Long-Lasting Patterns of Radon in Groundwater at Panzhihua, China: Results from DFA, Fractal Dimensions and Residual Radon Concentration

Geochemical Journal, Vol. 53, pp. 341 to 358, 2019 doi:10.2343/geochemj.2.0571

Long-lasting patterns of radon in groundwater at Panzhihua, China: Results from DFA, fractal dimensions and residual radon concentration

AFTAB ALAM,1,2,3 NANPING WANG,1,2* GUOFENG ZHAO,4 TAHIR MEHMOOD5 and DIMITRIOS NIKOLOPOULOS6

1Key Laboratory of Geo-detection, Ministry of Education, China University of Geosciences, Beijing 10083, China 2School of Geophysics and Information Technology, China University of Geosciences, Beijing 10083, China 3Centre for Earthquake Studies, National Centre for Physics, Islamabad, Pakistan 4China Earthquake Networks Centre, Beijing, China 5School of Natural Sciences (SNS), National University of Life Sciences (NUST), Islamabad, Pakistan 6University of West Attica, Department of Informatics and Computer Engineering, Athens, Greece

(Received December 31, 2018; Accepted August 17, 2019)

This paper reports chaos and long-memory trends hidden in radon (222Rn) variations in the groundwater of Panzhihua, Sichuan Province, China, between 2012 and 2017. The analysis is performed using sliding-window (a) detrended fluctuation analysis (DFA), (b) fractal dimension analysis with the methods of Higuchi, Katz and Sevcik and (c) residual radon concentration (RRC). Several fractional Brownian motion (fBm) persistent time series segments of high predictability are found, with DFA slopes above 1.5 and fractal dimensions, below 1.5. Numerous seven-day segments exhibit RRC out of the ±2s limits and are of noteworthy precursory value. Through a novel two-stage computational approach, the persistent pre-seismic fBm earthquake footprint segments are separated from the low-predictability ones. Several combined segments of dynamical complexity are found with fractal and long-memory behaviour. For these segments, associations are attempted with major (Mw ≥ 6.0) earthquakes occurred in China and border areas of near countries during the period of study. Out of seventeen earthquakes of the period, four earthquakes are identified with all combinations of methods, whereas the remaining earthquakes, with the combination of at least three methods. Trends of long-memory are identified and discussed. The findings are compatible with fractal, and SOC final phases of generation of earthquakes. Finally, potential geological sources are discussed and analysed.

Keywords: radon in groundwater, DFA, fractal dimension, residual radon, earthquakes

(Cicerone et al., 2009; Petraki et al., 2015a, b), which is 1. INTRODUCTION expected to be more pronounced in the regions of crust Earthquakes are natural phenomena with negative cracking and fracture (Khan et al., 2011). The efforts to impacts on human lives and property. The strong earth- forecast earthquakes are, in principle, multifaceted and quakes are of major concern not only due to their cata- for this reason, diverging techniques and multilevel ap- strophic nature, but also because they occur inevitably proaches are needed (Eftaxias et al., 2010; Nikolopoulos when certain geophysical conditions exist (e.g., Eftaxias et al., 2018a, b). The related prognosis research prereq- et al., 2010; Nikolopoulos et al., 2016a, 2016b, 2018a, uisites the gradual contraction of time, space and magni- 2018b). Despite the tremendous efforts, earthquakes are tude sizes in areas where strong earthquakes could occur still difficult to foresee (please see reviews of Cicerone (e.g., Petraki et al., 2015a, b). Apart from the electro- et al., 2009; Ghosh et al., 2009; Hayakawa and Hobara, magnetic disturbances of the ULF, LF, HF and VHF ranges 2010; Uyeda et al., 2009). For this reason, the identifica- (e.g., Hayakawa and Hobara, 2010; Petraki et al., 2015b; tion of earthquake precursors remains an elusive and chal- Uyeda et al., 2009) which are extensively used as earth- lenging task (Cantzos et al., 2018) within a general frame- quake precursors, radon-222 (henceforth, radon) has an work to discover credible and unambiguous pre-earth- equal long history in earthquake prognosis (e.g., reviews quake warnings (e.g., Molchanov and Hayakawa, 1998; of Cicerone et al., 2009; Ghosh et al., 2009; Petraki et Petraki et al., 2015a, b). Towards this, various types of al., 2015a). Radon is a radioactive and inert gas produced pre-seismic activity is recorded (e.g., ULF, LF, HF, VHF by the decay of 238U series with a half-life of 3.86 days disturbances, anomalous trace gas and radon emissions) (Nazarrof and Nero, 1988). Upon decay, radon dissolves in soil’s pores and fluids and from there, to surface and *Corresponding author (e-mail: [email protected]) underground waters and atmosphere (Nazarrof and Nero, Copyright © 2019 by The Geochemical Society of Japan. 1988). Radon can migrate at short or long distances from

341 its generation (Richon et al., 2007) and due to this prop- pressed by other investigators. For example, Talwani et erty, it is an efficient pre-earthquake precursor (Barkat et al. (2007) reported that the anomalous behaviour of ra- al., 2018; Cicerone et al., 2009; Nikolopoulos et al., 2012, don gas could be because of the opening of pore’s spaces 2013, 2014, 2015, 2016b, 2018a; Petraki et al., 2013a, during rock fracturing as a result of seismic events. Ex- 2013b, 2015a, 2015b). plosion tests have been performed to identify the rela- Regarding modelling radon underlying dynamics prior tionship between the dynamic loading effect and the ob- to earthquakes, Scholz et al. (1973) reported the served concentrations of radon (Yu et al., 1986). The ex- Dilatancy-Diffusion Model which associates anomalous perimental results revealed that the increase in radon val- radon variations with the mechanical crack growth rate ues was a consequence of seismic waves applied to the in the volume of a dilatancy. According to this model, a rock. According to other investigators (e.g., Awais et al., porous cracked saturated rock constitutes the initial me- 2017; Barkat et al., 2017; Jilani et al., 2017; Riggio and dium. With the increase of the tectonic stresses, the cracks Santulin, 2015), crustal activities have been identified as extend and disengage near the pores, leading to opening one of the reasons for radon emission. of favourably oriented cracks. This results in a decrease Regarding radon anomalies in groundwater, histori- in pore pressure in the total preparation zone, leading to cally the first evidence has been presented after the Great water flow into the zone from the surrounding medium. Tashkent Earthquake of 1966 (Sadovsky et al., 1972). The return of the pore pressure together with the increase Thereafter several studies (e.g., King, 1986; Kumar et al., of cracks may yield to abrupt changes of radon emana- 2012; Ohno and Wakita, 1996; Planinic et al., 2000; tion. Another model is the crack-avalanche (CA) (Lay et Pulinets et al., 1997; Ulomov and Mavashev, 1971; Virk al., 1998; Planninic et al., 2001), according to which, a et al., 2001; Walia et al., 2013; Zmazek et al., 2000) have cracked focal rock zone is formed by the increasing tec- suggested that the fluctuation of radon concentration in tonic stress. The shape and volume of this zone change water could be an efficient tool to predict earthquakes. slowly with time. According to the theory of stress corro- Negarestani et al. (2014) designed a continuous monitor- sion, the anomalous behaviour of radon concentration may ing network of radon for earthquake forecasting and found be associated with this slow crack growth, which is con- that hot springs are useful sources. Prior or post to earth- trolled by the stress corrosion in the rock matrix satu- quakes, radon levels in groundwater increase in the re- rated by groundwater (Anderson and Grew, 1977). gions where high-stress accumulation occurs in the crust Pulinets and Ouzounov (2011) reported the Lithosphere- (Tarakç et al., 2014). Meteorological parameters (precipi- Atmosphere-Ionosphere Coupling Model (LAIC). This tation, temperature, humidity, pressure) and local geologi- model explains the foundations of stress accumulation in cal conditions are factors controlling the subsurface ground due to the relative movement of tectonic blocks degassing process that force the radon gas emanation that latterly cause development of microcracks, fissures (Imme and Morelli, 2012), but the geophysical changes, and fractures. Radon gas emanation from micro-fractures when present, are the dominant factors (Prasad et al., mixes with water and reaches ground by different media. 2006). Transportation of radon from deep layers of the Earth to Despite the extensive published research, there is still the surface usually is performed by water and carrier gases no universal model to describe the various geo-physical (Gregoric et al., 2008). Nikolopoulos et al. (2012, 2013, phases prior to the occurrence of earthquakes 2014, 2018a) and Petraki et al. (2013a, b) proposed the (Nikolopoulos et al., 2012, 2013, 2014, 2015, 2016b, asperity model (Eftaxias et al., 2008) to explain radon 2018a; Petraki et al., 2013a, 2013b, 2015a, 2015b). The emanation during preparation of earthquakes. This model scientific community still debates the precursory value explains the fractional Brownian (fBm) class variations of the numerous reports of radon anomalies detected prior found in fractal and long-memory pre-seismic radon time to earthquakes (Eftaxias et al., 2010; Nikolopoulos et al., series. According to this model, the focal area consists of 2012, 2013, 2014, 2015, 2016b, 2018a; Petraki et al., a backbone of strong and large asperities that sustain the 2013a, 2013b, 2015a, 2015b). On the other hand, recent system. The asperities could be simulated as profiles of papers have presented methods, such as wavelet spectral the fBm-model. A strongly heterogeneous medium sur- fractal analysis, rescaled range analysis, monofractal and rounds the family of strong asperities. The fracture of the multifractal detrended fluctuation analysis (DFA, MDFA), heterogeneous system in the focal area obstructs the back- entropy and block entropy analysis through symbolic bone of asperities. At this stage, critical anti-persistent dynamics, to identify traces hidden in pre-seismic time radon anomalies occur. When strong antipersistent or series, based on the concepts of fractality, long-memory persistent fBm radon anomalies are emitted, the ‘siege’ and self-organization (Ghosh et al., 2009; Nikolopoulos begins, the fracture of the asperities starts and this et al., 2012, 2013, 2014, 2015, 2016b, 2018a; Petraki et signalises the unavoidable evolution of the process to- al., 2013a, 2013b, 2015a, 2015b). Among the aforemen- wards the global failure. Other aspects have been ex- tioned publications, Petraki et al. (2013a, 2013b, 2015b,

