Statistical Characteristics of atmospheric phase fluctuations observed by a VLBI system using a beacon wave from a geostationary Satellite

This paper reports the statistical characteristics of phase fluctuations obtained by a very long baseline interferometry, which received beacon waves from a geostationary satellite. Observations were made in different weather conditions by the 6-m Kagoshima and the 10-m Mizusawa radio telescopes, which were 1284 km apart from one another. Atmospheric phase fluctuations ranging from 0.2 to about 1000 s were detected. To study a variety of statistical characteristics of these phase fluctuations, the Allan standard deviation, σ_y(τ), the temporal structure function, D_φ(τ), and the square root of power spectrum, G_φ(f), were calculated from the observation results. These qualities were found to depend on the time interval τ or the frequency f (f=1/2τ) as follows: σ_y(τ)∝τ^-0.6, τ^-0.3, D_φ(τ)∝τ^0.9, τ^1.3 for 0.2 s<τ<1.5 s and 1.5 s<τ<400 s. G_φ(f)∝f^-0.8 for 2.5 Hz>f>0.33 Hz and G_φ(f)∝f^-1.3 for 0.33 Hz>f>0.00125 Hz. The curves of σ_y(τ) and D_φ(τ) exhibited shifts whose magnitudes followed the weather order clear, cloudy, and rainy. For τ>1.5 s (or f<0.33 Hz), the experimental results were consistent with the theoretical values predicted by Kolmogorov´s turbulence theory and a frozen-screen model, but for τ<1.5 s (or f>0.33 Hz), the model has to be modified to explain the experimental results.