Inverse Scattering Problems

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


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
$$\Delta E + {k^2}\varepsilon \left( {r,k} \right)E = 0$$
, 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.


Inverse Problem Born Approximation Fresnel Zone Paraxial Approximation Inverse Scattering Problem 
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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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