Traces of self-organisation and long-range memory in variations of environmental radon in soil: comparative results from monitoring in Lesvos Island and Ileia (Greece)

Abstract

This paper addresses issues of self-affinity, long-memory and self-organisation in variations of radon in soil recorded in Lesvos Island, Greece. Several techniques were employed, namely (a) power-law wavelet spectral fractal analysis, (b) estimation of Hurst exponents through (b1) rescaled-range, (b2) roughness-length, (b3) variogram and (a), (c) detrended fluctuation analysis, (d) investigation of fractal dimensions and (e) analysis of five block entropies: (e1) Shannon entropy, (e2) Shannon entropy per letter, (e3) conditional entropy, (e4) Tsallis entropy, and (e5) normalised Tsallis entropy. Long-lasting antipersistency was identified during a period of anomalous radon variations following fractional Brownian modelling. Remaining variations did not exhibit analogous behaviour and followed fractional Gaussian modelling. Antipersistent power-law-beta-exponent-values between 1.5 and 2.0 were detected during anomalies. Persistent values were also found. Hurst exponents were mainly within 0 < H < 0.5. Some persistent exponents (0.5 < H < 1) were also observed. Fractal dimensions were within 1.5 < D < 2. Radon anomalies presented lower fractal dimensions. Shannon entropy ranged between 0.77 ≤ H(n) ≤ 2.38, Shannon entropy per letter, between 0.19 ≤ h(n) ≤ 0.59, conditional entropy, between 0.01 ≤ h(n) ≤ 0.58, Tsallis entropy, between 0.55 ≤ Sq ≤ 1.01 and normalised Tsallis entropy between, 0.98 ≤ \(\hat{S}\) ≤ 5.42 (block-size n = 4). Entropies were lower during anomalies, indicating strong self-organisation. Persistency–antipersistency switching was observed, consistent with long-memory dynamics. Potential geological sources were discussed. The asperity-model was proposed. Findings were compared to results obtained under analogous methodologies in Ileia, Greece.