Uniform integral representation for the fluctuating field propagating through the multi-scale media

A uniform integral representation for the wave field propagating through the statistically homogeneous multi-scale medium was obtained. It is shown that the considered expression for the field contains the limiting cases for both the Born’s approximation for the single-scattered field and a phase approximation of geometric optics method. Hybrid method formulae for calculation of the fluctuation field, taking into account the effect of backscattering enhancement can be obtained from the investigated integral representation, provided that the spectrum of inhomogeneities can be represented as a sum of two uncorrelated components: small-scale and large-scale. The paper contains the numerical simulation results of the effect of average intensity enhancement of the backscattered field in the medium containing both large- and small-scale irregularities. Unlike the hybrid method of calculation, the proposed approach does not require explicit separation of the inhomogeneities spectrum into two uncorrelated components and allows investigating the effect of the average intensity enhancement of the backscattered field in a more general situation. In particular, numerical calculations have shown that the effect of enhancement of the backscattered signal may occur in the study of the high-latitude ionosphere by method of incoherent scattering of radio waves.