1887
Volume 9 Number 5
  • ISSN: 1569-4445
  • E-ISSN: 1873-0604

Abstract

ABSTRACT

Electrical resistivity imaging has been successfully used to monitor near‐surface hydrologic processes but use of standard measurement arrays may not provide the greatest data sensitivity to the imaged region. We present a method of experimental design based on the concept of informed imaging for creating an electrical resistivity imaging experiment to monitor flow beneath a recharge pond. Informed imaging is the integration of all available data about a site into the acquisition, inversion and interpretation of electrical resistivity data. Informed experimental design uses all available information to develop an model of the subsurface conductivity structure that guides the selection of measurement arrays for an electrical resistivity imaging experiment given spatial and temporal constraints on the acquisition. Selection of arrays focuses on maximizing the amount of unique information acquired with each source pair. We apply the method to the selection of arrays for imaging the top 5 m of the subsurface beneath a recharge pond in Northern California, which is part of an aquifer storage and recovery project. Decreasing infiltration rates over time reduce the effectiveness of the recharge pond. We seek to monitor infiltration processes at the contact between a fines‐rich sand layer and coarser sand layer in an effort to understand the hydrologic controls on infiltration. The performance of the arrays selected using informed experimental design relative to two standard arrays (Wenner and dipole‐dipole) is validated on two synthetic subsurface conductivity models, which are representative of conductivity structures that may arise during an infiltration event. Performance is evaluated in terms of a singular value decomposition of the sensitivity matrix produced by the three types of arrays, as well as a measure of the region of investigation. Results demonstrate that arrays selected using informed experimental design provide independent information about the imaged region and are robust in the presence of noise, improving the ability to image changes in a conductivity structure that result from infiltration processes.

Loading

Article metrics loading...

/content/journals/10.3997/1873-0604.2011027
2018-12-18
2024-04-19
Loading full text...

Full text loading...

