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Inverse Scattering Problems

  • Viacheslav E. Kunitsyn
  • Evgeny D. Tereshchenko
Chapter
  • 160 Downloads
Part of the Physics of Earth and Space Environments book series (EARTH)

Abstract

As shown in Sect. 1.2, for high sounding frequencies, vector equation (1.11) splits up into three scalar equations, and it is sufficient to consider the equation for one component of the field
$$\Delta E + {k^2}\varepsilon \left( {r,k} \right)E = 0$$
(3.1)
, where
$$\varepsilon \left( {r,w} \right) = 1 - \frac{{4\pi {r_e}N\left( r \right)}}{{{k^2}\left( {1 + i{\nu _{eff}}\left( r \right)/\omega } \right)}},{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} k = \frac{{2\pi f}}{c} = \frac{w}{c}$$
is the wave number, v eff (r) is the efficient electron collision frequency, N(r) is electron concentration, and the “ion” contribution to the dielectric permittivity may be neglected [Ginzburg, 1961]. The relation for ɛ has the same form both in the SI and cgs systems; only the expression for r e varies.

Keywords

Inverse Problem Born Approximation Fresnel Zone Paraxial Approximation Inverse Scattering Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Viacheslav E. Kunitsyn
    • 1
  • Evgeny D. Tereshchenko
    • 2
  1. 1.Physics Faculty, Atmospheric Physics Dept.M. Lomonosov Moscow State UniversityMoscowRussian Federation
  2. 2.Polar Geophysical InstituteMurmanskRussian Federation

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