342 A. Alam et al. 2016) and Nikolopoulos et al. (2018a) reported self-aff- tector system in standard methodology for radon in wa- ine persistent-antipersistent behaviour of radon anoma- ter measurements (Ren et al., 2012). The instrument con- lies similar to the ones of the pre-seismic electromagnetic ducts one measurement per hour with a lower detection disturbances in the ULF, LF and HF ranges. level of 0.1 Bq/L. Prior to measurements, the SD-3A This paper reported continuous measurements of ra- monitor is calibrated according to standard methodology don in the groundwater of a well located in Panzhihua (e.g., Kuo et al., 2006; Ren et al., 2012; Xu et al., 2010) Sichuan Province, China (Latitude: 26.51, Longitude: by using a radioactive solid radon source of predefined 101.74) recorded between 2012 and 2017. Chaos and activity. long-memory trends hidden in radon (222Rn) variations 2.2.2. Precipitation data were reported by a two-stage meta-analysis results from Precipitation is not monitored by CEA and hence such the outcomes of four different chaos analysis methods data is not available for the Panzhihua well. To overcome (detrended fluctuation analysis (DFA) and fractal dimen- this issue the precipitation dataset of the Tropical Rain- sion analysis with the methods of Higuchi, Katz and fall Measuring Mission (TRMM) satellite between 2012– Sevcik) in combination with the results from residual ra- 2017 was utilized in this paper. The TRMM dataset was don concentration (RRC) analysis. Associations were at- considered as the best solution among the available tempted with seismic events of the period occurred in sources of precipitation data for China. China and border areas of nearby countries. Finally, the 2.2.3. Statistical analysis of experimental parameters potential geological sources were discussed and analysed. Statistical analysis was performed using R package in the full-time series of radon concentration and precipitation. Stationarity tests of the full data set of radon and 2. MATERIALS AND METHODS precipitation were checked using the Augmented Dickey- 2.1. Geological setting Fuller (ADF), KPSS and Box-Ljung (BL) tests. The study area (Panzhihua) is located in the west mar- Autocorrelation of the full-time series was performed to gin of Yangtze Block and also the west part of Kangdian check the self-influence lags. Radon was checked versus complexes and the Emeishan large igneous province. This precipitation time series through cross-correlation. area is surrounded by several Quaternary faults, i.e., the Red River fault to the south, the Anninghe-Zemuhe faults 2.3. Theoretical aspects to the east, the Jinhe-Jinghe faults to the west (Liang et 2.3.1. Residual radon concentration al., 2016). The Yangtze Block comprises of a lower se- It is accepted that radon precursory activity prior to quence of Late Mesoproterozoic to Silurian strata, a mid- earthquakes is associated with abnormal concentrations dle sequence of Devonian to Triassic strata, and an upper in respect to the background values (e.g., Cicerone et al., sequence of Jurassic and younger strata. The upper se- 2009; Fu et al., 2009; Ghosh et al., 2009; Petraki et al., quence contains mostly terrestrial basin deposits, whereas 2015a). According to several publications (e.g., reviews the lower and middle sequences are basically marine sedi- of Cicerone at al., 2009; Ghosh et al., 2009 and Petraki et mentary rocks. According to Zhou et al. (2002), the west- al., 2015a and the papers of Barkat et al., 2017, 2018; Fu ern margin of the Yangtze Block is marked by abundant et al., 2017; Igarashi and Wakita, 1990; Jilani et al., 2017; Neoproterozoic granites and associated metamorphic Zmazek et al., 2000), radon concentrations exceeding the complexes, known as the Kangdian complexes. During limits of ±2s (s, standard deviation) have been consid- the Cenozoic, block-faulting and shallow-level shearing ered as noteworthy anomalies. dominated in the eastern part of the Yangtze Block, To identify the anomalous variation in radon values whereas thrusting and strike-slip faulting dominated in the RRC (dA(t)) was calculated as the difference between the western part (Burchfiel et al., 1995). the daily average (A(t)) and the seven-day moving average (RA(t)) according to Eq. (1) 2.2. Experimental techniques 2.2.1. Radon instrumentation dA(t) = A(t) – RA(t). (1) The radon in water dataset of this paper at the Panzhihua well is a part of the monitoring program of the Value s was calculated as the unbiased standard devia- China Earthquake Administration (CEA), which is the tion of all the RRC values between 2012 and 2017. Here- responsible Authority in China. CEA continuously con- after, RRC values greater or less than 2s were consid- ducts several sets of measurements at areas of enhanced ered as radon anomalies. seismicity (Ye et al., 2015). Panzhihua is one of such ar- 2.3.2. Chaos analysis methods eas located at the junction region between Sichuan and 2.3.2.1. Fractality, long-memory Yunnan. Radon at Panzhihua is measured by an SD-3A Nature exhibits fractal behaviour in several physical radon monitor. The SD-3A monitor uses a ZnS (Ag) de- systems. This is revealed when these systems are dilated,

