Rn gas concentration is monitored continuously for about three years from 2007 to 2010 as a capable precursor of seismic activity at NAFZ. All data are used in this study equal to (103,235) radon data for every 15 min interval. Prior to the ARIMA and MCS methods application, the data is divided into train and test parts as 80 % and 20 %, respectively. The test prediction part occupies 20 % in the tail of data, which is used to evaluate accuracy of the model in the prediction.
To determine the best model for data time series, Box-Jenkins recommended assurance of stationarity in time series. For this reason, more than one test it taken into consideration to assure the time series stationarity (Kwiatkowski et al. 1992), such as the KPSS test, augmented Dickey-Fuller (ADF) test, skewness test, (one-sample and paired-sample) t-test, and Leybourne-McCabe test (Cheung and Lai 1995; Hobijn et al. 2004; Leybourne and McCabe 1994). After checking the results of (KPSS test, Leybourne-McCabe, skewness-test, and t-test) it is observed that all support that the data is non-stationary despite ADF test. Hence, it is necessary to take the differentiation until the series becomes stationary. The same is valid for above-mentioned tests for radon data differentiation in a second time. After proving the time series data as stationary, the next step is the ARIMA model usage to find the best model fit to the Rn time-series. Model identification needs to determine values of p, and q from lags crossing the confidence significant lags bounds of the PACF (Partial Autocorrelation Function) and ACF (Autocorrelation Function) plot respectively. The ARIMA (8,1,13) model is the most suitable one for the prediction of the future value of 222Rn concentrations and the model has a satisfactory estimate, because simulation values are in good agreement with the real radon values, and the smallest standard deviation belongs to ARIMA (8,1,13) model, which is defined in Equation 3.1 in the below.
![](data:image/png;base64,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)
where coefficients of autoregressive is ϕ, and coefficients of moving average is θ, and c is a constant. Different ways are examined to test the validity of the recommended ARIMA model. For this reason, the ARIMA mode fit, residual plot, histogram plot, and Q-Q plot are obtained. To evaluate the power of the model in Figure 4 (a), and (b), it shows that the model has good fitting with radon data and the residual distribution plot fluctuates around the mean with some anomalies as in Figure 4 (c), and (d) one can see the histogram (number of repetitions of similar values for residual values regularity changes. The Q-Q graph produces a scatter plot between standard normal quantities with quantities of the input sample. In the sample, the data mostly fit the model with a little diffraction in both tails, which conforms that data fit with same anomalies. In Figure 5, the model data prediction average is shown.
After finding the best model fit to the time series, the ARIMA and the MCS methods can be employed for simulations to get probability distribution of future radon concentration values and identification of all possible future probability values. MCS is also used for time-series data prediction testing part, which consists of 20 % of data in the tail of the time-series data as in Figure 6. It can be seen that the MCS prediction result has a good fit with real radon data in (Panel A) and four different possible outputs for MCS prediction are shown in (Panel B). The four different possible outputs mean is plotted by the red line with real radon data in the graph, and it has a good fit with it.
1.1. Analysis of the Relation between Radon Gas and TEC with Earthquakes
The prediction part of radon data equal, which includes 20 % of all data and MCS results to soil radon data are used in this study based on the earthquake concentration. It is divided into four different groups, where each group includes 15 days for discussion about the relation and influence between soil radon gas and Total Electron Content (TEC) with seismic activity by considering the geomagnetic field activity effect.
1.1.1. First Group
The first group starts from 12 to 27 July 2009 with six micro-earthquake magnitude occurrences as 2.6 - 3.1. The TEC and radon concentration for the same period are shown in Figure 7.
