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Appreciation of Spherically Symmetric Models of Electrical Conductivity

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Electrical Properties of the Earth’s Mantle

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Abstract

A procedure is suggested of a more effective and faster computation of the impedance, the transfer function and amplitudes of the induced field in a spherically symmetric model of the electrical conductivity. The existing induction data have been supplemented by about 80 new values derived from the analysis of daily means. The fit of the existing 1-D models of the electrical conductivity of the mantle to the set of induction data is investigated. The characteristic equation for the free electromagnetic oscillations of a radially inhomogeneous Earth is derived and its possible importance in solving the inverse problem of electric conductivity is pointed out.

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References

  • Abramowitz, M. andStegun, I. A. (1970),Handbook of Mathematical Functions (Dover Publ., New York).

    Google Scholar 

  • Anderssen, R. S. (1979),The one-dimensional electromagnetic induction problem. Geophys. J. R. Astr. Soc.57,67.

    Article  Google Scholar 

  • Anderssen, R. S.,Devane, J. F.,Gustafson, S.-A. andWinch, D. E. (1979),The qualitative character of the global electrical conductivity of the Earth. Phys. Earth Planet Inter.20,15.

    Article  Google Scholar 

  • Banks, R. J. (1969),Geomagnetic variations and the electrical conductivity of the upper mantle. Geophys. J. R. Astr. Soc. 77,457.

    Google Scholar 

  • Banks, R. J. (1972),The overall conductivity distribution of the Earth. J. Geomagn. Geoelectr.24,337.

    Article  Google Scholar 

  • Banks, R. J. (1981),Strategies for improved global electromagnetic response estimates. J. Geomagn. Geoelectr.33,569.

    Article  Google Scholar 

  • Bailey, R. C. (1970),Inversion of the geomagnetic induction problem. Proc. Roy. Soc.315,185.

    Article  Google Scholar 

  • Berdichevsky, M. N.,Fainberg, E. B.,Rotanova, N. M.,Smirnov, J. B. andVanyan, L. L. (1976),Deep electromagnetic investigations. Ann. Geophys.32,143.

    Google Scholar 

  • Berdichevsky, M. N.,Vanyan, L. L.,Lagutinskaya, L. P.,Rotanova, N. M. andFainberg, E. B. (1970),The Experience of the Earth frequency sounding by the results of the spherical analysis of geomagnetic field variations,Goemagn. Aeronom.10,376 (in Russian).

    Google Scholar 

  • Debye, P. (1909),Der Lichtdruck auf Kugeln von beliebigen Material. Annal. Phys.30,57.

    Article  Google Scholar 

  • Devane, J. F. (1978),Monte Carlo inversion of geomagnetic induction data. Rep. 4 Workshop on EMI, Murnau 1978.

    Google Scholar 

  • Dmitriev, V. I.,Rotanova, N. M.,Balykina, O. N. andZakharova, O. K. (1977),About resolving power of curves of the deep magnetovariational sounding. Geomagn. Aeronom.17,1092 (in Russian).

    Google Scholar 

  • Ducruix, J.,Courtillot, V. andLeMouËl, J. L. (1980), The late 1960s secular variation impulse, the eleven year magnetic variation and the electrical conductivity of the deep mantle. Geophys. J. R. Astr. Soc.61,73.

    Article  Google Scholar 

  • Dziewonski, A. M. (1984),Mapping the lower mantle: determination of lateral heterogeneities in P velocity up to degree and order 6,J. Geophys. Res.89,No B7, 5929.

    Article  Google Scholar 

  • Eckhardt, D. H. (1963),Geomagnetic induction in a concentrically stratified Earth. J. Geophys. Res.68, 6273.

    Google Scholar 

  • HvoŽdara, M. andSirá, G. (1975),Penetration of longperiod geomagnetic variations to the core of the Earth. Acta F.R.N. Univ. Comen., Astr. Geophys.1,27.

    Google Scholar 

  • Kovtun, A. A. (1980),The Use of the Natural Electromagnetic Field in Studying the Electrical Conductivity of the Earth. (Leningrad. Univ.) (in Russian).

    Google Scholar 

  • Lahiri, B. N. andPrice, A. T. (1939),Electromagnetic induction in non-uniform conductors, and the determination of the conductivity of the Earth from terrestrial magnetic variations. Phil. Trans. R. Soc. London237,509.