Influence of earthquakes on the continuous groundwater radon data 343 translated, or rotated in space. These systems are charac- 2.3.2.3. Detrended Fluctuation Analysis (DFA) terized as self-affine or self-similar depending on their 2.3.2.3.1. General mathematical properties. Self-affinity and self-similarity During preparation of earthquakes, long-range power- characterize all parts of the system, in a way that any cho- law correlations emerge together with time series and er- sen part of the system is a small- or large-scale represen- ratic fluctuations (Skordas, 2014; Stanley, 1995). Pseudo- tation of it. Specifically, it is similar in shape and proper- sinusoidal trends, repeated temporal patterns and noise ties to a smaller part when magnified or to a larger part are many times observed, mostly related to the non-sta- when reduced in space or to it when translated or rotated. tionary features embedded in earthquake associated time These systems are fractals and, due to this property, they series (Petraki, 2016; Skordas, 2014). The autocorrelation can be studied by analysing their parts. The scaling and and spectrum-based techniques are not suitable due to the fractal properties of a system are linked with the proper- non-stationarity of the related time series. On the other ties of long-memory and complexity (see e.g., Mandelbrot hand, DFA has been established as a suitable and effec- and Ness, 1968; May, 1976; Morales et al., 2012; Musa tive technique for the detection of long-range power-law and Ibrahim, 2012; Sugihara et al., 1990), where the com- connections in non-stationary, noisy and short signals (Hu plexity is associated with the existence of linear mecha- et al., 2004; Nikolopoulos et al., 2015; Peng et al., 1993, nisms and orderliness. The long-memory analysis can 1998; Petraki et al., 2013a; Sarlis et al., 2013). This delineate the complexity of a system since, both are re- method has been successfully applied to many fields of lated and associated to the fractality of it (Nikolopoulos science such as DNA and heart dynamics (Ivanov et al., et al., 2016a, 2018a, 2018b; Petraki et al., 2016). The 1999; Peng et al., 1993), weather and climate fluctua- strength of associations among the past, present and fu- tions (Ivanova and Ausloos, 1999; Koscielny-Bunde et ture states of the system can be found by the long-memory al., 1998) and recently, in pre-earthquake recordings of analysis. DFA is a well-known method for studying the radon in soil (Nikolopoulos et al., 2015, 2018a; Petraki, long-memory of a system. The methods that calculate the 2016; Petraki et al., 2013a) and electromagnetic distur- fractal dimension can be utilized as well. Especially for bances of the kHz and MHz range (Nikolopoulos et al., the fractal methods, the ones that calculate the fractal di- 2018a; Petraki, 2016). mension directly are more valuable. In the following sec- Theoretically, DFA begins with the integration of the tions, DFA and three different fractal dimension calcula- original time signal. Then, the fluctuations, F(n), of the tion methods were discussed in detail, in parallel with integrated signal are calculated within a time window of the associated Hurst exponent. size n. The scaling exponent (a) of the integrated time- 2.3.2.2. Hurst exponent series is then estimated through a least-square fit to the A mathematical quantity which indicates the hidden log(F(n)) – log(n) linear transformation. The log(F(n)) – long-term memory patterns of time series is referred to log(n) line may show a crossover at the time scale where as the Hurst exponent, (Hurst, 1951; Hurst et al., 1965). the slope changes abruptly, depending on the scale n. It is used to evaluate the smoothness of time series and to There are cases where two crossovers can be addressed measure the scaling (fractal) properties of the series (Petraki, 2016; Petraki et al., 2013a). The inherent dy- (Turcotte, 1997). It was initially introduced for hydrol- namics of the system determines the crossovers and the ogy but has been used in fields such as climate dynamics power-law behaviour of it. (Rehman and Siddiqi, 2009), astronomy and astrophysics 2.3.2.3.2. Methodology of application of DFA (Kilcik et al., 2009), and plasma turbulence (Gilmore et Application of DFA for a one-dimensional signal, de- al., 2002). Importantly, it has been widely used in pre- noted by yi (i = 1, …, N), was implemented according to seismic activities (e.g., Cantzos et al., 2015, 2016, 2018; the following steps (Nikolopoulos et al., 2015; Petraki, Nikolopoulos et al., 2012, 2013, 2014, 2015, 2016b, 2016; Petraki et al., 2013a): 2018a, 2018b; Petraki et al., 2013a, 2013b, 2015a). Ac- (i) The time series y(i) was integrated to construct the cording to the aforementioned references, if H lies be- profile as in Eq. (2): tween 0.5 < H < 1, a long-lasting positive autocorrelation exists within the time series, which implies that high k present values will be probably followed by high future yk()= Â() yi()- y ()2 values and vice versa (persistency). On the other hand, if i=1 H lies between 0 < H < 0.5, then low present values will be probably followed by high future values, whereas low where y is the overall mean value of the time series, i.e., present values will be followed by high future values. This the mean over the whole time period. switching of low to high and high to low will continu- (ii) The integrated time series y(k) was divided into non- ously appear in many future samples (antipersistency). If overlapping segments of length n. H = 0.5, the time series follows a random walk, which means that they are uncorrelated (random).

344 A. Alam et al. (iii) In each segment, n, y(k) was fitted to a line function dist S,. S t2 t22 y y2 6 representing the trend in that segment. Polynomial fits ()ii+++1 =-() i i1 +-() i i1 () (order two or more) were not applied in the method as in previous publications (Nikolopoulos et al., 2015, 2018a; The total length of the curve of the distances of Eq. (6) Petraki, 2016; Petraki et al., 2013a). The y coordinate of was given by Eq. (7): the linear fit function in each segment was presented by yn(k). iN= (iv) The integrated signal y(k), was detrended by subtract- L dist S,. S 7 = Â ()ii+1 () ing the local trend yn(k), in each segment of length n. In i=1 d this way, the detrended signal yn (k) was then calculated according to Eq. (3): With the assumption that the curve of Eq. (7) did not cross itself, its planar extent (d) was given by Eq. (8): d yn (k) = y(k) – yn(k). (3) d = max(dist(Si, Si+1)), i = 2, 3,…, N. (8) (v) The root mean square fluctuations F(n) of the integrated and detrended signals were calculated for a given Equations (7) and (8) were used to calculate the Katz’s segment n according to Eq. (4): Fractal Dimension (D) as shown in Eq. (9)

N 1 2 log n D () 9 Fn()= yk()- yn () k . ()4 = () N Â{} Ê d ˆ k =1 logn + log () Ë L¯ (vi) The aforementioned steps were repeated for a wide –– range of segment sizes n to identify the relationship of where n = L/a, and a was the average distance of the F(n) versus n. Generally, F(n) increases with segment size points. n. 2.3.2.4.2. Higuchi’s method (vii) If long-lasting self-fluctuations were present, there To calculate the Fractal Dimension (D) of a finite time would be a power-law between the average root mean series y(1), y(2), y(3), …, y(N) recorded at regular inter- square fluctuations F(n) against the segment sizes n as in vals i = 1, 2, …, N by using the Higuchi’s method k Eq. (5): (Higuchi, 1988), a new sequence ym was constructed from the aforementioned series as shown below: F(n) µ na. (5) Nm yymymkymkk :, ,,210..., ymÊ È - ˘kˆ . Note that the DFA scaling exponent a quantifies the power m ()()+ ()+ Á + Í k ˙ ˜ () of the long-range correlations of the time series. If there Ë Î ˚ ¯ was a power-law connection such as Eq. (5), then there The length of the curve associated with each time series, would be a linear dependency between the logarithms of k the average root mean square fluctuations log(F(n)) ym was defined as (Higuchi, 1998) against the logarithms of the segment sizes n. This meant that the relation log(F(n)) versus log(n) was a linear func- Nm- Ê ˆ tion. By fitting this line through least squares, the scaling Ê k ˆ 1 Á ˜Á N -1 ˜ exponent was obtained as the slope of the line log(F(n)) Lkm ()=+ym() ik-+- ym() i1 k ()11 a k Á Â ()˜Á Nm- ˜ versus log(n). Á i=1 ˜Á È ˘k ˜ Ë ¯ Í k ˙ 2.3.2.4. Fractal dimension analysis Ë Î ˚ ¯ 2.3.2.4.1. Katz’s method To calculate the fractal dimension (D) using the Katz’s Where m and k were integers with m = 1, 2, …, k that method, this study started with the transpose array [S1, determined the time lag between samples, the symbol […] T S2, …, SN] of a time series Si, i = 1, 2, …, N where Si = represented the bigger integer part of a value (Gauss no- (ti, yi) and yi were the recorded values at time instances ti tation) and the term {(N–1)/[(N–m)/k]k} was a normali- (Katz, 1988; Raghavendra et al., 2010). Two sequential zation factor. If the curve was a fractal, the average value time series points Si and Si+1 were represented then by L(k) of the lengths of Eq. (11) followed a power law with the pairs of values (ti, yi) and (ti+1, yi+1). Their Euclidean a power equal to the negative fractal dimension (D), i.e.: distance was given by Eq. (6): –D L(k) µ k . (12)

