1887
Volume 15 Number 6
  • ISSN: 1569-4445
  • E-ISSN: 1873-0604

Abstract

ABSTRACT

We investigate the problem of determination of the volumetric ratio between the two components of a heterogeneous mixture with unknown internal structure. If both resistivity and permittivity of one component are known to be much higher than those of the other within a sufficiently wide frequency range, the volumetric ratio may be roughly estimated from measured electromagnetic response of the mixture by making use of the variational approach. Otherwise, such estimation requires the exact knowledge of the inherent electrical properties of the mixed materials and application of some universal mixing model, such as the weighted power mean formula.

The high‐frequency induced polarization measurements are strongly influenced by the presence of ice inclusions in an investigated rock formation, which is commonly used for mapping of frozen ground within the permafrost regions. We show that for sedimentary rocks with low clay content, it is also possible to roughly estimate the ice concentration from broadband induced polarization data by using the two‐component, weighted power mean model, which is confirmed by a lab experiment on a frozen core sample with known ice content.

Loading

Article metrics loading...

/content/journals/10.3997/1873-0604.2017043
2017-09-01
2024-03-28
Loading full text...

Full text loading...

References

  1. AspnesD.E.1982. Local‐field effects and effective‐medium theory: a microscopic perspective.American Journal of Physics50(8), 704–709.
    [Google Scholar]
  2. AutyR.P. and ColeR.H.1952. Dielectric properties of ice and D2O.Journal of Chemical Physics20(8), 1309–1314.
    [Google Scholar]
  3. BanhegyiG.1986. Comparison of electrical mixture rules for composites.Colloid & Polymer Science264(12), 1030–1050.
    [Google Scholar]
  4. BittellyM., FluryM. and RothK.2004. Use of dielectric spectroscopy to estimate ice content in frozen porous media.Water Resources Research40, 1–11.
    [Google Scholar]
  5. ColeK.S. and ColeR.H.1941. Dispersion and absorption in dielectrics.The Journal of Chemical Physics9, 341–351.
    [Google Scholar]
  6. DebyeP.1928. Polar Molecules.New York, USA: Chemical Catalogue Company, p. 172.
    [Google Scholar]
  7. DykhneA.M.1971. Conductivity of a two‐dimensional two‐phase system.Soviet Physics, Journal of Experimental and Theoretical Physics32(1), 63–65.
    [Google Scholar]
  8. EvansS.1965. Dielectric properties of ice and snow—A review.Journal of Glaciology5, 773–792.
    [Google Scholar]
  9. FlorschN., CamerlynckC. and RevilA.2012. Direct estimation of the distribution of relaxation times from induced‐polarization spectra using a Fourier transform analysis.Near Surface Geophysics10(6), 517–531.
    [Google Scholar]
  10. FullerB.D. and WardS.H.1970. Linear system description of the electrical parameters of rocks.IEEE Transactions on Geoscience ElectronicsGE‐8(1), 7–18.
    [Google Scholar]
  11. GladstoneJ.H. and DaleT.P.1863. Researches on the refraction, dispersion, and sensitiveness of liquids.Philosophical Transactions of the Royal Society of London153, 317–343.
    [Google Scholar]
  12. GrimmR.E. and StillmanD.E.2015. Field test of detection and characterization of subsurface ice using broadband spectral‐induced polarization.Permafrost and Periglacial Processes26, 28–38.
    [Google Scholar]
  13. HanaiT.1960. Theory of the dielectric dispersion due to the interfacial polarization and its application to emulsions.Kolloid‐Zeitsehrift171(1), 23–31.
    [Google Scholar]
  14. HardyG.H., LittlewoodJ.E. and PolyaG.1934. Inequalities.London‐Tokyo: Cambridge Press, p. 314.
    [Google Scholar]
  15. HashinZ. and ShtrikmanS.1962. A variational approach to the theory of the effective magnetic permeability of multiphase materials.Journal of Applied Physics10, 3125–3131.
    [Google Scholar]
  16. HelsingJ.1993. Bounds to the conductivity of some two‐component composites.Journal of Applied Physics73(3), 1240–1245.
    [Google Scholar]
  17. KennedyM.2015. Practical petrophysics. In: Developments in Petroleum Science, Vol. 62. (ed J.Cubitt ) Elsevier, Amsterdam‐Tokyo.
    [Google Scholar]
  18. KozhevnikovN.O. and AntonovE.Yu.2006. Fast‐decaying IP in frozen unconsolidated rocks and potentialities for its use in permafrost‐ related TEM studies.Geophysical Prospecting54, 383–397.
    [Google Scholar]
  19. KozhevnikovN.O., NikiforovS.P. and SnopkovS.V.1995. Field studies of fast‐decaying induced polarization in frozen rocks (in Russian).Geoecology2, 118–126.
    [Google Scholar]
  20. LandauL.D. and LifshitzE.M.1960. Electrodynamics of Continuous Media.London, UK: Pergamon Pressp. 417.
    [Google Scholar]
  21. LandauerR.1978. Electrical conductivity in inhomogeneous media.American Institute of Physics Conference Proceedings40(2), 2–43.
