Electrical conductivity at mid-mantle depths estimated from the data of Sq and long period geomagnetic variations

  • Oldřich Praus
  • Jana Pěčová
  • Václav Červ
  • Svetlana Kováčiková
  • Josef Pek
  • Jakub Velímský


We present results of a classical global induction analysis of the geomagnetic variation data in the range of daily Sq variations, as well as for long period variations within the period range of about 8 to 400 days. The Sq data from 88 to 94 world observatories are processed in two ways, first by constructing and analyzing average monthly daily variations for the whole months of the International Quiet Sun Year (IQSY) 1995, and second by analyzing the individual, especially quiet Q* daily records from the same year. The electrical images of the Sq response functions obtained via the Schmucker’s ρ* — z* procedure show a good fit with results of other induction studies, though especially our global impedance phases show a larger scatter than two other published data sets used for comparison.

The long period variations from three 3-years’ intervals with different solar and geomagnetic activities and for 44 to 57 world observatories have been processed by power spectral and Fourier analyses, as well as by a simplified GDS approach. The induction response functions show a good correspondence with other deep induction studies, the seasonal processing did not, however, allow us to detect any significant effects of the solar/geomagnetic activity on the transfer functions.

The obtained global geomagnetic induction functions along with other two published data sets are analyzed by a bayesian Monte Carlo analysis for the mantle conductivity distribution. We use a modified version of the Monte Carlo method with Markov chains based on an effective, data adaptive Metropolis sampling approach, and simulate samples from the posterior probability distribution of the resistivities in the mantle. Stochastic sampling provides comprehensive maps of the parameter space based on fairly ranking the models according to their ability to explain the experimental data, as well as on respecting the prior information on the model parameters. From four generally formulated and tested priors for the mantle resistivities, the non-informative distribution on strictly increasing conductance is the most non-restricting prior that, at the same, avoids the non-likely high-resistivity tails in the marginal resistivity distributions. A prediction power of the Monte Carlo sampling approach is demonstrated by a comparison of published maximum likelihood bounds on average conductivities in specific mantle zones with those produced simply by computing the average conductivities from the Markov chain of models.


geomagnetic depth sounding Monte Carlo analysis adaptive Metropolis sampling solar/geomagnetic activity 