Influence of earthquakes on the continuous groundwater radon data 345 Therefore, if L(k) was plotted versus k, k = 1, 2, ... , kmax 2.3. By using Sevcik’s method with D = Dh from Eq. (15) on a log-log graph, the Higuchi’s fractal dimension (D) for N = 256, which was equal to the length of the series in could be calculated as the slope of the linear regression each window that constituted the parameter L. of the plot. The interval time was taken as k, k = 1, ... , 3. Steps (i) and (ii) were repeated until the end of the kmax for kmax £ 4 (e.g., k = 1, 2, 3, 4, for kmax = 4) and as k signal with each sample glided one sample forward until (j–1)/4 = [2 ], j = 11, 12, 13,..., for k > 4 (hence, kmax > 4). the end of the signal. 2.3.2.4.3. Sevcik’s method 2.3.2.5. Further issues for chaos analysis A sampled time series of dimension N could be used 2.3.2.5.1. Chaos analysis class segmentation to approximate the Sevcik’s fractal dimension D (Sevcik, For further analysis, the following two categories were 2006). The Sevcik’s fractal dimension could be estimated established: from the Hausdorff dimension (Dh), of a curve according (a) Class I segments: These comprised the segments of to Eq. (13) (Raghavendra et al., 2010): the radon time-series that exhibited successful DFA be- 2 haviour (Spearman’s coefficient r ≥ 0.95) and simulta- neously are described by the fBm class, that is, they ex- log N È- ()()e ˘ hibit DFA scaling exponent between one and two, viz.1 < Dh = lim 13 0Í log ˙ () e Æ ÎÍ ()e ˚˙ a ⁄ D < 2 (for value conversion from power-law beta values please see e.g., equations (1)–(3) in Nikolopoulos et al. (2018b)). According to several publications, these where N(e) was the number of segments of length e, which segments were notable preseismic precursory value made up the curve. For a curve of length L, N(e) = L/2e (Cantzos et al., 2015, 2016, 2018; Nikolopoulos et al., and hence Dh became: 2012, 2013, 2014, 2015, 2016b, 2018a, 2018b; Petraki, 2013a, 2013b, 2015a) and especially the segments with È- log()L - log()2e ˘ distinct changes between anti-persistency (1.35 < a < 1.5 Dh = lim . 14 0Í log ˙ () 1.5 < D < 1.65) and persistency (1.5 < 2 1 D e Æ Î ()e ˚ ¤ £ a ¤ £ < 1.5) (for value conversions from power-law beta values also see e.g., equations (1)–(3) in Nikolopoulos et al. By mapping N points of curve L into a unit square of N ¥ N cells of a normalized metric space through a double (2018)). Notably, in other publications (see Eftaxias et linear transformation, Eq. (14) could be transformed into al., 2010), these Class I segments have been considered Eq. (15) (Raghavendra et al., 2010): as pre-earthquake footprints when the corresponding values are within 1.5 £ a < 2 ¤ 1 £ D < 1.5. (b) Class II segments: These consisted of the radon time- È logL log 2 ˘ series windows that did not follow the prominent fBm D ()- ()e h =+lim Í1 ˙. ()15 class, that is, DFA’s r2 < 0.95 and 1.5 < < 2 1 < D < NÆ• log 21()N - a ¤ ÎÍ ()˚˙ 1.5 or follow the fractional Gaussian noise (fGn) class (0 < a < 1). According to several publications, these seg- The Sevcik’s Fractal Dimension (D) was estimated using ments have been deemed of low or no precursory value Eq. (15) and was improved through N Æ •. (e.g., Cantzos et al., 2015, 2016, 2018; Nikolopoulos et 2.3.2.4.4. Calculation methodology of fractal dimensions al., 2012, 2013, 2014, 2015, 2016b, 2018a, 2018b; Petraki The following steps showed the calculation of Fractal et al., 2013a, 2013b, 2015a). Note that the Class II seg- Dimensions (D) by using the Katz’s, Higuchi’s and ments were the complement of the Class I ones. Moreo- Sevcik’s methods: ver, according to Eq. (17), both fBm and fGn classes ex- 1. The signal was divided in windows of 256 samples (ap- hibited fractal dimensions between one and two. proximately 10-day duration). Notably, the value of 256 2.3.2.5.2. Hurst exponent calculation was the power of two value closest to seven, that is, the The Hurst exponents are calculated from the scaling day length of the moving average window employed in exponents of DFA as (e.g., Nikolopoulos et al., 2018b) the RRC analysis 2. In each segment, the fractal dimension (D) was calcu- H = a – 1, if 1 < a £ 2 (16a) lated as follows: 2.1. By using Katz’s method with the parameter D from and Eq. (9) for n = 256 and a– = 1 sample per day, and thus the parameter L was constituted of the distance between the H = a, if 0 £ a < 1. (16b) points of the series. 2.2. By using Higuchi’s method with slope D of the best The Hurst exponents from fractal dimension values were fit line of the log-log plot of Eq. (12); that is, logL(k) calculated according to the Berry’s equation (Petraki, against log(k) for kmax = 16. 2016):

346 A. Alam et al. H = 2 – D. (17)

2.3.3. Results of Meta-Analysis The results from the application of all five methods of Subsection 2.3 (RRC, DFA, Katz’s, Higuchi’s and Sevcik’s fractal dimensions) were extracted in ASCII output for the purpose of meta-analysis in a two-stage procedure: (a) Each ASCII output results file was computationally searched for out-threshold values according to user-defined limits. RRC and DFA ASCII files were searched for over thresholds and fractal dimension ASCII files for under threshold values. The out-threshold values were written in new ASCII meta-analysis stage 1 files; (b) The meta-analysis ASCII files of (a) were further searched computationally to identify areas with common dates, under the constraint that each segment date was Fig. 1. Radon concentrations measured in the water of arbitrarily considered as the date of the first sample of Panzhihua well. this segment. Accounting that the analysis of each of the five methods was performed through a sliding window technique of one sample gliding, the aforementioned date groundwater of Panzhihua. The limit of R £ 1200 km for consideration, finally, yielded to a full cover of all dates Category-I earthquakes was selected following previous but the one of the last segments. The computational search studies (Cicerone et al., 2009; Ghosh et al., 2009; Petraki was iterated in all possible combination of five techniques, et al., 2015b) and referred to as epicentre distances. that is, per two, three, four and five techniques. (b) Category I earthquakes with magnitudes of Mw ≥ 6.0 were considered significant because their catastrophic Identical procedure has been followed with success in a potential was high. From category II earthquakes, only recent publication (Nikolopoulos et al., 2019). What is those with magnitudes of Mw ≥ 7.0 were included in the most important is not the procedure but its significant study. implications. According to extended argumentation and (c) Earthquakes with Dobrovolsky ratio (Dobrovolsky et discussion of recent publications (Nikolopoulos et al., al., 1979) above D/R > 0.5 were potentially effective to 2018a, b; Petraki, 2016), the important issue when ana- induce seismic disturbances to radon in groundwater of lysing preseismic time series to identify hidden pre-earth- Panzhihua; however, since this is not a strict criterion quake trends, is not just to locate some critical out-thresh- (Cicerone et al., 2009; Ghosh et al., 2009; Petraki et al., old values, but rather to locate common areas with dif- 2015b and papers therein), values above D/R > 1.0 were ferent techniques. When such common areas are found, potential precursors of pronounced predictability. Please the scientific evidence regarding the possibility of a pre- note that the parameter D = 100.43M was the effective pre- earthquake warning hidden in these areas is increased, cursor manifestation zone combining the strain radius with and hence a claim of pre-seismicity is increased. the earthquake magnitude (Dobrovolsky et al., 1979). 2.3.4. Earthquake data However, this ratio was only indicative, since the related Earthquake data of the period were retrieved by the theory did not consider modern aspects of fractal and SOC Seismological Network of China Earthquake Data Cen- propagation models of earthquake induced microcracks tre. The Network provides detailed earthquake catalogues and cracks (e.g., Eftaxias et al., 2008, 2010). with several data. On the other hand, CEA does not sup- ply information regarding the sensitivity of Panzhihua to 3. RESULTS AND DISCUSSION earthquakes. For this reason, criteria were set to restrict the earthquakes to the most significant ones in respect to Figure 1 presents the full set of radon measurements the Panzhihua radon monitoring station. In specific: in the water of Panzhihua well. The maximum concen- (a) Earthquakes with an epicentre distance of R £ 1200 tration was 258 Bq/L, and the minimum was the mini- km from Panzhihua were of Category I and were deemed mum detectable activity of SD-3A monitor. Figure 2 as exhibiting noteworthy recording potential. Remaining presents the RRC values calculated according to Eq. (1). earthquakes occurred in China and nearby border areas As aforementioned, a seven-day moving average was used were of Category II and were deemed as having notable for the calculation. As can be observed from Fig. 2, sev- possibility of inducing disturbances in radon of eral seven-day segments above the ±2s thresholds were

