Long-range memory patterns in variations of environmental radon in soil†
This paper addresses issues of long-range memory and self-organisation in variations of radon in soil in Greece. The methods of rescaled-range, roughness-length, variogram, fractal dimension and block entropy were employed through lumping. Sliding was utilised with the wavelet spectral fractal technique. Antipersistent Hurst exponents in the range 0 < H < 0.5 were mainly identified. Persistent exponents (0.5 < H < 1) were also detected. Switching between persistency and antipersistency was observed and considered consistent with an underlying geo-environmental long-memory self-organisation. Fractal dimensions were in the range 1.2 < D < 2. The anomalous parts of the 2008 radon signal presented significantly lower fractal dimensions. Value ranges of Shannon, Shannon-per-letter, conditional, Tsallis and normalised Tsallis block entropies were 0.67 ≤ H(n) ≤ 2.73, 0.2 ≤ h(n) ≤ 0.7, 0.2 ≤ h(n) ≤ 0.6, 0.36 ≤ Sq ≤ 1.11, 0.50 ≤ Ŝq ≤ 9.55 respectively. The entropy values were affected by the block-size n. The entropic index values of the radon anomalies were significantly lower indicating long-memory underlying patterns. Underlying sources are discussed. The asperity-model is proposed.