1887
Volume 65, Issue 6
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

The applied potential, or mise‐à‐la‐masse, method is used in mineral exploration and environmental applications to constrain the shape and extent of conductive anomalies. However, few simple calculations exist to help gain understanding and intuition regarding the pattern of measured electrical potential at the ground surface. While it makes intuitive sense that the conductor must come close to the ground surface in order for the lateral extent of the potential anomaly to be affected by the dimensions of the conductor rather than simply by the depth, no simple calculation exists to quantify this effect. In this contribution, a simple method of images solution for the case of a sphere of constant electrical potential in a conducting half‐space is presented. The solution consists of an infinite series where the first term is the same as the method of images solution for a point current source in an infinite half‐space. The higher order terms result from the interaction of the constant potential sphere with the no‐flux boundary condition representing the ground surface and cause the change in the shape of the potential anomaly that is of interest in the applied potential method. The calculation is relevant to applied potentials when the conductive anomaly is limited in all three space dimensions and is highly conductive. Using the derived formula, it is shown that, while the electrical potential at the ground surface caused by the sphere is affected even when the sphere is quite deep, the ratio of the potential to the current, a quantity that is more relevant to the applied potential method, is not affected until the centre of the sphere is within two radii of the ground surface. An expression for the contact resistance of the sphere as a function of depth is also given, and the contact resistance is shown to increase by roughly 45% as the sphere is moved from great depth to the ground surface.

Loading

Article metrics loading...

/content/journals/10.1111/1365-2478.12506
2017-02-24
2024-03-29
Loading full text...

Full text loading...

References

  1. BhattacharyaB.B., GuptaD., BanerjeeB. and ShalivahanS.2001. Mise‐à‐la‐masse survey for an auriferous sulfide deposit. Geophysics66, 70–77.
    [Google Scholar]
  2. BhattacharyaB.B. and ShalivahanS.2016. Geoelectric Methods: Theory and Application. New Delhi, India: McGraw Hill Education (India) Pvt. Ltd.
    [Google Scholar]
  3. BowkerA.1991. Quantitative interpretation on three‐dimensional mise‐à‐la‐masse date. A case history from Gairloch, northwest Scotland. Geoexploration28, 1–22.
    [Google Scholar]
  4. ButlerS.L. and SinhaG.2012. Forward modeling of applied geophysics methods using Comsol and comparison with analytical and laboratory analog models. Computers and Geosciences42, 168–176.
    [Google Scholar]
  5. ButlerS.L. and ZhangZ.2016. Forward modeling of geophysical electromagnetic methods using Comsol. Computers and Geosciences1–10.
    [Google Scholar]
  6. CookK.I. and Van NostrandR.G.1954. Interpretation of resistivity data overfilled sinks. Geophysics4, 761–770.
    [Google Scholar]
  7. De CarloL., PerriM.T., CaputoM.C., DeianaR., VurroM. and CassianiG.2013. Characterization of a dismissed landfill via electrical resistivity tomography and mise‐à‐la‐masse method. Journal of Applied Geophysics98, 1–10.
    [Google Scholar]
  8. DentithM. and MudgeS.T.2014. Geophysics for the Mineral Exploration Geoscientist. Cambridge University Press.
    [Google Scholar]
  9. DongP., FanJ.L., ChenZ.Z., WangL.S., GaoX.N and QinR.2008. Applying mise‐à‐la‐masse method to determine the length of reinforcement in bored in situ concrete piles. Journal of Environmental and Engineering Geophysics13, 51–56.
    [Google Scholar]
  10. ElorantaE.1984. A method for calculating mise‐à‐la‐masse anomalies in the case of high conductivity contrast by the integral equation technique. Geoexploration22, 77–88.
    [Google Scholar]
  11. FurnessP.1999. Mise‐à‐la‐masse interpretation using a perfect conductor in a piecewise uniform earth. Geophysical Prospecting47, 393–409.
    [Google Scholar]
  12. GrantF.S. and WestG.F.1965. Interpretation Theory in Applied Geophysics. New York, NY: McGraw‐Hill Book Co., Inc.
    [Google Scholar]
  13. GriffithsD.J.2013. Introduction to Electrodynamics. Pearson.
    [Google Scholar]
  14. JacksonJ.D.1998. Classical Electrodynamics. Wiley.
    [Google Scholar]
  15. LipskayaN.V.1949. The disturbance of electrical fields by spherical inhomogeneities (method of dipolar coordinates): Akad. Nauk. SSSR Izv. ser. geog. o. geofiz13, 335–347.
    [Google Scholar]
  16. MansinhaL. and MwenifumboC.J.1983. A mise‐à‐la‐masse study of the Cavendish geophysical test site. Geophysics48, 1252–1257.
    [Google Scholar]
  17. MwenifumboC.J.1980. Interpretation of mise‐à‐la‐masse data for vein type bodies . PhD thesis, University of Western Ontario, Canada.
  18. PantS.R.2004. Tracing groundwater flow by mise‐à‐la‐masse measurement of injected saltwater. Journal of Environmental and Engineering Geophysics9, 155–165.
    [Google Scholar]
  19. ParasnisD.S.1967. Three‐dimensional electric mise‐à‐la‐masse survey of an irregular lead‐zinc‐copper deposit in central Sweden. Geophysical Prospecting15, 407–437.
    [Google Scholar]
  20. ReynoldsJ.2011. An Introduction to Applied and Environmental Geophysics. Wiley‐Blackwell.
    [Google Scholar]
  21. ScurtuE.F.1972. Computer calculation of resistivity pseudosections of a buried spherical conductor body. Geophysical Prospecting20, 605–625.
    [Google Scholar]
  22. SinghL.N., BanglaniS. and GuptaD.2008. Mise‐à‐la‐masse survey in deciphering subsurface disposition of ore body in some mineral prospects of Rajasthan. Journal of the Geological Society of India72, 808–814.
    [Google Scholar]
  23. SinghS.K.1976. Fortran IV program to compute the apparent resistivity of a perfectly conducting sphere buried in a half‐space. Computers and Geosciences1, 241–245.
    [Google Scholar]
  24. SinghS.K. and EspindolaJ.M.1976. Apparent resistivity of a perfectly conducting sphere buried in a half‐space. Geophysics41, 742–751.
    [Google Scholar]
  25. SnyderD.D. and MerkelR.1973. Analytic models for the interpretation of electrical surveys using buried current electrodes. Geophysics38, 513–529.
    [Google Scholar]
  26. WebbJ.H.1931. Potential due to a buried sphere. Physical Review37, 292–302.
    [Google Scholar]
http://instance.metastore.ingenta.com/content/journals/10.1111/1365-2478.12506
Loading
/content/journals/10.1111/1365-2478.12506
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