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Basics of Magnetic Field Theory and Magnetization

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Inverse Magnetometry

Abstract

This chapter characterizes the components of the Earth’s magnetic field, but only to the extent needed for the book. An insight into the constituents of crustal geomagnetic field research is given.

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References

  1. Backus, G.E.: Poloidal and toroidal fields in geomagnetic field modeling. Rev. Geophys. 24, 75–109 (1986)

    Article  MathSciNet  Google Scholar 

  2. Backus, G.E., Parker, R., Constable, C.: Foundations of Geomagnetism. Cambridge University, Cambridge (1996)

    Google Scholar 

  3. Bayer, M.: Geomagnetic Field Modeling from Satellite Data by First and Second Generation Wavelets, Ph.-D. thesis. University of Kaiserslautern, Geomathematics Group, Aachen (1999)

    Google Scholar 

  4. Bayer, M., Beth, S., Freeden, W.: Geophysical field modeling by multiresolution analysis. Acta Geod. Geoph. Hung. 33, 289–319 (1998)

    Google Scholar 

  5. Bayer, M., Freeden, W., Maier, T.: A vector wavelet approach to iono- and magnetospheric geomagnetic satellite data. J. Atmos. Sol. Terr. Phys. 63, 581–597 (2001)

    Article  Google Scholar 

  6. Blakely, R.J.: Potential Theory in Gravity and Magnetic Application. Cambridge University, Cambridge (1996)

    Google Scholar 

  7. Freeden, W.: Decorrelative Mollifier Gravimetry–Basics, Concepts, Examples and Perspectives. Geosystems Mathematics, Birkhäuser (2021)

    Google Scholar 

  8. Freeden, W., Bauer, M.: Dekorrelative Gravimetrie—Ein innovativer Zugang in Exploration und Geowissenschaften. Springer Spektrum, Berlin (2020)

    Book  Google Scholar 

  9. Freeden, W., Gerhards, C.: Poloidal and toroidal modeling in terms of locally supported vector wavelets. Math. Geosci. 42, 817–838 (2010)

    Article  MathSciNet  Google Scholar 

  10. Freeden, W., Gerhards, C.: Geomathematically Oriented Potential Theory. CRC Press/Taylor and Francis, Boca Raton (2013)

    MATH  Google Scholar 

  11. Freeden, W., Gutting, M.: Special Functions of Mathematical (Geo)Physics. Birkhäuser, Basel (2013)

    Google Scholar 

  12. Freeden, W., Maier, T.: On multiscale denoising of spherical functions: basic theory and numerical aspects. Electron. Trans. Numer. Anal. (ETNA) 14, 40–62 (2002)

    Google Scholar 

  13. Freeden, W., Maier, T.: Spectral and multiscale signal-to-noise thresholding of spherical vector fields. Comput. Geosci. 7, 215–250 (2003)

    Article  MathSciNet  Google Scholar 

  14. Freeden, W., Mayer, C.: Wavelets generated by layer potentials. Appl. Comput. Harm. Anal. (ACHA) 14, 195–237 (2003)

    Google Scholar 

  15. Freeden, W., Schreiner, M.: Spherical Functions of Mathematical Geosciences: A Scalar, Vectorial, and Tensorial setup. 1st edn., Springer, Heidelberg (2009)

    Book  Google Scholar 

  16. Gerhards, C.: Spherical Multiscale Methods in Terms of Locally Supported Wavelets: Theory and Application to Geomagnetic Modeling, Ph.-D. thesis. University of Kaiserslautern, Geomathematics Group, Kaiserslautern (2011)

    Google Scholar 

  17. Glaßmeier, K.H., Soffel, H., Negendank, J. (eds.) Geomagnetic field variations. In: Advances in Geophysical and Environmental Mechanics and Mathematics. Springer, Berlin (2009)

    Google Scholar 

  18. Glaßmeier, K.H., Soffel, H., Negendank, J.: The geomagnetic field. In: Glaßmeier, K.H., Soffel, H., Negendank, J. (eds.) Geomagnetic field variations. Advances in Geophysical and Environmental Mechanics and Mathematics, pp. 1–23. Springer, Berlin (2009)

    Chapter  Google Scholar 

  19. Gubbins, D., Herrero-Bervera, E. (eds.): Encyclopedia of Geomagnetism and Paleomagnetism. Springer, Dordrecht (2007)

    Google Scholar 

  20. Gui, Y.F., Dou, W.B.: A rigorous and completed statement on Helmholtz theorem. Prog. Electromagn. Res. (PIER) 69, 287–304 (2007)