References

  1. AlfouzanF.A., LokeM.H. and NawawiM.N.M.2010. An evaluation of optimization strategies to automatically select the optimal set of array configurations for 2D electrical imaging surveys. Journal of Geophysics and Engineering7, 332–342.
    [Google Scholar]
  2. BardowA.2006. Optimal experimental design for ill‐posed problems. Proceedings of the 16th European Symposium on Computer Aided Process Engineering and 9th International Symposium on Process Systems Engineering, Expanded Abstracts, 173–178.
    [Google Scholar]
  3. BarthN. and WunschC.1990. Oceanographic experimental design by simulated annealing. Journal of Physical Oceanography20, 1249–1263.
    [Google Scholar]
  4. BoydS. and VandenbergheL.2004. Convex Optimization.Cambridge University Press.
    [Google Scholar]
  5. CherkevaE. and TrippA.C.1996. Optimal survey design using focused resistivity arrays. IEEE Transactions on Geoscience and Remote Sensing34, 358–366.
    [Google Scholar]
  6. ColesD.A. and MorganF.D.2009. A method of fast, sequential experimental design for linearized geophysical inverse problems. Geophysical Journal International178, 145–158.
    [Google Scholar]
  7. CurtisA.1999. Optimal design of focused experiments and surveys. Geophysical Journal International136, 205–215.
    [Google Scholar]
  8. CurtisA.2004a. Theory of model‐based geophysical survey and experimental design: Part 1 – Linear problems. The Leading Edge23, 997–1004.
    [Google Scholar]
  9. CurtisA.2004b. Theory of model‐based geophysical survey and experimental design: Part 2 – Nonlinear problems. The Leading Edge23, 1112–1117.
    [Google Scholar]
  10. DahlinT. and BingZ.2004. A numerical comparison of 2D resistivity imaging with 10 electrode arrays. Geophysical Prospecting52, 379–398.
    [Google Scholar]
  11. DahlinT. and LokeM.H.1998. Resolution of 2D Wenner resistivity imaging as assessed by numerical modeling. Journal of Applied Geophysics38, 237–249.
    [Google Scholar]
  12. DailyW., RamirezA., LaBrecqueD. and NitaoJ.1992. Electrical resistivity tomography of vadose water movement. Water Resources Research28, 1429–1442.
    [Google Scholar]
  13. Day‐LewisF.D., SinghaK. and BinleyA.M.2005. Applying petrophysical models to radar traveltime and electrical resistivity tomograms: Resolution‐dependent limitations. Journal of Geophysical Research110, B08206.
    [Google Scholar]
  14. FriedelS.2003. Resolution, stability and efficiency of resistivity tomography estimated from a generalized inverse approach. Geophysical Journal International153, 305–316.
    [Google Scholar]
  15. FurmanA., FerréT. and WarrickA.2004. Optimization of ERT surveys for monitoring transient hydrological events using perturbation sensitivity and genetic algorithms. Vadose Zone Journal3, 1230–1239.
    [Google Scholar]
  16. FurmanA., WarrickA.W. and FerréT.P.A.2002. Electrical potential distributions in a heterogeneous subsurface in response to applied current: Solution for circular inclusions. Vadose Zone Journal1, 273–280.
    [Google Scholar]
  17. GoesB.J.M. and MeekesJ.A.C.2004. An effective electrode configuration for the detection of DNAPLs with electrical resistivity tomography. Journal of Environmental and Engineering Geophysics9, 127–141.
    [Google Scholar]
  18. HaberE., HoreshL. and TenorioL.2008. Numerical methods for optimal experimental design of large‐scale ill‐posed problems. Inverse Problems24, 055012.
    [Google Scholar]
  19. HainesS., PidliseckyA. and KnightR.2009. Hydrogeologic structure underlying a recharge pond delineated with shear‐wave seismic reflection and cone penetrometer data. Near Surface Geophysics7, 329–339.
    [Google Scholar]
  20. HalihanT., PaxtonS., FenstemakerT. and RileyM.2005. Post‐remediation evaluation of a LNAPL site using electrical resistivity imaging. Journal of Environmental Monitoring7, 283–287.
    [Google Scholar]
  21. KnightR. and EndresA.L.2005. An introduction to rock physics for near‐surface applications. In: Near‐surface Geophysics, Volume 1: Concepts and Fundamentals (ed. D.Butler ), pp. 31–70. SEG.
    [Google Scholar]
  22. LehmanH.1994. Potential representation by independent configurations on a multi‐electrode array. Geophysical Journal International120, 331–338.
    [Google Scholar]
  23. LesmesD.P. and FriedmanS.P.2005. Relationships between the electrical and hydrogeological properties of rocks and soils. Hydrogeophysics50, 87–128.
    [Google Scholar]
  24. LiY. and OldenburgD.1998. ‐D inversion of gravity data. Geophysics63, 109–119.
    [Google Scholar]
  25. LokeM.H.1999. Electrical imaging surveys for environmental and engineering studies: A practical guide to 2‐D and 3‐D surveys. Accessed 22 January 2009; http://www.geomatrix.co.uk/appnotes.htm.
  26. LokeM.H., WilkinsonP. and ChambersJ.2010. Parallel computation of optimized arrays for 2‐D electrical imaging. Geophysical Journal International183, 1202–1315.
