# Identification of Groundwater Radon Precursory Anomalies by Critical Slowing down Theory: A Case Study in Yunnan Region, Southwest China

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

^{238}U in rock and soil in the subsurface environment, and therefore remains in the soil or dissolves in groundwater. There are many published studies on the relationship between radon and earthquakes, suggesting that radon has the potential to be a good indicator of the precursory process [6].

## 2. Geological and Hydrogeological Settings

## 3. Data Preprocessing

^{−4}J/m

^{3}[35], so we selected earthquakes with seismic energy density greater than 10

^{−4}J/m

^{3}as earthquakes whose precursor may occur at the stations. When the energy density is 10

^{−4}J/m

^{3}and the magnitude is 5, the maximum epicenter distance is 256.8 km; when the magnitude is 7, it is greater than 2300 km.

## 4. Method

#### 4.1. Wavelet Transform (WT)

#### 4.2. CSD Theory

## 5. Parameter Selection

- (1)
- The change in parameters has less influence on the variance but greater influence on AR-1. The results of AR-1 are complex and changeable, which may be because the calculation of AR-1 requires high sampling frequency data.
- (2)
- The influence of parameter changes on results derived from the high-frequency information is less than that from low frequency information. In the results of high-frequency information, the AR-1′s and variance’s anomalies under different WL and different levels of WD all appear at the same time point. This shows that the changes in parameter values have little effect on the high frequency information calculation results. However, the low frequency information calculation results vary greatly under different parameter values. With the increase in WL, the abnormal points of low frequency are delayed gradually; with the increase in level of WD, the resulting curve of low frequency gradually changes from fluctuation to stability until it approaches a straight line.

## 6. Results

#### 6.1. The Results of High-frequency Information (Residuals)

^{−4}J/m

^{3}as the recognition rate. The results show that the recognition rate of AR-1 in MD station is the highest, which is 81.82%; the variance recognition rate of LD station is the highest, which is 80%. The average recognition rate of AR-1 in 8 stations is 72.78%, which is greater than the 55.34% of the variance (Table 5).

#### 6.2. The Results of Low-frequency Information (Trend)

## 7. Discussion

#### 7.1. Interfering Factors

#### 7.2. Possible Explanations for Different Anomaly Characteristics

#### 7.3. Temporal and Spatial Characteristics of Radon Anomalies

#### 7.3.1. Relationship between Epicenter Distance and Anomaly Occurrence Time at Each Station

^{2}of the results are less than 0.1, reflecting that there is no certain linear correlation between the precursory time and epicentral distance. Considering that there may be too little data at a single station that may result in a great uncertainty of results, we drew a scatter diagram with all the stations’ data (Figure 8). Whether it is high-frequency or low-frequency data, or AR-1 or variance, the data points in the figures are randomly and irregularly distributed. R

^{2}of the correlation showed in the figures is far less than 0.1, indicating that there is almost no linear relationship between precursory time and epicentral distance.

^{2}of correlation between the epicentral distance and precursory time of variance (L), AR-1 (L) and variance (H) ranges from 0.051 to 0.245 (Figure 9), indicating that there may be a very weak or no positive correlation. However, the R

^{2}of the epicentral distance and precursory time of AR-1 (H) is close to 0.5, showing an obvious positive correlation. This may indicate that within 300 km, the larger the epicenter distance is, the earlier the occurrence time of water radon precursor anomalies. This conclusion is consistent with that of some previous studies.

#### 7.3.2. Relationship between Epicentral Distance and Anomaly Time of Three Large Earthquakes

^{2}values are less than 0.3, indicating that there is very weak or no significant correlation between them (Figure 10).

