1887
Volume 59, Issue 3
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

In this work a new algorithm for the fast and efficient 3D inversion of conventional 2D surface electrical resistivity tomography lines is presented. The proposed approach lies on the assumption that for every surface measurement there is a large number of 3D parameters with very small absolute Jacobian matrix values, which can be excluded in advance from the Jacobian matrix calculation, as they do not contribute significant information in the inversion procedure. A sensitivity analysis for both homogeneous and inhomogeneous earth models showed that each measurement has a specific region of influence, which can be limited to parameters in a critical rectangular prism volume. Application of the proposed algorithm accelerated almost three times the Jacobian (sensitivity) matrix calculation for the data sets tested in this work. Moreover, application of the least squares regression iterative inversion technique, resulted in a new 3D resistivity inversion algorithm more than 2.7 times faster and with computer memory requirements less than half compared to the original algorithm. The efficiency and accuracy of the algorithm was verified using synthetic models representing typical archaeological structures, as well as field data collected from two archaeological sites in Greece, employing different electrode configurations. The applicability of the presented approach is demonstrated for archaeological investigations and the basic idea of the proposed algorithm can be easily extended for the inversion of other geophysical data.

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2011-01-24
2024-03-29
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References

  1. ChambersJ.E, OgilvyR.D., KurasO. and MeldrumP.I.2002. 3D electrical imaging of known targets at a controlled environmental test site. Environmental Geology41, 690–704.
    [Google Scholar]
  2. ClarkA.1990. Seeing Beneath the Soil‐prospecting Methods in Archaeology . B.T. Batsford Ltd.
    [Google Scholar]
  3. ConstableS.C., ParkerR.L. and ConstableC.G.1987. Occam's inversion: A practical algorithm for generating smooth models from electromagnetic sounding data. Geophysics52, 289–300.
    [Google Scholar]
  4. DabasM., TabbaghA. and TabbaghJ.1994. 3D inversion in subsurface electrical surveying – I. Theory. Geophysical Journal International119, 975–990.
    [Google Scholar]
  5. DiamantiN.G, TsokasG.N., TsourlosP.I. and VafidisA.2005. Integrated interpretation of geophysical data in the archaeological site of Europos (Northern Greece). Archaeological Prospection12, 79–91.
    [Google Scholar]
  6. EllisR.G. and OldenburgD.W.1994. The pole‐pole 3D DC‐resistivity inverse problem: A conjugate gradient approach. Geophysical Journal International119, 187–194.
    [Google Scholar]
  7. GharibiM. and BentleyL.R.2005. Resolution of 3D electrical resistivity images from inversions of 2D orthogonal lines. Journal of Environmental and Engineering Geophysics10, 339–349.
    [Google Scholar]
  8. GüntherT., RückerC. and SpitzerK.2006. Three‐dimensional modelling and inversion of DC resistivity data incorporating topography – II. Inversion. Geophysical Journal International166, 506–517.
    [Google Scholar]
  9. LaBrecqueD.J., MilettoM., DailyW., RamirezA. and OwenE.1996. The effects of noise on Occam's inversion of resistivity tomography data. Geophysics61, 538–548.
    [Google Scholar]
  10. LanczosC.1950An iteration method for the solution of the eigenvalue problem of linear differential and integral operators. Journal of Research of the National Bureau of Standards45, 255–282.
    [Google Scholar]
  11. LesurV., CuerM. and StraubA.1999. 2‐D and 3‐D interpretation of electrical tomography measurements, part 2: The inverse problem. Geophysics64, 396–402.
    [Google Scholar]
  12. LokeM.H. and BarkerR.D.1996. Practical techniques for 3‐D resistivity surveys and data inversion. Geophysical Prospecting44, 499–524.
    [Google Scholar]
  13. MarescotL., LopesS.P., RigobertS. and GreenA.G.2008. Nonlinear inversion of geoelectric data acquired across 3‐D objects using a finite‐element approach. Geophysics73, F121–F133.
    [Google Scholar]
  14. MaurielloP., MonnaD. and PatellaD.1998. 3D geoelectrical tomography and archaeological applications. Geophysical Prospecting46, 543–570.
    [Google Scholar]
  15. McGillivrayP. and OldenburgD.1990. Methods for calculating Frechet derivatives and sensitivities for the non‐linear inverse problem: A comparative study. Geophysical Prospecting38, 499–524.
    [Google Scholar]
  16. NoletG.1983. Inversion and resolution of linear tomographic systems. EOS64, 775–776.
    [Google Scholar]
  17. NoletG.1985. Solving or resolving inadequate and noisy tomographic systems. Journal of Computational Physics61, 463–482.
    [Google Scholar]
  18. NoletG. and SniederG.1990. Solving large linear inverse problems by projection. Geophysical Journal International103, 565–568.
