Determination of random variations in ionosphere height from phase fluctuations of VLF signals

A feature of our problem of restoration of fluctuations in ionosphere height is that the experimental data ψ(t, κ{script}_k) obtained at a fixed reception point are functions of time, whereas the function φ{symbol}₁(u, y₂) to be restored is a function of the coordinates. If we use the assumption that the irregularities migrate transversely, coordinate y₂ can be "exchanged" for time t. Restoration with respect to the second coordinate u=x_i-x₀/2 is in effect obtained by using data ψ(t, κ{script}_k) on some set of carrier frequencies. The resultant solution of the restoration problem is in the form of an expansion of φ{symbol}₁(u, y₂) in known functions determined from the observed data ψ(t, κ{script}_k). We have evaluated the solution accuracy, which depends on the overall power signal-to-noise ratio at all frequencies used. We have demonstrated that the restoration algorithm contains an optimum number (with respect to accuracy) of coefficients to be evaluated.