the subsurface as well as the location and depth of the respective layers. However, these methods do not provide estimates of the uncertainty of the inferred subsurface properties. Here, we applied a formal Bayesian inversion methodology using the recently developed DiffeRential Evolution Adaptive Metropolis algorithm. This Markov Chain Monte Carlo simulation method rapidly estimates the (non‐linear) parameter uncertainty and helps to treat the measurement error explicitly. We found that the frequency range used in the inversion has an important influence on the posterior parameter estimates, essentially because parameter sensitivity varies with measurement frequency. Moreover, we established that the measurement error associated with the dispersion curve is frequency dependent and that the estimated model parameters become severely biased if this frequency‐dependent nature of the measurement error is not properly accounted for. We estimated these frequency‐dependent measurement errors together with the model parameters using the algorithm. The posterior distribution of the model parameters derived in this way compared well with inversion results for a reduced frequency bandwidth which is an alternative, yet subjective method to reduce the bias introduced by this frequency‐dependent measurement error. Altogether, our inversion procedure provides an integrated and objective methodology for the analysis of dispersive GPR data and appropriately treats the measurement error and parameter uncertainty.

© European Association of Geoscientists and Engineers © 2012 European Association of Geoscientists and Engineers
Loading

Article metrics loading...

/content/journals/10.3997/1873-0604.2012041
2012-03-01
2024-04-16

  • From This Site

    /content/journals/10.3997/1873-0604.2012041
    dcterms_title,dcterms_subject,pub_keyword
    -contentType:Journal -contentType:Contributor -contentType:Concept -contentType:Institution
    10
    5
Loading full text...

Full text loading...