## 8. Conclusions

- (1)
- When we selected earthquakes with seismic energy density greater than 10
^{−4}J/m^{3}as the potential earthquakes with precursors, through the analysis and calculation of the data on 1000 days in the seismic active period in eight groundwater radon monitoring stations in the study area, the results were as follows: among the high-frequency information data results of the eight stations, the recognition rate of AR-1 of MD station is the highest, which is 81.82%; the variance recognition rate of LD station is the highest, which is 80%; the average seismic recognition rate of AR-1 in the eight stations is 72.78%, and the average recognition rate of variance is 55.34%. In the calculation results of low-frequency information, the AR-1 recognition rate of LC station is the highest, which is 100%; ML station has the highest variance recognition rate of 60%. The average recognition rate of AR-1 in the eight stations is 88.24%, and the average recognition rate of variance is 45.08%. In contrast, the variance recognition rate of high-frequency information is higher, and the AR-1 recognition rate of low-frequency information is higher. - (2)
- The earthquake precursor anomalies of radon in groundwater can be divided into three categories according to their characteristics: sudden jump anomalies, persistent anomalies and fluctuation anomalies. The high-frequency information is dominated by sudden jump and fluctuation anomalies, and the low-frequency information is dominated by persistent and sudden jump anomalies. The autocorrelation is mainly sudden jump and fluctuation anomalies, and the variance is mainly persistent anomalies.
- (3)
- There was no correlation or weak correlation between radon concentration and meteorological factors in these stations in the selected period. This means that crustal movement is the main reason for the change in radon concentration in groundwater in the study area during the active period of earthquakes. In the process of earthquake preparation, the accumulation of stress and strain may cause changes in crustal permeability, which may provide an explanation for persistent anomalies. The development of the crustal deformation process outside the nucleation area leads to frequent rock micro fracturing for a period of time, which may provide an explanation for sudden jump anomalies and fluctuation anomalies. In addition, the difference in hydrogeological characteristics of each well (aquifer), and the differences in regional stress and strain changes of rock mass, may result in different responses of aquifers to block movements and anomalies in water radon concentration.
- (4)
- There was no correlation between precursory time and epicentral distance when taking all earthquakes studied into account. However, there was a good relationship between precursor time and epicentral distance if only earthquakes with an epicentral distance less than 300 km are considered. This may be related to different seismogenic modes, hydrological conditions and crustal movements in different regions.

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Geological settings, station distribution, and selected earthquakes in the study area. Tc: Tengchong block; Ba: Baoshan block; Ls: Lanping Simao back arc basin; Yl: Yanyuan-Lijiang depression; Dz: Central Yunnan depression; Kd: Kangdian paleouplift; Dd: Eastern Yunnan block.

**Figure 2.**Level decomposition of the WD process. H is the high-frequency filter and L is the low-frequency filter. D

_{j}are the detail coefficients and A

_{j}are the approximation coefficients.

**Figure 3.**The compared figures of the high−frequency information data. The blue line is AR-1 and the red line is the trend of AR-1. The green line is variance. The gray line indicates the time of the earthquake. (

**a**) is the figure with unprocessed data. (

**b**) is the figure with processed data.

**Figure 4.**The compared figure of the low−frequency information data. The blue line is AR-1 and the red line is trend of AR-1. The green line is variance. The gray line indicates the time of the earthquake. (

**a**) is the figure with unprocessed data. (

**b**) is the figure with processed data.

**Figure 5.**The AR-1 and variance of 8 stations with high frequency information data. The vertical dotted lines are the date of earthquake with high e (>10

^{−4}J/m

^{−3}) at each station. The results’ values are the power functions of AR-1 and variance. The black arrow is the first peak date between two earthquakes within 83 days before the next earthquake. Red circles indicate sudden jump anomalies; the yellow circle indicates a fluctuation anomaly; the blue circle indicates a persistent anomaly. Note: the results for the station: (

**a**) MD; (

**b**) NJ; (

**c**) CN; (

**d**) TC; (

**e**) LC; (

**f**) LD; (

**g**) SM; (

**h**) ML.

**Figure 6.**The AR-1 and variance of 8 stations calculated with low-frequency information data. The vertical dotted lines are the dates of earthquakes with high e (>10

^{−4}J/m

^{−3}) at each station. The results’ values are the power functions of AR-1 and variance. Note: the results for the station: (

**a**) MD; (

**b**) NJ; (

**c**) CN; (

**d**) TC; (

**e**) LC; (

**f**) LD; (

**g**) SM; (

**h**) ML.

**Figure 7.**WTC analysis between radon and air temperature, radon and air pressure, and radon and precipitation. The thick black outline represents the 95% confidence level, and the bright color area represents the area within the cone of influence (COI).