    [Google Scholar]
  22. LesmesD.P. and MorganF.D.2001. Dielectric spectroscopy of sedimentary rocks.Journal of Geophysical Research106(B7), 13329–13346.
    [Google Scholar]
  23. LimaO.A.L. and SharmaM.M.1992. A generalized Maxwell‐Wagner theory for membrane polarization in shaly sands.Geophysics57(3), 431–440.
    [Google Scholar]
  24. LooyengaH.1965. Dielectric constants of heterogeneous mixtures.Physica31, 401–406.
    [Google Scholar]
  25. MacnaeJ.2015. Comment on: Tarasov, A. & Titov, K. , 2013, On the use of the Cole‐Cole equations in spectral induced polarization, Geophys. J. Int., 195, 352–356. Geophysical Journal International 202, 529–532.
    [Google Scholar]
  26. MaddenT.R.1976. Random networks and mixing laws.Geophysics41 (6A), 1104–1125.
    [Google Scholar]
  27. MarshallD.J. and MaddenT.R.1959. Induced polarization, a study of its causes.Geophysics24, 790–816.
    [Google Scholar]
  28. MaxwellJ.C.1873. A Treatise on Electricity and Magnetism.Oxford: Clarendon Press, p. 425.
    [Google Scholar]
  29. MillerM.N.1969. Bounds for effective electrical, thermal, and magnetic properties of heterogeneous materials.Journal of Mathematical Physics10(11), 1988–2004.
    [Google Scholar]
  30. OlhoeftG.1985. Low‐frequency electrical properties.Geophysics50, 2492–2503.
    [Google Scholar]
  31. PeltonW.H., SillW.R. and SmithB.D.1983. Interpretation of complex resistivity and dielectric data. Part I. Geophysical Transactions29, 297–330.
    [Google Scholar]
  32. PeltonW.H., WardS.H., HallofP.G., SillW.R. and NelsonP.H.1978. Mineral discrimination and removal of inductive coupling with multi‐ frequency IP.Geophysics43, 588–609.
    [Google Scholar]
  33. PetrenkoV. F. and WhitworthR.W.1999. Physics of Ice.New York, USA: Oxford University Press, 386.
    [Google Scholar]
  34. SeguinM.K. and FrydeckiJ.1990. Geophysical detection and possible estimation of ice content in permafrost in northern Quebec.The Leading Edge of Exploration9(10), 25–29.
    [Google Scholar]
  35. SeigelH.O.1959. Mathematical formulation and type curves for induced polarization.Geophysics24, 547–565.
    [Google Scholar]
  36. SeigelH.O., VanhalaH., and SheardS.N., 1997. Some case histories of source discrimination using time‐domain spectral IP, Geophysics, 62, 1394–1408.
    [Google Scholar]
  37. SenP.N., ScalaC. and CohenM.H.1981. A self‐similar model for sedimentary rocks with application to the dielectric constant of fused glass beads.Geophysics46(5), 781–795.
    [Google Scholar]
  38. ShueyR.T. and JohnsonM.1973. On the phenomenology of electrical relaxation in rocks.Geophysics38, 37–48.
    [Google Scholar]
  39. SihvolaA.2008. Electromagnetic Mixing Formulas and Applications, reprinted edition. London, UK: Institution of Engineering and Technology, p. 284.
    [Google Scholar]
  40. SillarsR.W.1937. The properties of a dielectric containing semi‐conducting particles of various shapes.Journal of the Institute of Electrical Engineers80, 378–394.
    [Google Scholar]
  41. SimpkinR.2010. Derivation of Lichtenecker’s logarithmic mixture formula from Maxwell’s equations.IEEE Transactions on Microwave Theory and Techniques58(3), 545–550.
    [Google Scholar]
  42. StillmanD.E., GrimmR.E. and DecS.F.2010. Low‐frequency electrical properties of ice‐silicate mixtures.Journal of Physical Chemistry B114, P. 6065–6073.
    [Google Scholar]
  43. TabbaghA., CosenzaP., GhorbaniA., GuerinR. and FlorschN.2009. Modelling of Maxwell‐Wagner induced polarisation amplitude for clayey materials.Journal of Applied Geophysics67, 109–113.
    [Google Scholar]
  44. TarasovA. and TitovK.2013. On the use of the Cole‐Cole equations in spectral induced polarization.Geophysical Journal International195(1), 352–356.
    [Google Scholar]
  45. UlabyF., MooreR. and FungA.1986. Microwave Remote Sensing: Active and Passive, From Theory to Applications, Vol. 3, p. 2162. Artech House, Dedham, Massachusetts.
    [Google Scholar]
  46. WagnerK.W.1914. Erklarung der dielektrischen Nachwirkungsvorgange auf Grund Maxwellscher Vorstellungen.Archiv fur Elektrotechnik2(9), 371–387.
    [Google Scholar]
  47. WarburgE.1899. Ueber das Verhalten sogenannter unpolarisirbarer Elektroden gegen Wechselstrom.Annalen der Physik303, 493–499.
    [Google Scholar]
  48. ZakriT., LaurentJ.P. and VauclinM.1998. Theoretical evidence for Lichtenecker’s mixture formulae based on the effective medium theory.Journal Of Physics D—Applied Physics31, 1589–1594.
    [Google Scholar]
  49. ZorinN.2015. Spectral induced polarization of low and moderately polarizable buried objects. 2015. Geophysics80(5), E267–E276.
    [Google Scholar]
http://instance.metastore.ingenta.com/content/journals/10.3997/1873-0604.2017043
Loading
/content/journals/10.3997/1873-0604.2017043
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