References

  1. ArconeS.A.1984. Field Observations of Electromagnetic Pulse‐Propagation in Dielectric Slabs. Geophysics49, 1763–1773.
     [Google Scholar]
  2. ArconeS.A., PeapplesP.R. and LiuL.B.2003. Propagation of a ground‐penetrating radar (GPR) pulse in a thin‐surface waveguide. Geophysics68, 1922–1933.
     [Google Scholar]
  3. BohidarR.N. and HermanceJ.F.2002. The GPR refraction method. Geophysics67, 1474–1485.
     [Google Scholar]
  4. BradfordJ.H.2008. Measuring water content heterogeneity using multifold GPR with reflection tomography. Vadose Zone Journal7, 184–193
     [Google Scholar]
  5. BuddenK.G.1961. The Wave‐Guide Mode Theory of Wave Propagation. Prentice‐Hall Inc., London
  6. DannowskiG. and YaramanciU.1999. Estimation of water content and porosity using combined radar and geoelectrical measurements. European Journal of Environmental and Engineering Geophysics4, 71–85.
     [Google Scholar]
  7. EndresA.L., ClementW.P. and RudolphD.L.2000. Ground penetrating radar imaging of an aquifer during a pumping test. Ground Water38, 566–576.
     [Google Scholar]
  8. GalagedaraL.W., ParkinG.W. and RedmanJ.D.2003. An analysis of the ground‐penetrating radar direct ground wave method for soil water content measurement. Hydrological Processes17, 3615–3628.
     [Google Scholar]
  9. GaramboisS., SenechalP. and PerroudH.2002. On the use of combined geophysical methods to assess water content and water conductivity of near‐surface formations. Journal of Hydrology259, 32–48.
     [Google Scholar]
  10. GelmanA. and RubinD.B.1992. Inference from Iterative Simulation Using Multiple Sequences. Statistical Science7, 457–472.
     [Google Scholar]
  11. GerhardsH., WollschlagerU., YuQ., SchiwekP., PanX. and RothK.2008. Continuous and simultaneous measurement of reflector depth and average soil‐water content with multichannel ground‐penetrating radar. Geophysics73, J15–J23.
     [Google Scholar]
  12. GreavesR.J., LesmesD.P., LeeJ.M. and ToksozM.N.1996. Velocity variations and water content estimated from multi‐offset, ground‐penetrating radar. Geophysics61, 683–695.
     [Google Scholar]
  13. GroteK., HubbardS. and RubinY.2003. Field‐scale estimation of volumetric water content using ground‐penetrating radar ground wave techniques. Water Resources Research39, 1321.
     [Google Scholar]
  14. HaarderE.B., LoomsM.C., JensenK.H. and NielsenL.2011. Visualizing Unsaturated Flow Phenomena Using High‐Resolution Reflection Ground Penetrating Radar. Vadose Zone Journal10, 84–97.
     [Google Scholar]
  15. HinnellA.C., FerreT.P.A., VrugtJ.A., HuismanJ.A., MoyseyS., RingsJ. and KowalskyM.B.2010. Improved extraction of hydrologic information from geophysical data through coupled hydrogeophysical inversion. Water Resources Research46, W00D40.
     [Google Scholar]
  16. Huisman, J.A., Bouten, W. and Vrugt, J.A.2004. Accuracy of frequency domain analysis scenarios for the determination of complex dielectric permittivity. Water Resources Research40, W02401
     [Google Scholar]
  17. HuismanJ.A., HubbardS.S., RedmanJ.D. and AnnanA.P.2003a. Measuring Soil Water Content with Ground Penetrating Radar: A Review. Vadose Zone Journal2, 476–491.
     [Google Scholar]
  18. HuismanJ.A., RingsJ., VrugtJ.A., SorgJ. and VereeckenH.2010. Hydraulic properties of a model dike from coupled Bayesian and multi‐criteria hydrogeophysical inversion. Journal of Hydrology380, 62–73.
     [Google Scholar]
  19. HuismanJ.A., SnepvangersJ.J.J.C., BoutenW. and HeuvelinkG.B.M.2003b. Monitoring temporal development of spatial soil water content variation: Comparison of ground‐penetrating radar and time domain reflectometry. Vadose Zone Journal2, 519–529.
     [Google Scholar]
  20. HuismanJ.A., SperlC., BoutenW. and VerstratenJ.M.2001. Soil water content measurements at different scales: Accuracy of time domain reflectometry and ground‐penetrating radar. Journal of Hydrology245, 48–58.
     [Google Scholar]
  21. IrvingJ. and SinghaK.2010. Stochastic inversion of tracer test and electrical geophysical data to estimate hydraulic conductivities. Water Resources Research46, W11514.
     [Google Scholar]
  22. JacobR.W. and HermanceJ.F.2004. Assessing the precision of GPR velocity and vertical two‐way travel time estimates. Journal of Environmental and Engineering Geophysics9, 143–153.
     [Google Scholar]
  23. KavetskiD., KuczeraG. and FranksS.W.2006. Bayesian analysis of input uncertainty in hydrological modeling: 1. Theory. Water Resources Research42, W03407.
     [Google Scholar]
  24. van der KrukJ.2006. Properties of surface waveguides derived from inversion of fundamental and higher mode dispersive GPR data. IEEE Transactions on Geoscience and Remote Sensing44, 2908–2915.
     [Google Scholar]
  25. van der KrukJ., ArconeS.A. and LiuL.2007. Fundamental and higher mode inversion of dispersed GPR waves propagating in an ice layer. IEEE Transactions on Geoscience and Remote Sensing45, 2483–2491.
     [Google Scholar]
  26. van der KrukJ., JacobR.W. and VereeckenH.2010. Properties of precipitation‐induced multilayer surface waveguides derived from inversion of dispersive TE and TM GPR data. Geophysics75, WA263–WA273.
     [Google Scholar]
  27. van der KrukJ., SteelmanC. M., EndresA. L. and VereeckenH.2009. Dispersion inversion of electromagnetic pulse propagation within freezing and thawing soil waveguides. Geophysical Research Letters36, L18503–L18507.
     [Google Scholar]
  28. van der KrukJ., StreichR. and GreenA.G.2006. Properties of surface waveguides derived from separate and joint inversion of dispersive TE and TM GPR data. Geophysics71, K19–K29.