Influence of earthquakes on the continuous groundwater radon data 347 analysis methods revealed hidden Class-I fractal fBm trends which were associated with preseismic activity according to several aforementioned references (Cantzos et al., 2015, 2016, 2018; Eftaxias et al., 2008, 2010; Nikolopoulos et al., 2012, 2013, 2014, 2015, 2016b, 2018a, 2018b; Petraki, 2016; Petraki et al., 2013a, 2013b, 2015a). As part (b) was essential, it was analysed thor- oughly in the following paragraphs concerning the RRC method as described in the methods section. Figure 3 presents the results of the application of DFA at the radon time series recorded at the Panzhihua well. It is observed that the profile of the scaling exponent a in Fig. 3 differs from the one of the radon time-series. This is characteristically shown in the area between samples 4 4 1.75 ¥ 10 and 3.25 ¥ 10 of Fig. 3a. In this area, the measured profile of radon in the water of Panzhihua well Fig. 2. RRC processed by the seven-day moving average showed a peak, whereas the profile of the DFA scaling method. In colour: Red dotted lines are the ±2s threshold lim- exponent a did not show similar peaking. On the con- its and dark blue line is residual radon concentration s = 3.957 trary, it exhibited quite different variations from the ra- –1 Bq·L . don ones. This fact has been emphasized. Indeed, these areas corresponding to non-stationary patterns were hidden in the radon time-series that were revealed by DFA. identified. The value s employed in this figure corre- Several values of the exponent a corresponded to Class- sponded to the standard deviation of the full RRC data I segments (Subsection 2.3.2.5.1), namely successful fBm 2 set and equalled to 3.957 Bq/L. Setting the threshold equal segments (Spearman’s r < 0.95 and 1 < a < 2). As al- to 2s, the first stage of the meta-analysis of the ASCII ready explained, these segments demonstrated notable results of the RRC data of Fig. 2 revealed 724 seven-day preseismic precursory value (e.g., Cantzos et al., 2015, segments at scattered dates between 2012 and 2017. As 2016, 2018; Nikolopoulos et al., 2012, 2013, 2014, 2015, aforementioned and stated in several publications (e.g., 2016b, 2018a, 2018b; Petraki et al., 2013a, 2013b, 2015a) Cicerone et al., 2009; Ghosh et al., 2009; Petraki et al., and especially the ones with distinct changes between 2005a, b; Barkat et al., 2017, 2018; Fu et al., 2017; anti-persistency (1.35 < a < 1.5) and persistency (1.5 £ a Igarashi and Wakita, 1990; Jilani et al., 2017; Zmazek et < 2). Figure 2b shows several interchanging areas, im- al., 2000), the 724 EEC values that exceeded the limits plying a potential preseismic source of the concurrent of ±2s were considered as anomalies. These anomalies radon variations. Several persistent Class-I segments could be attributed to hydrological sources and preseismic could be found a ≥ 1.5. According to several publications sources. Regarding the former case, all stationarity tests (e.g., Eftaxias et al., 2008, 2010), these segments were (ADF, KPSS and BL, Subsection 2.2.3) showed that both essential because they implied the potential association hydrological and radon time series were stationary at the with earthquakes of the period. DFA is a robust method 95% confidence interval (CI). Indeed, for 30-lag order, (e.g., Sarlis et al., 2013; Skordas, 2014; Telesca and the p-values for both radon and rainfall time series were Lasaponara, 2006), and for this reason, it was considered 0.01 for the ADF test, 0.1 for the KPSS test and below as a reference method for the identification of implicit –6 2.2 ¥ 10 for the BL test. The stationarity of both hydro- patterns and hidden long-memory trends. The persistent logical and radon time series was a prerequisite for the Class-I segments (i.e., those with a ≥ 1.5) have been de- application of the cross-correlation test. This latter test clared as footprints of forthcoming earthquakes (Eftaxias revealed a harmonic pattern for 30 lags with a maximum et al., 2008, 2010). Similar findings, as those of the ra- at the 20th lag. These results indicated that rainfall vari- don time series of the Panzhihua well, have been derived ations might affect both positively and negatively the ra- from preseismic time series of radon in soil recorded in don time series variations with a positive or negative Ileia and Lesvos island (Nikolopoulos et al., 2012, 2013, maximum at 20 min after a change in rainfall. These re- 2016b, 2018b; Petraki et al., 2013a, 2013b, 2016). These sults indicated a non-systematic long-term bias between findings have also been accepted as evidence for the radon and rainfall series. Two related issues were: (a) the preseismic electromagnetic time series (Cantzos et al., seven-day moving average of Fig. 2 smoothed the time- 2015, 2016, 2018; Eftaxias et al., 2008, 2010; Petraki, series and hence also smoothed potential short-term non- 2016; Petraki et al., 2015a; Sarlis et al., 2013, Skordas, systematic bias between radon and rainfall; (b) the chaos- 2014; Uyeda et al., 2009). The similarities have been ad-

348 A. Alam et al. Fig. 3. Evolution of the DFA scaling exponent for the radon time series of Fig. 1. From bottom to top: (a) The radon time-series; (b) the Spearman’s r2 correlation coefficient of the goodness of the linear fit of log(F(n)) versus log(n) in every 256-sample window; (c) the scaling exponent a (DFA slope). Horizontal axis is in sample number or minute from the beginning of measurements.

