Correlation Dimension of Underground Muon Time Series

This paper presents results obtained for the correlation dimension of cosmic ray muon time series detected at a depth underground of 570 hg/cm² over a period of 8 years. The corresponding galactic primaries have rigidities of the order of a few teravolts and are therefore at least partially under the influence of solar modulation effects. The principal indication is that the physical mechanisms which shape the muon time series in the frequency range below 2 × 10−5 Hz are entirely stochastic in behavior and have a monofractal structure. The correlation dimension is finite and shows an inverse dependence on the level of solar activity, oscillating between 4.5 ± 0.4 at solar maximum and 6.2 ± 0.6 at solar minimum.