**Figure 8.**Relationship between epicentral distance and abnormal days before earthquake (including all earthquakes studied). Blue points represent the high-frequency information and green points the low-frequency information. The red line indicates positive correlation; the black line indicates negative correlation.

**Figure 9.**Relationship between epicentral distance and abnormal days before earthquake (including the earthquakes within the epicentral distance of 300 km). Blue points represent the AR-1 and green points represent the variance. The red line indicates positive correlation.

**Figure 10.**The relationship between epicentral distance and anomaly advance days for LJ, WD and ML earthquakes. (

**a**) The results for high frequency and (

**b**) the results for low frequency. The red line indicates positive correlation; black lines indicate negative correlation.

Station | Longitude | Latitude | Types of Wells and Springs | Formation Lithology | Well Depth |
---|---|---|---|---|---|

MD | 100.5 | 25.35 | Artesian thermal water well | Silicified limestone | 32.9 |

NJ | 100.52 | 25.05 | Bedrock fissure water | Cambrian metamorphic rocks | |

CN | 99.61 | 24.83 | Fault rising spring | Ordovician sericite schist | |

TC | 98.54 | 25.02 | Structural fissure water | Olivine basalt | 121 |

LC | 100.1 | 23.98 | Fissure confined water | Granite | 213 |

LD | 103.56 | 27.19 | Contact descending spring | Permian limestone | 39 |

SM | 100.98 | 22.79 | Fissure confined water (artesian) | Cretaceous sandstone | 112.27 |

ML | 99.59 | 22.34 | Fissure confined water (non artesian) | Cretaceous sandstone | 100.38 |

No. | Name | Time | Latitude | Longitude | Mag | Epicentral Distance/(km) | Energy Density/(J·m^{−3}) | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

MD | NJ | CN | TC | LC | LD | SM | ML | MD | NJ | CN | TC | LC | LD | SM | ML | ||||||

1 | Puer | 1993/7/17 | 28.011 | 99.636 | 5.4 | 308.09 | 340.79 | 353.72 | 350.00 | 450.62 | 397.28 | 596.02 | 630.60 | 0.0002 | 0.0002 | 0.0001 | 0.0002 | 0.0001 | |||

2 | Longquan | 1993/8/14 | 25.44 | 101.545 | 5.2 | 105.45 | 111.84 | 206.26 | 305.84 | 218.31 | 279.64 | 300.19 | 397.88 | 0.0030 | 0.0025 | 0.0004 | 0.0001 | 0.0003 | 0.0002 | 0.0001 | |

3 | Luocheng | 1993/10/14 | 28.629 | 103.419 | 5 | 465.35 | 490.98 | 566.96 | 628.71 | 613.66 | 160.61 | 693.66 | 797.80 | 0.0004 | |||||||

4 | Tanai | 1994/1/11 | 25.231 | 97.203 | 6.1 | 331.73 | 334.49 | 246.57 | 136.63 | 324.22 | 670.44 | 469.90 | 402.87 | 0.0018 | 0.0018 | 0.0045 | 0.0273 | 0.0020 | 0.0002 | 0.0006 | 0.0010 |

5 | Myitkyina | 1994/4/6 | 26.188 | 96.867 | 5.9 | 375.53 | 387.48 | 313.96 | 212.15 | 407.75 | 674.12 | 562.04 | 509.14 | 0.0006 | 0.0006 | 0.0011 | 0.0037 | 0.0005 | 0.0001 | 0.0002 | 0.0003 |