Fig. 4 Evolution of fractal dimension for the radon time series of Fig.1. From bottom to top: (a) the radon signal and the fractal dimensions according to the algorithms of (b) Katz (KFD); (c) Higuchi (HFD) and (d) Sevcik (SFD).

dressed between preseismic radon and electromagnetic analysis results derived through a computational search time series regarding the underlying fractal, long-memory on the ASCII results of DFA (Subsection 2.3.3) were vi- and SOC trends (Nikolopoulos et al., 2018a, b; Petraki, tal. Accounting the aforementioned argumentation, a strict 2016; Petraki et al., 2013a, 2015a, 2015b). The meta- threshold of DFA a was set to 1.5, equal to the critical

Influence of earthquakes on the continuous groundwater radon data 349 Fig. 5. Locations of the earthquakes listed in Table 1 together with major geological faults. The location of Panzhihua radon station is also presented.

value corresponding to persistency. A total of 1915 DFA sions calculated from the Higuchi’s method were signifi- segments were persistent and exhibiting a ≥ 1.5 (maxi- cantly higher than those derived from the Katz’s method. mum value, amax = 1.992) at various intervals between The fractal dimensions of Fig. 4 could be associated to 2012 and 2017. These segments corresponded to critical the DFA exponents of Fig. 3 through Eqs. (16) and (17). long-lasting fractal epochs of the geo-system that gener- For special cases of precursory Class-I fBm segments, ated, possibly, the radon variations shown in Figs. 1 and the relation D = 3 – a was valid (conversion through Hurst 2. According to the argumentation presented so far, the exponent). Specifically, for the meta-analysis successful associated radon time series recorded at the Panzhihua (r2 > 0.95) segments, the calculated DFA exponents were well were most possibly preseismic i.e., they are linked within 1.5 £ a £ 1.992 (maximum DFA exponent amax = to earthquakes occurred in the surrounding of radon moni- 1.992). These values corresponded to a fractal dimension toring station. range within 1.008 £ D £ 1.5. Under this conversion, the Figure 4 presents the results of the fractal dimensions majority of D-values of the Sevcik’s and Katz’s algorithms calculated using the Katz’s, Higuchi’s and Sevcik’s meth- were within this range. Similar discrepancies have been ods. The fractal dimensions of Fig. 4 varied. Discrepan- reported between the Katz’s, Higuchi’s and Sevcik’s al- cies were observed between the D values calculated from gorithms in a recent paper discussing fractal trends of the three fractal dimension algorithms. These discrepan- radon in soil variations (Nikolopoulos et al., 2018a) and cies could be attributed to the different methodology in another recent paper (Nikolopoulos et al., 2019) of fractal D calculation between the three methods. Fractal dimen- trends in environmental air pollution series. It should be

350 A. Alam et al. Table 1. Strong earthquakes according to the criteria a and b of Subsection 2.3.4 that occurred in China during the period of measurements (2012–2017) and related data. Abbreviations: CN: code number, C: category, Lat.: Latitude, Long.: Longitude, Mag.: Magnitude, ED: epicentre distance

from Panzhihua, SR: strain radius, DR: Dobrovolsky ratio (C II earthquakes).

CN C Date Lat. Long. Mag ED (R) SR (D) DR Location (Mw) (km) (km) (%) E1 I 2012/11/11 22.8 96 7.0 711.6 1023.3 1.40 Burma E2 I 2013/04/20 30.3 103 7 439.07 1023.29 2.33 Lushan, Sichuan E3 I 2013/07/22 34.5 104.2 6.7 919.07 760.33 0.83 Minxian, Gansu E4 I 2013/08/12 30 98 6.1 533.57 419.76 0.79 Zuo Gong, Tibet E5 II 2014/02/12 36.1 82.5 7.3 2110.3 1377.21 0.65 Yutian, Xinjiang E6 I 2014/05/30 25 97.8 6.1 428.79 419.76 0.98 Yingjiang, Yunnan E7 I 2014/08/03 27.1 103.3 6.5 168.15 623.73 3.71 Ludian, Yunnan E8 I 2014/10/07 23.4 100.5 6.6 367.71 688.65 1.87 Jinggu, Yunnan E9 I 2014/11/22 30.3 101.7 6.3 421.45 511.68 1.21 Kangding, Sichuan E10 II 2015/04/25 28.2 84.7 8.1 1691.9 3040.9 1.80 Nepal E11 II 2015/04/25 28.3 84.8 7.0 1682.6 1023.3 0.60 Nepal E12 II 2015/05/12 27.8 86.1 7.5 1553 1678.8 1.10 Nepal E13 II 2015/11/14 31.0 128.7 7.2 2668.3 1247.4 0.50 East China sea E14 II 2016/01/21 37.7 101.6 6.4 1244.34 564.94 0.45 Menyuan, Qinghai E15 I 2016/10/17 32.8 94.9 6.2 961.79 463.45 0.48 Zaduo, Qinghai E16 I 2017/08/08 33.2 103.8 7 769.91 1023.29 1.33 Jiuzhaigou Sichuan E17 I 2017/11/18 29.8 95 6.9 755.06 926.83 1.23 Milin, Tibet

emphasized that according to recent publications (Petraki, ably linked to time-epochs of critical fractal and long- 2016; Nikolopoulos et al., 2018a, b), the in-situ relation- memory behaviour of the radon time series of the ship between DFA’s a, Hurst exponent H and fractal di- Panzhihua well. mension D is linear; however, different relations than the As explained in Subsection 2.3.3.b, in the second stage ones of Eqs. (16) and (17) may be valid. This view seems of the meta-analysis of the results of the five methods to be confirmed by the results of Figs. 3 and 4 and could employed in this paper (RRC, DFA, Katz’s, Higuchi’s and be another reason for the addressed discrepancies. Nev- Sevcik’s fractal dimension calculation algorithms), the ertheless, the latter is out of the scope of this paper and is ASCII outcomes of these were computationally searched not studied further. As with the discussion of the results for common areas for all possible combinations of the of Fig. 3 the time variations of all fractal dimensions of five techniques. As aforementioned, any combination of Fig. 4 were completely different from the concurrent ra- techniques provided stronger evidence regarding the don time series variations. This is a significant finding preseismic origin of the radon time series of Fig. 1. From that has been acknowledged by numerous investigators the discussion presented so far, the evidence supported (Cantzos et al., 2015, 2016, 2018; Eftaxias et al., 2008, the viewpoint that numerous parts of the radon time se- 2010; Nikolopoulos et al., 2012, 2013, 2014, 2015, 2016b, ries were pre-earthquake footprints. In this aspect, Table 2018a, 2018b; Petraki, 2016; Petraki et al., 2013a, 2013b, 1 presents all strong earthquakes according to the criteria 2015a). As discussed by the aforementioned publications, a and b of Subsection 2.3.4. Figure 5 shows the locations the employed fractal dimension methods revealed hidden of the earthquakes of Table 1. Table 1 and Fig. 5 demon- patterns in the time series, and for this reason, their time strate that 17 strong earthquakes occurred during the pe- evolution was different from that of the time series. Sev- riod of measurements: 12 earthquakes occurred in the eral windows were spotted with significantly low fractal Mainland China, one in the East China Sea and the re- dimensions. In accordance with the DFA scaling expo- maining ones in the border areas with other countries nent threshold a = 1.5, the fractal dimension threshold (three in Nepal and one in Burma). Eleven earthquakes was set to D = 1.5, which was the value calculated from listed in Table 1 were Category I (near earthquakes) and the relation D = 3 – a. According to the discussion so far, the other six were Category II (far earthquakes). E1, E2, the fractal dimensions D £ 1.5 corresponded to precur- E5, E7, E10, E11, E12, E13 and E16 were strong earth- sory Class-I fBm segments. A total of 51461 Class-I fBm quakes. E10 was an extremely strong earthquake of Mw = segments were identified by the Katz’s algorithm between 8.0. The strong earthquake E11 was almost concurrent 2012 and 2017; 2567 by the Higuchi’s algorithm between with E10 and from a near epicentre. This probably indi- 2014 and 2017; and 50419 by the Sevcik’s method be- cated a post activity of E10. In terms of near distance, tween 2012 and 2017. These segments were most prob- Category I earthquakes E1, E2, E7, E8, E9 and E16 had

Influence of earthquakes on the continuous groundwater radon data 351 Fig. 6. Overview of the full computational meta-analysis results per five, four and three methods. Abbreviations: ‘¥’: DFA versus all methods (5 techniques), ‘+’ RRC versus all fractal dimension techniques (4 techniques), ‘᭺’ RRC versus Higuchi’s and Katz’s methods (3 techniques), ‘diamond’ RRC versus Higuchi’s and Sevcik’s methods (3 techniques), ‘^’ DFA versus Higuchi’s and Katz’s methods (3 techniques), ‘⁄’ DFA versus Higuchi’s and Sevcik’s methods (3 techniques) and ‘square’ DFA versus Katz’s and Sevcik’s methods (3 techniques)

