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Validity of a selective summation technique in analysis of wave propagation through random media
Author(s) -
Tateiba Mitsuo
Publication year - 1982
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1029/rs017i002p00339
Subject(s) - moment (physics) , mathematical analysis , dirac delta function , physics , function (biology) , mathematics , wave equation , second moment of area , quantum mechanics , geometry , evolutionary biology , biology
The so‐called 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 n th 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.