6 | Sidoktaya | 1994/5/29 | 20.556 | 94.16 | 6.5 | 839.72 | 821.17 | 733.62 | 669.20 | 719.97 | 1206.55 | 747.12 | 595.90 | 0.0004 | 0.0004 | 0.0006 | 0.0008 | 0.0007 | 0.0001 | 0.0006 | 0.0012 |

7 | Homalin | 1994/8/9 | 24.721 | 95.2 | 6.1 | 538.49 | 537.84 | 445.38 | 338.58 | 503.15 | 879.52 | 626.13 | 519.94 | 0.0004 | 0.0004 | 0.0008 | 0.0017 | 0.0005 | 0.0003 | 0.0005 | |

8 | Mae Chai | 1994/9/11 | 19.586 | 99.516 | 5.2 | 648.84 | 616.27 | 583.19 | 612.51 | 492.30 | 940.67 | 387.24 | 306.33 | 0.0001 | |||||||

9 | Pacific | 1994/11/21 | 25.54 | 96.657 | 5.9 | 386.44 | 392.15 | 307.44 | 197.96 | 388.50 | 711.67 | 534.58 | 464.13 | 0.0006 | 0.0006 | 0.0012 | 0.0045 | 0.0006 | 0.0002 | 0.0003 | |

10 | Luocheng | 1994/12/30 | 29.079 | 103.79 | 5.1 | 526.97 | 552.69 | 628.27 | 688.32 | 675.33 | 211.25 | 753.56 | 859.19 | 0.0003 | |||||||

11 | Kamaing | 1995/5/6 | 24.987 | 95.294 | 6.4 | 525.44 | 526.59 | 435.61 | 327.13 | 499.04 | 860.85 | 627.50 | 527.25 | 0.0012 | 0.0012 | 0.0022 | 0.0052 | 0.0014 | 0.0003 | 0.0007 | 0.0012 |

12 | Menglian | 1995/7/12 | 21.966 | 99.196 | 6.8 | 399.02 | 368.53 | 321.25 | 346.11 | 242.31 | 729.33 | 205.04 | 58.10 | 0.0109 | 0.0138 | 0.0210 | 0.0167 | 0.0495 | 0.0017 | 0.0823 | 3.8023 |

13 | Wuding | 1995/10/24 | 26.003 | 102.227 | 6.2 | 187.68 | 201.41 | 293.41 | 385.79 | 310.72 | 187.05 | 378.92 | 487.26 | 0.0145 | 0.0117 | 0.0037 | 0.0016 | 0.0031 | 0.0147 | 0.0017 | 0.0008 |

14 | Lijiang | 1996/2/3 | 27.291 | 100.276 | 6.6 | 216.98 | 250.37 | 281.62 | 306.24 | 368.59 | 324.85 | 505.48 | 554.86 | 0.0355 | 0.0230 | 0.0161 | 0.0125 | 0.0071 | 0.0104 | 0.0027 | 0.0020 |

^{−4}J/m

^{3}and the bold value means the energy density greater than 10

^{−3}J/m

^{3}.

Earthquake No. | MD | NJ | CN | TC | LC | LD | SM | ML |
---|---|---|---|---|---|---|---|---|

1 | 12 | nan | nan | 44 | 56 | |||

2 | 94 | 106 | nan | nan | nan | nan | 72 | |

3 | nan | nan | ||||||

4 | 241 | 190 | 189 | 234 | 251 | 242 | 242 | 197 |

5 | 317 | 299 | 275 | 277 | 281 | 292 | nan | nan |

6 | 375 | 365 | 387 | 346 | 349 | 377 | nan | nan |

7 | 414 | 417 | 462 | nan | 420 | 420 | nan | |

8 | nan | |||||||

9 | 539 | 537 | 504 | 504 | nan | 516 | 513 | |

10 | nan | |||||||

11 | nan | nan | 652 | 691 | 692 | nan | 655 | 707 |

12 | nan | 788 | nan | 750 | 782 | 772 | 796 | 797 |

13 | 875 | 817 | 826 | 853 | 856 | 868 | 817 | 834 |

14 | 922 | 962 | 939 | nan | 981 | nan | 930 | 930 |

^{−4}J/m

^{3}, bold indicates that the seismic energy density is >10

^{−3}J/m

^{3}, and nan indicates that the seismic energy density is >10

^{−4}J/m

^{3}, but there is no abnormality.