Dobrovolky ratio values above 1.0 (DR ≥ 1.0), but only history in pre-earthquake geosystems (e.g., Petraki et al., E2 and E7 had notable ratios (DR > 2.3); specifically, they 2015a, b) provided strong evidence on the preseismic exhibited strong potential to induce seismic disturbances nature of the related time series in these segments. to radon in the underground water of Panzhihua. In terms II. Three methods of fractal dimension calculation, justi- of far distance, Category II, only earthquakes E10 and fied, from another aspect, the persistency and the long- E11 had Dobrovolky ratios above 1.0 (DR ≥ 1.0). The lasting interactions within several segments. These seg- earthquakes hence of greater interest were the twin earth- ments were theoretically linked through Eqs. (16) and (17) quakes E10 and E11 and E2, E5, E12, E13, E16 and E17. to the DFA segments of I (i.e., through Hurst exponent). From the discussion presented so far, it is evident that The identification of radon in groundwater segments of numerous disturbances of radon in groundwater of the low fractal dimensions (high Hurst values) also provided Panzhihua well between 2012 and 2017 are most possi- strong evidence regarding the predictability of the time bly pre-earthquake due to the following evidence: series and its preseismic nature. As aforementioned, it has I. A total of 1915 disturbance DFA segments were per- been used with success in radon in soil pre-earthquake sistent with scaling exponent a ≥ 1.5. DFA was a refer- disturbances (e.g., Nikolopoulos et al., 2018a; Petraki et ence method to identify fractal and long-memory trends al., 2013b). In this sense, the persistent 51461 segments hidden in time series. The robustness of DFA and its long identified with Katz’s, 2567 with Higuchi’s and the 50419

352 A. Alam et al. with the Sevcik’s methods, were most probably the employed methods of this paper. It is significant here preseismic. to draw the attention of the reader to warnings without III. A total of 748 segments were recognized as poten- earthquake occurrence. These could be due to critical tially preseismic according to the findings of the RRC behaviour of far strong earthquakes not included in this technique. Although RRC was not a fractal or long- paper, post activity of some earthquakes of Fig. 6 (e.g., memory identification technique, it had a long history E15), early warnings of others (e.g., E6, E16 and E17) or (e.g., Cicerone et al., 2009; Ghosh et al., 2009) in reveal- were false warnings of the method. According to papers ing potentially preseismic radon disturbances. In this (e.g., Cicerone at al., 2009; Ghosh et al., 2009; Petraki et sense, these 748 segments could also be preseismic. al., 2005a, b), the early warnings are within the predic- In the consensus of the aforementioned evidence, the re- tion window of radon in relation to earthquakes. Account- sults and discussion of the paper up to now and the logic ing the evidence presented in several paper regarding the of Subsection 2.3.3, Fig. 6 presents all data from the com- asperity modelling of the pre-earthquake radon anoma- bination of techniques together with the earthquakes of lies, the probability of false critical behaviour prior to the period. Figure 6 is generated through GNU Octave earthquakes is small, nevertheless, not negligible. It on the basis of the stage 2 meta-analysis results of all should also be mentioned that any combination of fractal methods. All the meta-analysis (Subsection 2.3.3) was and long-memory techniques in Fig. 6 is advantageous conducted using a fully computational method; thus, Fig. when compared to the combination of the accepted RRC 6 is an effort of a visual presentation of the most signifi- technique with two other chaos analysis methods. cant outcomes out of 13 ASCII combination files. It This study presented evidence regarding potential as- presents the results from a combination of three, four or sociations between radon in the ground water of five methods. The combination of RRC with the Sevcik’s Panzhihua with strong earthquakes that occurred between and Katz’s methods is not presented in Fig. 6 for brevity 2012–2017 in China and its surrounding border regions. since it covers all the periods between the presented earth- A novel approach was reported which combined fine- quakes of Table 1. This means Katz’s that all earthquakes tuned chaos analysis techniques with the RRC technique of the period were identified as preseismic with the com- to reveal preseismic trends hidden in radon gas concen- bination of the three techniques, namely RRC, Sevcik’s tration variations in the groundwater of Panzhihua. The and Katz’s methods. Under these aspects, earthquakes E9, approach showed that numerous fractal fBm pre-earth- E10, E11, E14 and E17 probably provided preseismic quake segments with long-lasting interactions were possi- disturbances in radon in the groundwater of Panzhihua bly associated with the seismic activity of the period. This well. This means that the radon variations during these was significant for earthquake precursory studies because earthquakes presented characteristic critical epochs of of the direct relationship between the rock-and water in- fractal and SOC behaviour. As analysed in Section 1 and teraction before and after seismic activity. Indeed, com- the whole text, these epochs corresponded to the fractal pression and dilation stress can deform the porous me- propagation of micro-cracks and cracks during the prepa- dium of an aquifer and causes variation in the porosity ration of these earthquakes. According to several papers and pore pressure, affecting the whole hydrodynamic state (Eftaxias et al., 2008, 2010; Nikolopoulos et al., 2012, and thus changing radon concentration (Arora et al., 2017; 2013, 2014, 2015, 2016b, 2018a; Petraki et al., 2013a, Barkat et al., 2018; Che et al., 1997; Fu et al., 2009; 2013b, 2015a, 2015b), each micro-crack is a different Kumar et al., 2009; Ramola et al., 2008; Walia et al., 2013; scale imitation of bigger cracks that are produced by the Woith, 2015; Zafrir et al., 2016). For example, a decreas- propagation of the micro-cracks in a fractal manner ing trend in radon concentration monitored just before through the self-organization of the micro-cracks during Gansu earthquake on 2013/07/22, the concentration in- the preparation of earthquakes. While the micro-cracks creased 24 days before the earthquake and then suddenly and cracks were self-organizing and branching within the started decreasing to the day of the earthquake. Similar crust of Panzhihua, effective pathways were produced, results were reported by Wang et al. (2018). Nikolopoulos which induced critical variations in radon in groundwater. et al. (2012, 2013, 2014, 2015, 2016a, 2016b, 2018a) and During this procedure, critical fBm-profile variations were Petraki et al. (2013a, 2013b, 2016) also reported anoma- found. The results indicated this process since all critical lous radon concentrations one to two months prior to the segments of Fig. 6 had persistent DFA exponent a ≥ 1.5 occurrence of significant earthquakes in Greece. Kumar and exhibited associated fractal dimensions D £ 1.5, a et al. (2012) reported that the amplitude of radon anomaly fact which was related to fBm modelling (e.g., Eftaxias and the epicentre distance increase with the increase in et al., 2008, 2010). During these phases of earthquake the magnitude of the earthquake, whereas several rela- generation, the radon geo-system of Panzhihua produced tions were reported in the reviews of Cicerone et al. (2009) critical warning of forthcoming earthquakes. Such warn- and Ghosh et al. (2009). In addition, diverging values of ings were hidden in the radon variations and revealed with precursory time of earthquakes occurrence were reported