In the first group, a positive anomaly can be seen in the soil radon concentration and increase over prediction MCS redline value by 40 Bq/m3, which is related to the first two earthquakes magnitudes, 2.7 and 3 in two days and 18 hours before the event, respectively. The TEC variations for both events are not suitable to count as an anomaly in the range between the upper and lower boundaries (mean ± two standard deviation) in all stations. Three earthquakes with 3.1, 2.8, and 2.6 magnitudes occurred on 20 July 2009 during 18 hours before earthquakes increasing (50 Bq/m3) of 222Rn and over the MCS prediction there is an anomaly is related to earthquakes and a short negative anomaly in the TEC can be seen in all stations especially in the nearest one to Ankara TEC station, where one day before is related to events, because of geomagnetic activities are quite well in this period. Last earthquake in this group with ML=2.7 during three days before the earthquake, there is an anomaly in the radon sharp increase over the MCS prediction due to the earthquake. In contrast, Total Electron Content uprising on 22 July is not reliable as earthquake anomaly due to variations in the (Kp and Dst) magnitudes as shown in Figure 8.
From Figure 8, on 22 July 2009, the disturbance in the geomagnetic can be seen as a result of disturbance in the earth’s magnetic field, which is caused by the solar wind (Kp) equal to 58, which is more than 40 and it counted as a quiet condition Disturbance time storms (Dst) is equal normally to -80 nT and it should be in the range from 20 to -20 nT with the source for TEC anomaly in all stations. In the same graph, one can see the density of a solar microwave flux having as 10.7 cm wavelength value, which is below 70 sfu, and hence, the condition is considered as quiet.
1.1.2. Second Group
The second group evaluates four earthquakes with other parameters starting from 16 August 2009 to 1 October 2009. The results for TEC variations for three nearest international stations are shown in Figure 9 with radon gas concentration and seismic activities.
In the Figure 9 graph shows that there is no clear and significant pre-seismic or co-seismic anomaly in the 222Rn gas concentration. This may be due to the large distance epicenter with radon station and low magnitude, but after the earthquake (ML=2.7) there is a post-seismic increase in soil 222Rn gas concentration. The small uprising can be seen in the TEC peaks on 19, 20, and 22 of August middays due to earthquake ML =3.1 in 26 August., The increase is clearly that more in the (Ankara city) station compared to other stations. The reason for this small variation in the TEC is the earthquake with low magnitude, pressure production in the ground, which causes to stress generation on rocks and heavily charged ion clusters, distribution in the electric field between ground and atmosphere could be lead to this TEC variation in the ionosphere a few days before the earthquake. Another anomaly in the TEC on 30 August can be seen, but this variation is related to geomagnetic variations as shown in Figure 10.
In the Figure 10, all three parameters at (19, 20, and 22 of August) have normal values. It approves that the TEC variation source in earthquake ML =3.1 on 26 August causes to geomagnetic activities on 30 to 31 August with an increase in the (Kp index) over normal value (40) increasing towards it to (58). The variation in disturbance storm time (Dst) is under -20 nT), with these anomalies in the geomagnetic activity, they are the main factors for ionospheric TEC anomalies on 30 August over the upper bound, which is equal to mean plus two standard deviations (μ+2σ) as can be seen in all three stations in the midday.
1.1.3. Third Group
The third group includes observation radon and TEC data with earthquakes from 30 August to 16 October 2009, which leads to discussion on the relation between parameters as shown in Figure 11.
This group consists of five micro-earthquakes magnitudes between 2.7 to 3.9. According to observations, there is a positive Rn anomaly on 4, 8, and 10 October with approximate increase (40 Bq m-3) over the prediction magnitude estimation by MCS. This variation is counted as a pre-seismic anomaly with 3.9 and 2.8 magnitude earthquakes that occurred on 10 October. For the second series of microseismic events that occurred on 12 October, there is a co-seismic increase in the Rn gas emanated in the soil due to produced pressure on soil pores and the number of micro-cracks increases is helpful to allow radon gas migration. TEC response for seismic events and soil Rn variations under quiet geomagnetic at the period of increasing Rn gas on 4 October, the TEC increased one day after variation Rn gas. There is another anomaly in the TEC Ankara, Tubi, and Istanbul stations on 11 October exactly one day before the second series of seismic events. The effect of this positive anomaly in the TEC in all stations is a seismic activity because the geomagnetic activity for the same time is approximately quiet, and the variations of geomagnetic activity parameters (Kp, Dst, and F10.7 flux) are shown in Figure 12.