    [Google Scholar]
  27. MaurerH. and BoernerD.E.1998. Optimized and robust experimental design: A non‐linear application to EM sounding. Geophysical Journal International132, 458–468.
    [Google Scholar]
  28. MaurerH., BoernerD.E. and CurtisA.2000. Design strategies for electromagnetic geophysical surveys. Inverse Problems16, 1097–1117.
    [Google Scholar]
  29. MillerC.R. and RouthP.S.2007. Resolution analysis of geophysical images: Comparison between point spread function and region of data influence measures. Geophysical Prospecting55, 835–852.
    [Google Scholar]
  30. OldenborgerG.A, RouthP.S. and KnollM.D.2005. Sensitivity of electrical resistivity tomography data to electrode position errors. Geophysical Journal International163, 1–9.
    [Google Scholar]
  31. OldenborgerG.A, RouthP.S. and KnollM.D.2007. Model reliability for 3D electrical resistivity tomography: Application of the volume of investigation index to a time‐lapse monitoring experiment. Geophysics72, F167–F175.
    [Google Scholar]
  32. OldenburgD.W. and LiY.1999. Estimating depth of investigation in dc resistivity and IP surveys. Geophysics64, 403–416.
    [Google Scholar]
  33. ParasnisD.S.1986. Principles of Applied Geophysics,4th edn. Chapman and Hall.
    [Google Scholar]
  34. ParkS.K. and VanG.P.1991. Inversion of pole‐pole data for 3‐D resistivity structure beneath arrays of electrodes. Geophysics56, 951–960.
    [Google Scholar]
  35. PazmanA.1986. Foundations of Optimum Experimental Design.D. Reidel Publishing Company.
    [Google Scholar]
  36. PidliseckyA., HaberE. and KnightR.2007. RESINVM3D: A MATLAB 3‐D resistivity inversion package. Geophysics72, H1–H10.
    [Google Scholar]
  37. PidliseckyA. and KnightR.2008. FW2_5D: A MATLAB 2.5‐D electrical resistivity modeling code. Computers and Geosciences34, 1645–1654.
    [Google Scholar]
  38. PidliseckyA. and KnightR.2011. The use of wavelet analysis to derive infiltration rates from 1D resistivity records. Vadose Zone Journal10.
    [Google Scholar]
  39. PukelsheimF.1993. Optimal Design of Experiments.John Wiley & Sons.
    [Google Scholar]
  40. RabinowitzN. and SteinbergD.M.1990. Optimal configuration of a seismographic network: A statistical approach. Bulletin of the Seismologic Society of America80, 1033–1036.
    [Google Scholar]
  41. SchmidtC., FischerA., RaczA., Los HuertosM. and LockwoodB.2009. Process and controls on rapid nutrient removal during managed aquifer recharge. Hydrovision18, 19–22.
    [Google Scholar]
  42. SpitzerK.1998. The three‐dimensional DC sensitivity for surface and subsurface sources. Geophysical Journal International134, 736–746.
    [Google Scholar]
  43. StummerP., MaurerH. and GreenA.G.2004. Experimental design: Electrical resistivity data sets that provide optimum subsurface information. Geophysics69, 120–139.
    [Google Scholar]
  44. StummerP., MaurerH., HorstmeyerH. and GreenA.G.2002. Optimization of DC resistivity data acquisition: Real‐time experimental design and a new multi‐electrode system. IEEE Transactions on Geoscience and Remote Sensing40, 2727–2735.
    [Google Scholar]
  45. TrippA.C., HohmannG.W. and SwiftJr.C.M.1984. Two‐dimensional resistivity inversion. Geophysics49, 1708–1717.
    [Google Scholar]
  46. Van den BergJ., CurtisA. and TrampertJ.2003. Optimal nonlinear Bayesian experimental design: An application to amplitude versus offset experiments. Geophysical Journal International155, 411–421.
    [Google Scholar]
  47. WilkinsonP.B., ChambersJ.E., MeldrumP.I., OgilvyR.D. and CauntS.2006b. Optimization of array configurations and panel combinations for the detection and imaging of abandoned mineshafts using 3D cross‐hole electrical resistivity tomography. Journal of Environmental and Engineering Geophysics11, 213–221.
    [Google Scholar]
  48. WilkinsonP.B., MeldrumP.I., ChambersJ.E., KurasO. and OgilvyR.D.2006a. Improved strategies for the automatic selection of optimized sets of electrical resistivity tomography measurement configurations. Geophysical Journal International167, 1119–1126.
    [Google Scholar]
  49. WilkinsonP.B., MeldrumP.I., KurasO., ChambersS.J., HolyoakeS.J. and OgilvyR.D.2010. High‐resolution electrical resistivity tomography monitoring of a tracer test in a confined aquifer. Journal of Applied Geophysics70, 268–276.
    [Google Scholar]
  50. XuB. and NoelM.1993. On the completeness of data sets with multi‐electrode systems for electrical resistivity survey. Geophysical Prospecting41, 791–801.
    [Google Scholar]
  51. ZhouB. and DahlinT.2003. Properties and effects of measurement errors on 2D resistivity imaging surveying. Near Surface Geophysics1, 105–117.
    [Google Scholar]
http://instance.metastore.ingenta.com/content/journals/10.3997/1873-0604.2011027
Loading
/content/journals/10.3997/1873-0604.2011027
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