    Google Scholar 

  21. Hulot, G., Finlay, C.C., Constable, C., Olsen, N., Mandea, M.: The magnetic field of planet earth. Space Sci. Rev. 152, 159–222 (2010)

    Article  Google Scholar 

  22. Hulot, G., Olsen, N., Sabaka, T.J., Fournier, A.: The Present and Future Geomagnetic Field (2015). DOI: 10.1016/B978-0-444-53802-4.00096-8

    Google Scholar 

  23. Kono, M. (ed.): Geomagnetism, Treatise on Geophysics, vol. 5. Elsevier, Amsterdam (2009)

    Google Scholar 

  24. Langel, R.A., Hinze, W.J.: The magnetic field of the Earth’s lithosphere: the satellite perspective. Cambridge University, Cambridge (1998)

    Book  Google Scholar 

  25. Lowes, F.J.: Spatial power spectrum of the main geomagnetic field, and extrapolation to the core. Geophys. J. R. Astron. Soc. 36, 717–730 (1974)

    Article  Google Scholar 

  26. Lühr, H., Korte, M., Mandea, M.: The recent geomagnetic field and its variations. In: Glaßmeier, K.H., Soffel, H., Negendank, J. (eds.) Geomagnetic Field Variations. Advances in Geophysical and Environmental Mechanics and Mathematics, pp. 25–64. Springer, Berlin (2009)

    Chapter  Google Scholar 

  27. Maier, T.: Multiscale geomagnetic field modeling from satellite data: theoretical aspects and numerical applications, Ph.-D. thesis. University of Kaiserslautern, Geomathematics Group, Kaiserslautern (2002)

    Google Scholar 

  28. Maier, T.: Wavelet-Mie-representation for solenoidal vector fields with applications to ionospheric geomagnetic data. SIAM J. Appl. Math. 65, 1888–1912 (2005)

    Article  MathSciNet  Google Scholar 

  29. Mauersberger, P.: Das Mittel der Energiedichte des geomagnetischen Hauptfeldes an der Erdoberfläche und seine säkulare Änderung. Gerlands Beiträge zur Geophysik 65, 207–215 (1956)

    Google Scholar 

  30. Mayer, C.: Wavelet modeling of ionospheric currents and induced magnetic fields from satellite data, Ph.-D. thesis. University of Kaiserslautern, Geomathematics Group, Kaiserslautern (2003)

    Google Scholar 

  31. Mayer, C., Maier, T.: Separating inner and outer Earth’s magnetic field from CHAMP satellite measurements by means of vector scaling functions and wavelets. Geophys. J. Int. 167, 1188–1203 (2006)

    Article  Google Scholar 

  32. Morse, P.M., Feshbach, H.: Methods of Theoretical Physics. McGraw-Hill, New York (1953)

    MATH  Google Scholar 

  33. Morse, P.M., Feshbach, H., Hill, E.L.: Methods of Theoretical Physics. McGraw-Hill, New York (1953)

    MATH  Google Scholar 

  34. Olsen, N., Glassmeier, K.-H., Jia, X.: Separation of the magnetic field into external and internal parts. Space Sci. Rev. 152, 159–222 (2010)

    Article  Google Scholar 

  35. Olsen, N., Hulot, G., Sabaka, T.J.: Sources of the geomagnetic field and the modern data that enable their investigation. In: Freeden, W., Nashed, Z., Sonar, T. (eds.) Handbook of Geomathematics, 1st edn, vol. 1, pp. 106–124. Springer, London (2010)

    MATH  Google Scholar 

  36. Sprössig, W.: On Helmholtz decompositions and their generalizations—An overview. Math. Meth. Appl. Sci. 33, 374–383 (2010)

    MathSciNet  MATH  Google Scholar 

  37. Vogt, J., Sinnhuber, M., Kallenrode, M.B.: Effects of geomagnetic variations on system Earth. In: Glaßmeier, K.H., Soffel, H., Negendank, J. (eds.) Geomagnetic Field Variations. Advances in Geophysical and Environmental Mechanics and Mathematics, pp. 159–208. Springer, Berlin (2009)

    Chapter  Google Scholar 

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Blick, C., Freeden, W., Nashed, M.Z., Nutz, H., Schreiner, M. (2021). Basics of Magnetic Field Theory and Magnetization. In: Inverse Magnetometry. Lecture Notes in Geosystems Mathematics and Computing. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-79508-5_2

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