  1. Banks R.J., 1969. Geomagnetic variations and the electrical conductivity of the Upper Mantle. Geophys. J. R. Astr. Soc., 17, 457–487.Google Scholar
  2. Backus G.E. and Gilbert J.F., 1968. The resolving power of gross Earth data. Geophys. J. R. Astr. Soc., 16, 169–205.Google Scholar
  3. Backus G.E. and Gilbert J.F., 1970. Uniqueness in the inversion of inaccurate gross Earth data. Phil. Trans. R. Soc. Lond. A, 266, 187–269.Google Scholar
  4. Berdichevski M.N., Vanijan L.L., Lagutinskaja V.P., Rotanova N.M. and Fajnberg E.B., 1970. Experiment with the frequency sounding of the Earth using the results of spherical analysis of geomagnetic field variations. Geomagnetism and Aeronomy (Geomagnetizm i Aeronomiya), X, Moscow, 374–377 (in Russian).Google Scholar
  5. Campbell W.H. and Schiffmacher E.R., 1986. A comparison of upper mantle sub continental electrical conductivity for North America, Europe and Asia. J. Geophys., 59, 56–61.Google Scholar
  6. Constable S.C., Parker R.L. and Constable C.G., 1987. Occam’s inversion — a practical algorithm for generating smooth models from electromagnetic sounding data. Geophysics, 52, 289–300.CrossRefGoogle Scholar
  7. Constable S., 1993. Constraints on mantle electrical conductivity from field and laboratory measurements. J. Geomagn. Geoelectr., 45, 707–728.Google Scholar
  8. Constable S. and Constable C., 2004, Observing geomagnetic induction in magnetic satellite measurements and associated implications for mantle conductivity. Geochem. Geophys. Geosyst., 5, Q01006.CrossRefGoogle Scholar
  9. Dmitriev V.I., Rotanova N.M., Zakharova O.K. and Fiskina M.V., 1987. Models of deep electrical conductivity obtained from data on global magnetic variational sounding. Pure Appl. Geophys., 125, 409–426.CrossRefGoogle Scholar
  10. Everett M.E. and Schultz A., 1996. Geomagnetic induction in a heterogenous sphere: Azimuthally symmetric test computations and the response of an undulating 660-km discontinuity. J. Geophys. Res., 101, 2765–2783.CrossRefGoogle Scholar
  11. Grandis H., Menvielle M. and Roussignol M., 1999. Bayesian inversion with Markov chains — I.: The magnetotelluric one-dimensional case. Geophys. J. Int., 138, 757–768.CrossRefGoogle Scholar
  12. Haario H., Saksman E. and Tamminen J., 2003. Componentwise Adaptation for MCMC. Preprint 342, Department of Mathematics, University of Helsinki, Finland, 20 pp. ( Scholar
  13. Haario H., Laine M., Lehtinen M., Saksman E. and Tamminen J., 2004. Markov chain Monte Carlo methods for high dimensional inversion in remote sensing. J. R. Stat. Soc. Ser. B-Stat. Methodol., 66, 591–607.CrossRefGoogle Scholar
  14. Hansen P.C., 1992. Analysis of discrete ill-posed problems by means of the L-curve. SIAM Rev., 34, 561–580.CrossRefGoogle Scholar
  15. Honkura Y. and Matsushima M., 1998. Electromagnetic response of the mantle to long-period geomagnetic variations over the globe. Earth Planets Space, 50, 651–662.Google Scholar
  16. Barton C.E., Baldwin R.T., Barraclough D.R., Bushati S., Chiappini M., Cohen Y., Coleman R., Hulot G., Kotze P., Golovkov V.P., Jackson A., Langel R.A., Lowes F.J., McKnight D.J., Macmillan S., Newitt L.R., Peddie N.W., Quinn J.M., Sabaka T.J., 1996. International geomagnetic reference field, 1995 revision. Geophys. J. Int., 125, 318–321.CrossRefGoogle Scholar
  17. Kuvshinov A.V., Olsen N., Avdeev D.B. and Pankratov O.V., 2002. Electromagnetic induction in the oceans and the anomalous behaviour of coastal C-responses for periods up to 20 days. Geophys. Res. Lett., 29, Art.No.1595, DOI: 10.1029/2001GL014409.Google Scholar
  18. Kuvshinov A. and Olsen N., 2006. A global model of mantle conductivity derived from 5 years of CHAMP, Oersted, and SAC-C magnetic data. Geophys. Res. Lett., 33, Art.No.L18301, DOI: 10.1029/2006GL027083.Google Scholar
  19. Medin A.E., Parker R.L. and Constable S., 2007. Making sound inferences from geomagnetic sounding. Phys. Earth Planet. Inter., 160, 51–59.CrossRefGoogle Scholar
  20. Olsen N., 1992. Day-to-day C-response estimation for Sq from 1 cpd to 6 cpd using the Z:Ymethod. J. Geomagn. Geoelectr., 44, 433–447.Google Scholar
  21. Olsen N., 1998. The electrical conductivity of the mantle beneath Europe derived from C-responses from 3 to 720 hr. Geophys. J. Int., 133, 298–308.CrossRefGoogle Scholar
  22. Olsen N., 1999a. Long-period (30 days — 1 year) electromagnetic sounding and the electrical conductivity of the lower mantle beneath Europe. Geoph. J. Int., 138, 179–187.CrossRefGoogle Scholar
