Multifractal detrended fluctuation analysis of soil radon (222Rn) and thoron (220Rn) time series

We present results of Multifractal Detrended Fluctuation Analysis (MF-DFA) of soil radon (222Rn) and thoron (220Rn) time series to examine the scaling and multifractal features. Data consists of 15,692 measurements taken each over forty-minute interval. RTM 1688–2, 222Rn/220Rn electronic device has been used for measurement purposes. Seasonal periodicities have been removed from the data and MF-DFA was employed on de-seasonalized data. Original 222Rn and 220Rn time series have been converted into surrogated and shuffled time series. MF-DFA has also been applied to the surrogated and shuffled series to examine the multifractality nature. Results of the study show that Orig222Rn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}_{{{\text{Orig}}}}^{222} {\text{Rn}}$$\end{document}, Surr222Rn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}_{{{\text{Surr}}}}^{222} {\text{Rn}}$$\end{document} and Orig220Rn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}_{{{\text{Orig}}}}^{220} {\text{Rn}}$$\end{document}, Surr220Rn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}_{{{\text{Surr}}}}^{220} {\text{Rn}}$$\end{document} time series are long-range positively correlated and an increase or decrease in either of radionuclide concentrations will be followed by another increase or decrease of concentrations in future measurements. The Shuff220Rn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}_{{{\text{Shuff}}}}^{220} {\text{Rn}}$$\end{document} time series has an independent or short-range dependent structure called white noise and the shuffled time series exhibit a very weak multifractality.