    Article  Google Scholar 

  • Lamb, H. (1883),On electrical motion in a spherical conductor. Phil. Trans. R. Soc. London174,519.

    Article  Google Scholar 

  • Martinec, Z. andP, K. (1986),Normal earth density models. Studia Geoph. Geod.30,124.

    Article  Google Scholar 

  • Nataf, H.-C.,Nakanishi, I. andAnderson, Don L. (1984),Anisotropy and shear-velocity heterogeneities in the upper mantle. Geophys. Res. Lett.11,109.

    Article  Google Scholar 

  • Parker, R. L. (1970),The inverse problem of electrical conductivity in the mantle. Geophys. J. R. Astr. Soc.22,14.

    Google Scholar 

  • Parker, R. L. (1983),The magnetotelluric inverse problem. Geophys. Surveys 6, 5.

    Article  Google Scholar 

  • Pěč, K. andMartinec, Z. (1984),Constraints to the three-dimensional non hydrostatic density distribution in the Earth. Studia Geoph. Geod.28,364.

    Article  Google Scholar 

  • Pěč, K.,Martinec, Z. andPová, J. (1985),Matrix approach to the solution of electromagnetic induction in a spherically layered Earth. Studia Geoph. Geod.29,139.

    Article  Google Scholar 

  • PěčováJ.,Pěč, K. andPraus, O. (1980),Remarks on spatial distribution of long period variations in the geomagnetic field over European area. J. Geomagn. and Geoelectr.32,Supplement I, SI 171.

    Google Scholar 

  • Pěčová, J. andPěč ,K. (1982),Models of electrical conductivity in the upper mantle. Studia Geoph. Geod.26,196.

    Article  Google Scholar 

  • Price, A. T. (1950),Electromagnetic induction in a semiinfinite conductor,Quart. J. Mech. Appl. Math.3, 385.

    Article  Google Scholar 

  • Price, A. T. (1962),The theory of magnetotelluric method when the source is considered,J. Geophys. Res.67,4309.

    Article  Google Scholar 

  • Rikitake, T., (1951),Electromagnetic induction within the Earth and its relation to electrical state of the Earth’s interior Part III. Bull. Earthq. Res. Inst.29,61.

    Google Scholar 

  • Rokityansky, I. I.,Induction sounding of the Earth(in Russian), (Naukova Dumka, Kiev 1981).

    Google Scholar 

  • Schmucker, U. (1974),Erdmagnetische Tiefensondierung mit langperiodischen Variationen,Protokoll über das Kolloquium: Erdmagnetische Tiefensondierung, Grafrath/Bayern, 313.

    Google Scholar 

  • Smylie, D. E. (1965),Magnetic diffusion in a spherically symmetric conducting mantle. Geophys. J. Astr. Soc. 9, 169.

    Article  Google Scholar 

  • Srivastava, S. P. (1966),Theory of magnetotelluric method for a spherical conductor,Geophys. J. R. Astr. Soc.11,373.

    Article  Google Scholar 

  • Stratton, J. A. (1941),Electromagnetic Theory(McGraw Hill, New York).

    Google Scholar 

  • Tarantola, A. andValette, B. (1982),Generalized nonlinear inverse problems solved using the least-squares criterion,Rev. Geophys. Space Phys.20,219.

    Article  Google Scholar 

  • Wiggins, R. A. (1972),The general linear inverse problem: implication of surface waves and free oscillations for Earth structure. Rev. Geophys. Space Phys.10,251.

    Article  Google Scholar 

  • Woodhouse, J. H. andDziewonski, A. M. (1984),Mapping the lower mantle: three-dimensional modelling of Earth structure by inversion of seismic waveforms. J. Geophys. Res.89,No. B7, 5953.

    Article  Google Scholar 

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© 1987 Birkhäuser Verlag, Basel

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Pěčová, J., Martinec, Z., Pěč, K. (1987). Appreciation of Spherically Symmetric Models of Electrical Conductivity. In: Campbell, W.H. (eds) Electrical Properties of the Earth’s Mantle. Pageoph Topical Volumes. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7373-4_6

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  • DOI: https://doi.org/10.1007/978-3-0348-7373-4_6

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-7375-8

  • Online ISBN: 978-3-0348-7373-4

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