     [Google Scholar]
  29. LagariasJ.C., ReedsJ.A., WrightM.H. and WrightP.E.1998. Convergence properties of the Nelder‐Mead simplex method in low dimensions. Siam Journal on Optimization9, 112–147.
     [Google Scholar]
  30. LuntI.A., HubbardS.S. and RubinY.2005. Soil moisture content estimation using ground‐penetrating radar reflection data. Journal of Hydrology307, 254–269.
     [Google Scholar]
  31. MosegaardK. and TarantolaA.1995. Monte Carlo sampling of solutions to inverse problems. Journal of Geophysical Research100, 12431–12448.
     [Google Scholar]
  32. MoyseyS. and KnightR.2004. Modeling the field‐scale relationship between dielectric constant and water content in heterogeneous systems. Water Resources Research40, 10.
     [Google Scholar]
  33. van OvermeerenR.A., SariowanS.V. and GehrelsJ.C.1997. Ground penetrating radar for determining volumetric soil water content; Results of comparative measurements at two test sites. Journal of Hydrology197, 316–338.
     [Google Scholar]
  34. ParkC.B., MillerR.D. and XiaJ.X.1998. Imaging dispersion curves of surface waves on multi‐channel record. In: Imaging dispersion curves of surface waves on multi‐channel record, pp. 1377–1380.
     [Google Scholar]
  35. PettinelliE., VannaroniG., Di PasquoB., MatteiE., Di MatteoA., De SantisA. and AnnanP.A.2007. Correlation between near‐surface electromagnetic soil parameters and early‐time GPR signals: An experimental study. Geophysics72, A25–A28.
     [Google Scholar]
  36. RhimH.C.2011. Measurements of dielectric constants of soil to develop a landslide prediction system. Smart Structures and Systems7, 319–328.
     [Google Scholar]
  37. SambridgeM. and MosegaardK.2002. Monte Carlo methods in geophysical inverse problems. Reviews of Geophysics40, 1009.
     [Google Scholar]
  38. ScharnaglB., VrugtJ.A., VereeckenH. and HerbstM.2011. Inverse modelling of in situ soil water dynamics: Investigating the effect of different prior distributions of the soil hydraulic parameters. Hydrology and Earth System Sciences15, 3043–3059.
     [Google Scholar]
  39. SchoupsG. and VrugtJ.A.2010. A formal likelihood function for parameter and predictive inference of hydrologic models with correlated, heteroscedastic, and non‐Gaussian errors. Water Resources Research46, 17.
     [Google Scholar]
  40. SlobE.2010. Uncertainty in ground penetrating radar models. Proceedings of 13th International Conference on Ground Penetrating Radar (GPR) 2010, doi: 10.1109/ICGPR.2010.5550154
  41. SteelmanC.M. and EndresA.L.2010. An examination of direct ground wave soil moisture monitoring over an annual cycle of soil conditions. Water Resources Research46, 16.
     [Google Scholar]
  42. SteelmanC.M. and EndresA.L.2011. Comparison of Petrophysical Relationships for Soil Moisture Estimation using GPR Ground Waves. Vadose Zone Journal10, 270–285.
     [Google Scholar]
  43. SteelmanC.M., EndresA.L. and van der KrukJ.2010. Field Observations of Shallow Freeze and Thaw processes using High‐Frequency Ground‐Penetrating Radar. Hydrological Processes24, 2022–2033.
     [Google Scholar]
  44. StrobbiaC. and CassianiG.2007. Multilayer ground‐penetrating radar guided waves in shallow soil layers for estimating soil water content. Geophysics72, J17–J29.
     [Google Scholar]
  45. TuressonA.2006. Water content and porosity estimated from ground‐penetrating radar and resistivity. Journal of Applied Geophysics58, 99–111
     [Google Scholar]
  46. VrugtJ.A. and BoutenW.2002. Validity of first‐order approximations to describe parameter uncertainty in soil hydrologic models. Soil Science Society of America Journal66, 1740–1751.
     [Google Scholar]
  47. VrugtJ.A., ter BraakC.J.F., ClarkM.P., HymanJ.M. and RobinsonB.2008. Treatment of input uncertainty in hydrologic modeling: Doing hydrology backwards with Markov chain Monte Carlo simulation. Water Resources Research44, W00B09.
     [Google Scholar]
  48. VrugtJ.A., ter BraakC.J.F., DiksC.G.H., RobinsonB.A., HymanJ.M. and HigdonD.2009. Accelerating Markov Chain Monte Carlo Simulation by Differential Evolution with Self‐Adaptive Randomized Subspace Sampling. International Journal of Nonlinear Sciences and Numerical Simulations10, 273–290.
     [Google Scholar]
  49. VrugtJ.A., ter BraakC.J.F., GuptaH.V. and RobinsonB.A.2009. Equifinality of formal (DREAM) and informal (GLUE) Bayesian approaches in hydrologic modeling?Stochastic Environmental Research and Risk Assessment23, 1011–1026.
     [Google Scholar]
  50. WestermannS., WollschlägerU. and BoikeJ.2010. Monitoring of active layer dynamics at a permafrost site on Svalbard using multi‐channel ground‐penetrating radar. Cryosphere4, 475–487.
     [Google Scholar]
  51. WollschlägerU., GerhardsH., YuQ. and RothK.2010. Multi‐channel ground‐penetrating radar to explore spatial variations in thaw depth and moisture content in the active layer of a permafrost site. Cryosphere4, 269–283.
     [Google Scholar]
http://instance.metastore.ingenta.com/content/journals/10.3997/1873-0604.2012041
Loading
Integrated analysis of waveguide dispersed GPR pulses using deterministic and Bayesian inversion methods
Near Surface Geophysics 10, 641 (2012); https://doi.org/10.3997/1873-0604.2012041
/content/journals/10.3997/1873-0604.2012041
/content/journals/10.3997/1873-0604.2012041
Loading

Data & Media loading...

  • Article Type: Research Article

Most Cited This Month Most Cited RSS feed

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