Earthquake No. | MD | NJ | CN | TC | LC | LD | SM | ML |
---|---|---|---|---|---|---|---|---|

1 | nan | 25 | 14 | 21 | 32 | |||

2 | 91 | 104 | nan | 107 | nan | 97 | nan | |

3 | nan | nan | ||||||

4 | 192 | nan | nan | nan | nan | 216 | 186 | nan |

5 | nan | nan | 274 | nan | 327 | nan | 257 | nan |

6 | nan | nan | 386 | nan | nan | 350 | 358 | 373 |

7 | nan | 409 | 463 | nan | nan | 406 | nan | |

8 | nan | |||||||

9 | nan | nan | 502 | 484 | nan | nan | nan | |

10 | nan | |||||||

11 | 662 | nan | 694 | 726 | nan | 707 | 680 | nan |

12 | nan | 768 | 773 | 749 | 775 | 763 | 755 | 797 |

13 | 830 | 850 | nan | 860 | 875 | 893 | nan | 875 |

14 | nan | 932 | 955 | 930 | 980 | 951 | 930 | nan |

^{−4}J/m

^{3}, bold indicates that the seismic energy density is >10

^{−3}J/m

^{3}, and nan indicates that the seismic energy density is >10

^{−4}J/m

^{3}, but there is no abnormality.

Recognition Rate | MD | NJ | CN | TC | LC | LD | SM | ML | Average |
---|---|---|---|---|---|---|---|---|---|

AR-1 | 81.82% | 75.00% | 72.73% | 72.73% | 80.00% | 60.00% | 80.00% | 60.00% | 72.78% |

variance | 36.36% | 50.00% | 72.73% | 63.64% | 40.00% | 80.00% | 70.00% | 30.00% | 55.34% |

Earthquake No. | MD | NJ | CN | TC | LC | LD | SM | ML |
---|---|---|---|---|---|---|---|---|

1 | 55 | 42 | 76 | 44 | 53 | |||

2 | 91 | nan | nan | 91 | 43 | nan | 54 | |

3 | 115 | |||||||

4 | 213 | 186 | 192 | 215 | 219 | 204 | 219 | 215 |

5 | 283 | 279 | 277 | 275 | 298 | 279 | 300 | 267 |

6 | nan | nan | 379 | 364 | 375 | 375 | 347 | 364 |

7 | 412 | 443 | 406 | 411 | 409 | 443 | 439 | |

8 | 475 | |||||||

9 | 501 | 523 | 507 | 503 | 506 | 524 | nan | |

10 | 598 | |||||||

11 | 684 | 667 | 686 | nan | 667 | 653 | 652 | 699 |

12 | 774 | 759 | 739 | nan | 748 | 748 | nan | 748 |

13 | 876 | 842 | 822 | nan | 855 | 844 | 823 | 847 |

14 | 923 | 928 | 940 | 939 | 983 | 923 | 927 | 928 |

^{−4}J/m

^{3}, the bold indicates that the seismic energy density is >10

^{−3}J/m

^{3}, and nan indicates that the seismic energy density is >10

^{−4}J/m

^{3}, but there is no abnormality.

