Representation of Plane Geopotential Fields in the Form of the Cauchy-Type Integral

  • Michael S. Zhdanov


This chapter is devoted to two-dimensional (plane) potential fields. The main geopotential fields dealt with in geophysics are the gravitational and constant magnetic fields. The physical nature of these fields is outlined comprehensively in many treatises on general and applied geophysics. That is why, within the scope of this book, we will dwell only on the problems of mathematical theory of analysis, integral transforms, and interpretation of geopotential fields. Moreover, we shall confine ourselves just to the issues resolved most efficiently in terms of the Cauchy-type integral. How wide the range of these issues is will be shown below.


Vector Field Gravitational Field Continuous Partial Derivative Field Source Cauchy Kernel 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Michael S. Zhdanov
    • 1
  1. 1.Institute of Terrestrial Magnetism, Ionosphere and Radiowave PropagationAcademy of SciencesIzmiran, Troitsk, Moscow RegionUSSR

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