The geomagnetic activity or ground base due to seismic activity are considered during observations for clarifying the TEC anomalies sources. Variation in the TEC on 4 October can see a small negative anomaly under the lower bound as equal to mean minus two standard deviations (μ - 2σ) in all stations. It is due to increasing soil radon gas at the same time because all three (Kp, Dst, F10.7) parameters and are approximately quiet. For the second TEC anomaly on 11 October the seismic events are the main source for these positive anomalies over the upper bound in all stations, because during observations, Kp index, F10.7 flux is in the quiet range with a small increase in the Dst.
1.1.4. Fourth Group
The fourth group includes the observation data from 22 Jan to 7 Feb 2010 and the most powerful seismic events during this study belongs to this group and the effects on the soil radon gas concentration and TEC are presented in Figure 13.
The Alpha meter 611 detector detects an increase 70 Bq m-3 in a short time in the Rn gas concentration 18 hours before the earthquake magnitude ML = 3.4 on 24 January and sharply decreases after the earthquake to the previous level of concentration. Two days later radon increases 15 hours before the ML=3.3 magnitude earthquake on 27 January. Both earthquakes create an effect on soil Rn emanation, and TEC positively responds with record anomaly above the upper bound (μ + 2σ), at the same time for Rn variations, but cannot be counted as earthquake precursory due to high solar F10.7 flux.
The most powerful earthquake among all earthquakes is observed in this study magnitude equal to 4.7, which has some aftershocks with magnitudes 3.1, 2.9, 2.8, and 2.7, respectively. The average 222Rn gas increases due to these seismic events at approximately 50 Bq m-3 in three days, which is not satisfactory for the measure as an anomaly, but, the epicenter distance to Yolkonak radon station is the main reason for this kind response of radon concentration to seismic events.
The abnormal variation in the 222Rn concentration on 1 February nearly for about five days could be due to earthquake blasts for false recording, high rainfall and snow for the same period, and water was accumulated on the detector as a consequence of flooding at the measurement site; surface sensor severely affected by humidity for short-circuits, by continuation of irregular and unpredictable records up 34000 Bq/m3 just for 15 min. This kind of records for Alpha Meter detector could only be a possibility in the case of short-circuit occurrence inside the Alpha meter detector. This effect is confirmed in the literature by this article (Thomas et al. 1992).
The variation of TEC in the all-stations path through the upper and lower boundaries on 3 to 4 February is a response for negative variation in the disturbance time storm (Dst) as in Figure 14.
Results in the Figure 14. show that the abnormal increase in the solar flux F10.7 to the range 77 sfu on 27 January is the primary source for variation in the TEC in all stations, nonetheless other two parameters, namely, Dst and Kp index record the normal quite magnitude at the same time.
It can be said that the main source for both positive and negative anomalies in TEC in all stations is due to the disturbance time storms Dst variation, which is equal to -24 nT, and other parameters have the quite normal magnitude in the period.
1.2. Relation between Lithosphere and Ionosphere
The relation between soil radon concentration, TEC and seismic activity for all stations are shown in Figure 15. This study discusses all three parameters together for the first time in the literature.
The peaks are time lag between the 222Rn gas, and the TEC with seismic events. It is important that the anomaly peaks are bigger and wider in stations far from the epicenter, which means that after emanation radon gas by earthquake produced pressure, and it takes some time to affect the ionosphere and TEC. The reason is that the wider peaks are functioned for exchange in the energy and effect between the lithosphere and ionosphere through the seismic events in the preparation period before the main-shock time (Ryu et al. 2014; Shah et al. 2019).