Earthquake No. | MD | NJ | CN | TC | LC | LD | SM | ML |
---|---|---|---|---|---|---|---|---|

1 | nan | nan | nan | 37 | 24 | |||

2 | nan | 83 | nan | nan | nan | nan | nan | |

3 | nan | |||||||

4 | 229 | nan | 224 | 187 | nan | nan | nan | 200 |

5 | nan | nan | 289 | nan | 304 | nan | 315 | nan |

6 | nan | 356 | 351 | nan | 344 | nan | nan | 350 |

7 | nan | 411 | 448 | nan | nan | nan | 410 | |

8 | nan | |||||||

9 | nan | nan | nan | nan | nan | 515 | 515 | |

10 | 549 | |||||||

11 | nan | 704 | 708 | nan | nan | nan | nan | 677 |

12 | nan | nan | nan | 770 | 758 | 766 | 769 | nan |

13 | 848 | 852 | nan | 847 | 833 | 864 | 838 | 889 |

14 | 930 | nan | 932 | 964 | 933 | nan | 951 | nan |

^{−4}J/m

^{3}, the bold indicates that the seismic energy density is >10

^{−3}J/m

^{3}, and nan indicates that the seismic energy density is >10

^{−4}J/m

^{3}, but there is no abnormality.

Recognition Rate | MD | NJ | CN | TC | LC | LD | SM | ML | Average |
---|---|---|---|---|---|---|---|---|---|

AR-1 | 90.91% | 81.82% | 90.91% | 72.73% | 100% | 90.91% | 90% | 90% | 88.24% |

Variance | 27.27% | 33.33% | 54.55% | 45.45% | 50.00% | 40.00% | 50.00% | 60.00% | 45.08% |

Raw-PR | L-PR | H-PR | Raw-T | L-T | H-T | Raw-PRS | L-PRS | H-PRS | |
---|---|---|---|---|---|---|---|---|---|

MD | −0.1344 | −0.1965 | −0.0200 | −0.2905 | −0.5135 | 0.0239 | 0.1577 | 0.2931 | −0.0239 |

NJ | −0.0439 | −0.0827 | 0.0506 | −0.4253 | −0.4917 | −0.0107 | 0.2800 | 0.3205 | 0.0122 |

CN | 0.0619 | 0.0657 | 0.0268 | 0.1886 | 0.2836 | 0.0150 | −0.0344 | −0.0190 | −0.0289 |

TC | 0.0536 | 0.0484 | 0.0324 | −0.0376 | −0.0404 | 0.0123 | 0.1768 | 0.1775 | 0.0106 |

LC | 0.0943 | 0.1282 | −0.0198 | 0.0909 | 0.1018 | 0.0124 | 0.0968 | 0.1105 | 0.0101 |

LD | −0.0275 | −0.0636 | 0.0227 | −0.0886 | −0.1502 | 0.0208 | −0.1571 | −0.2031 | −0.0231 |

SM | 0.0657 | 0.1145 | 0.0079 | 0.0676 | 0.1346 | −0.0020 | −0.0570 | −0.0507 | −0.0360 |

ML | 0.1006 | 0.1579 | −0.0169 | 0.1838 | 0.2640 | −0.0058 | −0.1528 | −0.2423 | 0.0281 |

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## Share and Cite

**MDPI and ACS Style**

Qiao, Z.; Wang, G.; Fu, H.; Hu, X.
Identification of Groundwater Radon Precursory Anomalies by Critical Slowing down Theory: A Case Study in Yunnan Region, Southwest China. *Water* **2022**, *14*, 541.
https://doi.org/10.3390/w14040541

**AMA Style**

Qiao Z, Wang G, Fu H, Hu X.
Identification of Groundwater Radon Precursory Anomalies by Critical Slowing down Theory: A Case Study in Yunnan Region, Southwest China. *Water*. 2022; 14(4):541.
https://doi.org/10.3390/w14040541

**Chicago/Turabian Style**

Qiao, Zhiyuan, Guangcai Wang, Hong Fu, and Xiaojing Hu.
2022. "Identification of Groundwater Radon Precursory Anomalies by Critical Slowing down Theory: A Case Study in Yunnan Region, Southwest China" *Water* 14, no. 4: 541.
https://doi.org/10.3390/w14040541