Validity of a selective summation technique in analysis of wave propagation through random media
Abstract
The socalled moment equation for a successively forward scattered wave was derived under a definite condition. The condition shows that the applicability of the equation is much more extensive. When a selective summation technique is applied to the derivation of the moment equation, another condition besides the above is necessary for the existence of the equation. The extra condition is due to the selective summation of scattered waves and shows the validity of the technique for the nth moment of forward scattered waves. For example, if the waves propagate along the z axis, a necessary condition for the technique to be valid for the first, second, and fourth moments is k^{2}l^{2}B(0, 0) ≪ 1 where k is the wave number in free space and l and B(r, z) are the correlation length and the correlation function of fluctuation of the medium, respectively. For all the higher moments the technique is applicable only to the case of B(r, z) = B_{r},(r)δ(z) where δ(z) is the Dirac delta function.
 Publication:

Radio Science
 Pub Date:
 April 1982
 DOI:
 10.1029/RS017i002p00339
 Bibcode:
 1982RaSc...17..339T
 Keywords:

 Forward Scattering;
 Numerical Analysis;
 Random Processes;
 Wave Propagation;
 Wave Scattering;
 Dirac Equation;
 Fourier Transformation;
 Markov Processes;
 Maxwell Equation