On the Problem of True Values of the Spectrum Indices for Small-scale Ionospheric Turbulence

Abstract

We consider the problem of obtaining reliable values of the local-spectrum indices of the electron number density fluctuations for small-scale ionospheric turbulence. It is shown that the use of a multifractal analysis in combination with the synchronous correlation processing of the received signals in the experiments on remote radio sounding of the ionosphere by satellite signals permits one to solve the posed problem. In this case, the true values of the local-spectrum indices of smallscale ionospheric turbulence, which are measured in such specialized experiments under natural conditions and during modification of the ionosphere by high-power HF radio emission, can differ notably from their standard values obtained within the framework of the classical method of radio scintillations, in which only correlation processing of the data is used.In theoretical paper [1], we considered the problem of true values of the local-spectrum indices of the electron number density fluctuation for small-scale ionospheric turbulence. In particular, it was shown that the classical multifractal analysis of weak amplitude fluctuations of the received signals during remote radio sounding of the ionosphere from the satellites in combination with the conventional correlation processing yields the necessary information on the fractal dimension D A of samples of the signal-amplitude fluctuations and the corresponding index p A of the amplitude fluctuation spectra. In turn, knowledge of the parameters D A and p A makes it possible to determine the true values of the local-spectrum indices of the electron number density fluctuations for small-scale ionospheric turbulence and find the values of the fractal dimension of the space occupied by small-scale irregularities of these fractal structures in the ionosphere.However, during the first specialized experiments on radio sounding of the midlatitude ionosphere by signals of orbital satellites in 2005−2006, it was found that the structure of developed ionospheric turbulence cannot always be described in terms of the generally accepted multifractal model. In the analysis of the results of the measurements performed in the course of those experiments, it was established that for the structural functions of fluctuations of the received-signal amplitude A(t) and a small temporal separation τ , the following relationship is valid [2,3]:where T is the temporal range of the analyzed sample of the signal amplitude, ϕ A (q) is the scaling index during approximation of the experimentally measured qth-order structural functions of amplitude fluctuations, and D A (α q ) is the fractal dimension of amplitude fluctuations of the received signals, which is determined on the set q of structural functions from the parametric dependence [2, 3] D A (α q ) = 1 ± [α q q − ϕ A (q)], α q = dϕ A (q)/dq.