    [Google Scholar]
  19. OsellaA., VegaM. and LascanoE.2005. 3‐D electrical imaging of archaeological sites using electrical and electromagnetic method. Geophysics70, 101–107.
    [Google Scholar]
  20. PaigeC. and SaundersM.1982. LSQR: An algorithm for sparse linear equations and sparse least squares. ACM Transactions on Mathematical Software8, 43–71.
    [Google Scholar]
  21. PainC.C., HerwangerJ.V., WorthingtonM.H. and de OliveiraC.R.E.2002. Effective multidimensional resistivity inversion using finite element techniques. Geophysical Journal International151, 710–728.
    [Google Scholar]
  22. PapadopoulosN.G., TsourlosP., TsokasG.N. and SarrisA.2006. Two‐dimensional and three‐dimensional resistivity imaging in archaeological site investigation. Archaeological Prospection13, 163–181.
    [Google Scholar]
  23. PapadopoulosN.G., TsourlosP., TsokasG.N. and SarrisA.2007. Efficient ERT measuring and inversion strategies for 3D imaging of buried antiquities. Near Surface Geophysics5, 349–362.
    [Google Scholar]
  24. PapazachosC.B. and NoletG.1997. Non‐linear arrival time tomography. Annali di GeophysicaXL, 85–97.
    [Google Scholar]
  25. ParkS.K. and VanG.P.1991. Inversion of pole‐pole data for 3‐D resistivity structures beneath arrays of electrodes. Geophysics56, 951–960.
    [Google Scholar]
  26. PetrickW.R.Jr., SillW.R. and WardS.H.1981. Three‐dimensional resistivity inversion using alpha centers. Geophysics46, 1148–1162.
    [Google Scholar]
  27. PidliseckyA., HaberE. and KnightR.2007. RESINVM3‐D: A MATLAB 3‐D resistivity inversion package. Geophysics72, H1–H10.
    [Google Scholar]
  28. PressW.H., TeukolskyS.A., VetterlingW.T. and FlanneryB.P.1992. Numerical Recipes in C: The Art of Scientific Computing , 2nd edn. Cambridge University Press.
    [Google Scholar]
  29. PridmoreD.F., HohmannG.W., WardS.H. and SillW.R.1981. An investigation of finite‐element modelling for electrical and electromagnetic data in three dimensions. Geophysics46, 1009–1024.
    [Google Scholar]
  30. SambridgeM.S.1990. Non‐linear arrival time inversion: constraining velocity anomalies by seeking smooth models in 3‐D. Geophysical Journal International102, 653–677.
    [Google Scholar]
  31. SarrisA., PapadopoulosN., TrigkasV., LolosY. and KokkinouE.2007. Recovering the urban network of ancient Sikyon through multi‐component geophysical approaches. CAA Berlin, 2–6 April, Expanded Abstracts.
  32. SasakiY.1994. 3‐D inversion using the finite element method. Geophysics59, 1839–1848.
    [Google Scholar]
  33. ScalesJ.1987. Tomographic inversion via the conjugate gradient method. Geophysics52, 179–185.
    [Google Scholar]
  34. ShimaH.1992. 2‐D and 3‐D resistivity image reconstruction using crosshole data. Geophysics57, 1270–1281.
    [Google Scholar]
  35. StummerP., MaurerH. and GreenA.G.2004. Experimental design: Electrical resistivity data sets that provide optimum subsurface information. Geophysics69, 120–139.
    [Google Scholar]
  36. TarantolaA.1987. Inverse Problem Theory . Elsevier.
    [Google Scholar]
  37. TikhonovA.N., LeonovA.S. and YagolaA.G.1998. Non‐linear Ill‐posed Problems . Chapman and Hall.
    [Google Scholar]
  38. TsokasG.N., GiannopoulosA., TsourlosP., VargemezisG., TealbyJ.M., SarrisA. et al . 1994. A large scale geophysical survey in the archaeological site of Europos (northern Greece). Journal of Applied Geophysics32, 85–98.
    [Google Scholar]
  39. TsourlosP. and OgilvyR.1999. An algorithm for the 3‐D inversion of tomographic resistivity and induced polarization data: Preliminary results. Journal of the Balkan Geophysical Society2, 30–45.
    [Google Scholar]
  40. VafidisA., SarrisA., SourlasG. and GaniatsosY.1999. Two and three‐dimensional electrical tomography investigations in the archaeological site of Itanos, Crete, Greece. 2nd Balkan Geophysical Congress and Exhibition, Istanbul , Turkey , 5–9 July, Expanded Abstracts.
    [Google Scholar]
  41. Van Der SluisA. and Van der VorstH.A.1987. Numerical solution of large, sparse algebraic systems, arising from tomographic problems. In: Seismic Tomography (ed. G.Nolet ), pp. 49–84. Reidel.
    [Google Scholar]
  42. Van Der SluisA. and Van der VorstH.A.1990. SIRT‐ and CG‐type methods for the iterative solutions of sparse linear least‐squares problems. Linear Algebra and its Applications130, 257–302.
    [Google Scholar]
  43. YaoZ.S., RobertsR.G. and TryggvasonA.1999. Calculating resolution and covariance matrices for seismic tomography with the LSQR method. Geophysical Journal International138, 886–894.
    [Google Scholar]
  44. YiM.J., KimJ.H., SongY., ChoS.J., ChungS.H. and SuhJ.H.2001. Three‐dimensional imaging of subsurface structures using resistivity data. Geophysical Prospecting49, 483–497.
    [Google Scholar]
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  • Article Type: Research Article
Keyword(s): 3D resistivity inversion; Archaeological prospection; Jacobian matrix; LSQR

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