Influence of earthquakes on the continuous groundwater radon data 353 starting from few days to several months (Ghosh et al., the fracture of the heterogeneous system in the focal area 2009; Petraki et al., 2015a; Zmazek et al., 2000). In the obstructed the backbone of asperities, but when the per- present study, the precursory time variability shown in sistent radon anomalies of Fig. 6 occurred, the ‘siege’ Fig. 6 was in agreement with these studies. It should be began, and the fracture of the asperities started, which noted also that the anomalous variations of radon con- signalized the unavoidable evolution of the process to- centration prior to earthquakes appeared also in wells and wards the global failure. springs located far from the epicentre (Li, 1986; Roeloffs, The results reported in this paper were encouraging, 1988). These anomalous preseismic radon variations were despite from only one radon station. For a better under- associated with the a) magnitudes of forthcoming earth- standing of subsurface processes, more multiparametric quakes; b) type of nearby and far geological structures; studies were needed with continuous in-situ monitoring c) existence of regional and local faults and d) elastic of environmental parameters such as the water tempera- properties of strata. The aforementioned cases could be ture and level. The lack of such measurements constituted characteristically observed in Fig. 6. Moreover, the stress a limitation of the present study. The use of TRMM data on fault rupture area allowed more space to open, which, was another limitation. However, the novel approach of in turn, permitted the free movement of gaseous parti- combining computationally different chaos analysis meth- cles. After the blustering of rock matrices, the ods with the RRC data provided strong evidence regard- radionuclides presented in rock mix with water and car- ing the preseismic nature of the investigated radon varia- rier gasses, which changed the concentration of radon gas tion data. As emphasized in several sections, chaos meth- in a fractal fBm manner. ods outlined the hidden trends in the radon data of Post seismic effects have been reported by other in- groundwater in Panzhihua and delineated the fractal and vestigators. For example, Ren et al. (2012) reported post- SOC stages of the earthquake induced radon disturbances. seismic effects in radon concentration after the 2008 Even under this view, earthquake prediction and associa- Wenchuan earthquake (Ms = 8.0). As mentioned, some of tion with recorded radon anomalies were far to be solved, the meta-analysis results of Fig. 6 might be such post- and hence more scientific approaches were required for seismic effects, however, they were difficult to identify. fruitful achievements in this field of research. This study proposed the reason was because no one to one correspondence was found between a single radon 4. CONCLUSION anomaly or a batch of nearby anomalies and a forthcoming earthquake. This has been acknowledged in previous 1. This paper reported the six-year time series of ra- publications as well (Eftaxias et al., 2008, 2010; don concentration in the groundwater in Panzhihua, Nikolopoulos et al., 2013, 2014, 2015, 2016b, 2018a, China, prior to a series of strong earthquakes in China 2018b; Petraki, 2016; Petraki et al., 2013b, 2015a). As and border regions of near countries. Several significant mentioned by Cierone et al. (2009), it is a serendipitous radon anomalies were observed between 2012 and 2017. fact to record a very strong earthquake near a monitoring 2. The results of DFA showed several segments with station. Such a case has been reported for the Ileia signal, slopes above 1.5. The Higuchi’s, Katz’s and Sevcik’s Greece (Nikolopoulos et al., 2012; Petraki, 2013a). The methods exhibited numerous segments of low-fractal di- irregularities of radon concentrations prior to earthquakes mensions below 1.5. Both thresholds referred to Class-I can also be due meteorological parameters. The multi- segments of fBm persistency and high predictability. The directional approach adopted in this paper supported the RRC technique identified several seven-day segments out aspect of a preseismic nature of the anomalies of Fig. 6. of the ±2s range, which were considered of notable ra- Moreover, the hydrological parameters were found to be don variation. of less significance. Towards this direction, Friedmann 3. The data were analysed through DFA, three differ- (2011) concluded that environmental parameters have a ent methods of fractal dimension analysis (Higuchi’s, small influence on groundwater and springs water, espe- Katz’s and Sevcik’s methods) and the RRC technique. All cially in deep origins. On the other hand, the chaos analy- methods were applied through a novel two-stage compu- sis and the meta-analysis results indicate several fBm tational approach, where the persistent fBm pre-seismic fractal trends with long-lasting interactions. All these were footprints hidden in time series segments were identified related to the last phases of the earthquake preparation and separated from remaining segments of low-predict- period. The fractal fBm behaviour of radon in the ability and earthquake-related significance. groundwater of Panzhihua was associated with the asper- 4. Several combined segments were found with dy- ity model. During the preparation of the identified earth- namical complex fractal behaviour and long-memory cor- quakes in Fig. 6, the focal area consisted of a backbone responding to fBm modelling pre-earthquake footprints. of strong and large asperities that sustained the system, Four earthquakes were identified with all combinations which were modelled as fBm profiles. At a first stage, of methods, whereas the remaining earthquakes were de-

354 A. Alam et al. termined by the combination of at least three methods. Cantzos, D., Nikolopoulos, D., Petraki, E., Nomicos, C., 5. Trends of long-memory were identified and dis- Yannakopoulos, P. H. and Kottou, S. (2015) Identifying cussed. The findings were compatible with fractal, long- long-memory trends in pre-seismic MHz Disturbances memory and SOC phases of generation of earthquakes. through Support Vector Machines. J. Earth. Sci. Clim. Change 6(263), 1-9. Cantzos, D., Nikolopoulos, D., Petraki, E., Yannakopoulos, P. AUTHOR CONTRIBUTION H. and Nomicos, C. D. (2016) Fractal Analysis, Informa- tion-Theoretic Similarities and SVM Classification for A. Alam: RRC method conceptualization, RRC and Multichannel, Multi-Frequency Pre-Seismic Electromag- earthquake data curation, formal analysis, investigation, origi- netic Measurements. J. Earth. Sci. Clim. Change 7(367), 2. nal draft writing and preparation, revision and review, editing Cantzos, D., Nikolopoulos, D., Petraki, E., Yannakopoulos, P. and preparation. and Nomicos, C. (2018) Earthquake precursory signatures N. Wang: data recording and caution, laboratory analy- in electromagnetic radiation measurements in terms of day- sis, investigation, original draft writing and preparation, revi- to-day fractal spectral exponent variation: analysis of the sion and review. eastern Aegean 13/04/2017-20/07/2017 seismic activity. J. G. Zhao: data processing, revision writing, review and Seismol. 22(6), 1499-1513. editing. Che, Y. T., Yu, J. Z. and Liu, C. L. (1997) The hydrodynamic T. Mehmood: formal analysis, investigation, original mechanism of water radon anomaly. Seismol. Geol. 19(4), draft writing 353–357 (in Chinese). D. Nikolopoulos: chaos analysis methods Cicerone, R., Ebel, J. and Britton, J. (2009) A systematic com- conceptualization, chaos-analysis and earthquake data curation, pilation of earthquake precursors. Tectonophysics 476, 371- formal analysis, software production, investigation, revision 396. writing, review, editing and preparation. Dobrovolsky, I. P., Zubkov, S. I. and Miachkin, V. I. (1979) Estimation of the size of earthquake preparation zones. Pure Acknowledgments—This research is supported by the National Appl. Geophys. 117, 1025-1044. Natural Science Foundation of China (41674111). Eftaxias, K., Contoyiannis, Y., Balasis, G., Karamanos, K., The authors would like to thank China Earthquake Data Centre Kopanas, J., Antonopoulos, G., Koulouras, G. and Nomicos, (http://data.earthquake.cn) for providing the radon data. C. (2008) Evidence of fractional-Brownian-motion-type Aftab Alam is grateful to Dr. Xiaoyu Chen and Dr. Qui Liang asperity model for earthquake generation in candidate pre- (China University of Geosciences, Beijing) for sharing knowl- seismic electromagnetic emissions. Nat. Hazard Earth Syst. edge on geological settings of the area. 8, 657-669. Eftaxias, K., Balasis, G., Contoyiannis, Y., Papadimitriou, C., Kalimeri, M. et al. (2010) Unfolding the procedure of char- REFERENCES acterizing recorded ultra-low frequency, kHZ and MHz elec- Anderson, O. L. and Grew, P. C. (1977) Stress corrosion theory tromagnetic an anomalies prior to the L’Aqua earthquake of crack propagation with applications to geophysics. Rev. as pre-seismic ones—Part 2. NHESS 10, 275–294. Geophys. 15(1), 77-104. Friedmann, H. (2011) Radon in earthquake prediction research. Arora, B. R., Kumar, A., Walia, V., Yang, T. F., Fu, C. C., Liu, Radiation Protection Dosimetry 149(2), 177–184. T. K. and Chen, C. H. 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