  23. Olsen N., 1999b. Induction studies with satellite data. Surv. Geophys., 20, 309–340.CrossRefGoogle Scholar
  24. Parker R.L., 1980. The inverse problem of electromagnetic induction: existence and construction of solutions based on incomplete data. J. Geophys. Res., 85, 4421–4428.CrossRefGoogle Scholar
  25. Pěč K., Martinec Z. and Pěčová J., 1985. Matrix approach to the solution of electromagnetic induction in a spherically layered Earth. Stud. Geophys. Geod., 29, 139–162.CrossRefGoogle Scholar
  26. Praus O. and Pěčová J., 1994. Deep electrical structure under Central Europe. Stud. Geophys. Geod., 38, 57–70.CrossRefGoogle Scholar
  27. Roberts R.G., 1984. The long period electromagnetic response of the Earth. Geophys. J. R. Astron. Soc., 78, 547–572.Google Scholar
  28. Roberts R.G., 1986. Global electromagnetic induction. Surv. Geophys., 8, 339–374.CrossRefGoogle Scholar
  29. Rokityanskij I.I., 1982. Geoelectromagnetic Investigation of the Earth’s Crust and Mantle. Springer-Verlag, New York, 381 pp.Google Scholar
  30. Schultz A. and Semenov V.Yu., 1993. Modeling of the mid-mantle geoelectrical structure. Izv.-Phys. Solid Earth, 10, 39–43.Google Scholar
  31. Schmucker U., 1970. Anomalies of geomagnetic variations in the southwestern United States. Bull. Scripts Inst. Oceanogr., 13, 55–86.Google Scholar
  32. Schmucker U., 1987. Substitute conductors for electromagnetic response estimates. Pure Appl. Geophys., 125, 341–367.CrossRefGoogle Scholar
  33. Schmucker U., 1999. A spherical harmonic analysis of the solar daily variations in the years 1964–1965; response estimates and source fields for global induction — I. Methods. Geoph. J. Int., 136, 439–454.CrossRefGoogle Scholar
  34. Schultz A. and Larsen J.C., 1987. On electrical conductivity of mid-mantle — I. Calculation of equivalent scalar magnetotelluric response functions. Geophys. J. R. Astron. Soc., 88, 733–761.Google Scholar
  35. Semenov V.Yu. and Kharin E.P., 1985a. Analysis of geomagnetic hourly means for deep global sounding. Geomagnetism and Aeronomy (Geomagnetizm i Aeronomiya), 25, 341–342 (in Russian).Google Scholar
  36. Semenov V.Yu. and Kharin E.P., 1985b. The geomagnetic field continuum spectrum method for obtaining the apparent resistivity curve. Geomagnetism and Aeronomy (Geomagnetizm i Aeronomiya), 25, 482–487 (in Russian).Google Scholar
  37. Semenov V.Yu. and Kharin E.P., 1988. Electromagnetic investigations at periods longer than four hours. Geomagnetic Researches, No.31, Acad. Sci. USSR, Soviet Geophys. Committee, Moscow, Russia, 50–58 (in Russian).Google Scholar
  38. Semenov V.Yu., 1998. Regional conductivity structures of the Earth’s mantle. Publ. Inst. Geophys. Pol. Acad. Sci., C-95(302), 119 pp.Google Scholar
  39. Semenov V.Yu. and Józwiak W., 1999. Model of the geoelectrical structure of the mid- and lower mantle in the Europe-Asia region. Geophys. J. Int., 138, 549–552.CrossRefGoogle Scholar
  40. Semenov V.Yu. and Jozwiak W., 2006. Lateral variations of the mid-mantle conductance beneath Europe. Tectonophysics, 416, 279–288.CrossRefGoogle Scholar
  41. Semenov V.Yu., Vozár J. and Shuman V., 2007. A new approach to gradient geomagnetic sounding. Izv.-Phys. Solid Eart, 43, 592–596.CrossRefGoogle Scholar
  42. Velímský J., Martinec Z. and Everett M., 2006. Electrical conductivity in the Earth’s mantle inferred from CHAMP satellite measurements — I. Data processing and 1-D inversion. Geophys. J. Int., 166, 529–542.CrossRefGoogle Scholar
  43. Vozár J. and Semenov V.Yu., 2010. Compatibility of induction methods for mantle soundings. J. Geophys. Res., 115, B03101, DOI: 10.1029/2009JB006390.CrossRefGoogle Scholar
  44. Weidelt P., 1972. The inverse problem of geomagnetic induction. Z. Geophys., 38, 257–289.Google Scholar
  45. Weiss C.J. and Everett M.E., 1998. Geomagnetic induction in a heterogeneous sphere: fully threedimensional test computations and the response of a realistic distribution of oceans and continents. Geophys. J. Int., 135, 650–662.CrossRefGoogle Scholar
  46. Wessel P. and Smith W.H.F., 1991. Free software helps map and display data. EOS Trans. AGU, 72, 441.CrossRefGoogle Scholar

Copyright information

© Institute of Geophysics of the ASCR, v.v.i 2011

Authors and Affiliations

  • Oldřich Praus
    • 1
  • Jana Pěčová
    • 1
  • Václav Červ
    • 1
  • Svetlana Kováčiková
    • 1
  • Josef Pek
    • 1
  • Jakub Velímský
    • 2
  1. 1.Institute of Geophysics v.v.i.Acad. Sci. Czech Rep.Praha 4Czech Republic
  2. 2.Faculty of Mathematics and PhysicsCharles UniversityPraha 8Czech Republic

Personalised recommendations