The ionosphere is an ionised region of the Earths atmosphere which lies above the mesosphere and extends from approximately 80km to 1000km above the surface. It gains its ionised characteristic from interactions between atoms in the atmosphere and incoming energetic solar radiation, namely Extreme Ultraviolet (EUV) and X-Ray solar emissions. The structure of the ionosphere is inhomogeneous and dynamic both spatially and temporally as it is influenced by the changes in solar activity and seasonal and diurnal effects. Due to spectral variability in solar radiation and the different number density profiles of atmospheric species, the ionosphere is separated into layers called the D, E and F layers.
The fluctuations in electron density within the ionosphere cause any propagating wave to be refracted and delayed due to changes in the mediums refractive index. These special variations in electron density also cause rapid fluctuations in a propagating waves parameters, which is known as scintillation. The strength of the scintillation is dependent on the frequency of the propagating wave as well as the local electron density. Ionospheric scintillation causes adverse effects on the signals used in various communications, navigations and location systems, therefore the study and understanding of the underlying physics and structure would be beneficial to improve the accuracy of transionospheric transmissions. Amongst the numerous remote sensing methods used to study the ionosphere, the most well developed and documented is radio probing. Radio signals can be either transmitted through the ionosphere or can be reflected off specific layers within, with this paper focusing on the former.
The primary process investigated in this paper is the effects of scintillation on a transionospheric radio signal. For simulation purposes, using an ultrasonic wave would allow a model to be run at a much smaller scale. By recording the amplitude and phase of the perturbed wave it is possible to use scintillation indices to characterise the severity of the fluctuations. The main index used for determining amplitude scintillation is the S4 index, which is defined as the normalised root mean square deviation of irradiance I:
S_4= √((〈I^2 〉-〈I〉^2)/〈I〉^2 ) (1)
Here the angled brackets denote temporal averages. Due to the current widespread use of S4 measurements, as well as the availability of long-term archives, the S4 index is still a worthwhile means (Beach, et al., 2004). The σφ index is used to describe the behaviour of carrier phase fluctuations.
σ_φ=√(〈φ^2 〉-〈φ〉^2 ) (2)
Due to the Coronavirus epidemic and resulting lockdown measures, it was not possible to fully complete the scintillation simulation in the laboratory. Thus, a secondary process was investigated: the use of tomography in geophysical studies of the ionosphere. Ionospheric tomography allows for large two-dimensional areas to be analysed for the special distribution of electron density. Radio probing methods have been the most contributary way of investigating the structure of the ionosphere, and with the development of computational tomography in the 1970’s the first application for ionospheric imaging was reported in 1986 (Austen, et al., 1986). The process involves taking the line integral of total electron content (TEC) along numerous intersecting transionospheric ray paths. To reconstruct the distribution of TEC using the measured line integrals an algebraic reconstruction technique is used. Considering ART as an iterative solver of the system of equations:
Ax=b (3)
with x being a column vector of the unknown TEC of the output images pixels, A is a sparse matrix containing the length of each ray path through the pixels, and b is the column vector of the measured line integrals of all the ray paths. An approximation to the solution of the system of equations can be reached with the formula:
a_i^n=a_i^(n-1)-λ((∑_i▒〖a_i^(n-1)∙l_ij-A_j 〗)/(∑_i▒l_ij^2 ) l_ij ) (4)
where ain is the absorptivity of pixel I in the previous iteration, λ is the relaxation factor used to slow the convergence of the system, lij is the length of ray path j in pixel I, Aj is the measured line integral of absorption along path j, and n is the iteration number. In this paper the iterative method was automated to allow for more accurate results.