# Influence of the Gyeongju Earthquake on Observed Groundwater Levels at a Power Plant

^{*}

## Abstract

**:**

## 1. Introduction

_{x}, K

_{y}, and K

_{z}= the values of hydraulic conductivity in the x, y, and z directions, respectively, along Cartesian coordinate axes, which is the volumetric flow per unit of time per cross-sectional unit area of the aquifer; h = hydraulic head; W = volumetric flux per unit volume which represents sinks or sources; t = time; and S = the storativity or storage coefficient of the porous material, which is equal to S

_{S}B + S

_{y}, where S

_{y}is the specific yield of the aquifer materials, B = the thickness of the aquifer, and S

_{S}= the specific storage of the porous material. The specific storage is:

_{w}= the specific weight of water; n = the porosity of the material; β

_{p}= the compressibility of the bulk aquifer material; and β

_{w}= the compressibility of water. Note that:

_{t}= total volume or the control volume; σ

_{e}= effective stress; V

_{w}= volume of water; and p = pore water pressure. These basically describe the change in total volume or water volume per change with applied stress. The unconfined groundwater table is typically derived from the hydraulic head solution to Equation (1). Different assumptions and constraints to Equation (1) allow for simplification and analytic solutions.

_{y}is typically much larger than S

_{S}in practice. Nonetheless, the mechanics allow for observation.

_{W}= 5.5 Gyeongju earthquake epicenter was located nearby important industrial facilities, such as large power plants as well as the Wolseong Low and Intermediate Level Radioactive Waste Disposal Center. Prior to this event, the stable continental region had relatively few earthquakes of magnitudes M

_{W}> 5.0 [16,17,18]. Interestingly, this event was preceded by several foreshocks, the largest being an M

_{W}= 5.1 event on 12 September 2016 at 10:44 UTC, approximately 11 km southwest of the epicenter of the main shock [17,18,19]. Figure 1 shows the earthquake epicenter and Modified Mercalli Intensity (MMI) scale intensity contours [16]. Earthquake intensity measures the effects of earthquakes as observed by people. The MMI scale is from 1 to 12, with higher intensities indicative of extreme shaking and damage [20,21]. For the 2016 Gyeongju earthquake, the intensity contours ranged from 4 to 5.5, with a reported maximum of 7, and covered a wide region in the southeastern area of South Korea. The 2016 Gyeongju foreshocks had similar MMI contours, but at a lower range of 3.5 to 5.5, with a reported maximum of 6. The effects of the 2016 Gyeongju earthquake were broadcast on major television shows and there was significant coverage commenting if South Korea was seismically safe or how resilient South Korea was to potentially larger earthquakes, especially considering the ongoing effects of the 2011 Fukushima disaster.

## 2. Materials and Methods

#### 2.1. Study Site

#### 2.2. Cross-Correlation Analysis

_{y}and μ

_{x}= average of the y and x time series, respectively; i = time series element index; N = total number of data elements in the time series; lag = the delay in the index of the time series. This technique assumes that the original time series are equally spaced and identical in the number of elements. When using the complete data series, the number of elements in time series y is shifted accordingly to account for the lagged x series.

_{1}= 2cos(x), y

_{2}= 5cos(x) + 0.5, and y

_{3}= 5cos(x + 45) + 0.5. The bottom part of the figure shows the results of cross-correlation analysis with harmonic functions y

_{2}and y

_{3}against y

_{1}. Note that one unit of lag is equivalent to 5°. When comparing harmonic functions y

_{2}and y

_{1}, the highest correlation of 1 appears at a lag of 0. The correlation of 1 shows that comparing two series does not depend on amplitude or offset. However, when comparing harmonic series y

_{3}and y

_{1}, the highest correlation of 1 appears at a lag of −9, equivalent to −45°, which was the difference between harmonic series y

_{2}and y

_{3}. This example reveals what phase shifts exist between two series, independent of amplitude or offset. A lag of −9 is interpreted as y

_{3}being 45° ahead of y

_{1}. More formally, when time series x shows a negative lag to y, it is said that x leads y, and when x shows a positive lag to independent time series y, it is said that x lags y. In this example, y

_{3}leads y

_{1}.

#### 2.3. Granger Causality Test

_{i}) in the time series from past values (i.e., Y

_{i−j}) indicated by the lag, which shares similar nomenclature with cross-correlation analysis but is applied differently. A comparison is made between the regression in Equation (7) to a similar regression that incorporates additional variables, typically called the unrestricted or full model, represented as:

_{0}= drift coefficient, b

_{0}= trend coefficient, γ, δ = regressed coefficients, and r = regression residual. Regression is performed using ordinary least squares. For simplicity, a

_{0}and b

_{0}will be treated as 0 unless otherwise noted. The null hypothesis:

## 3. Results

#### 3.1. Power Plant Environment

#### 3.2. Groundwater Monitoring Wells

#### 3.3. Cross-Correlation Analysis

#### 3.4. Granger Causality Tests

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Map of South Korea showing locations of major thermal and nuclear power plant sites as well as the Wolseong Low and Intermediate Level Radioactive Waste Disposal Center. The 2016 Gyeongju earthquake epicenter is also shown, along with MMI earthquake intensity contours. Recreated and modified from [16,22].

**Figure 2.**Map showing the 2016 Gyeongju earthquake epicenter and the nearby power plant study site. The inset shows the locations of five groundwater observation wells within the power plant site.

**Figure 3.**Example demonstrating how cross-correlation would look like for different series. The top part plots y

_{1}= 2cos(x), y

_{2}= 5cos(x) + 0.5, and y

_{3}= 5cos(x − 45) + 0.5. The bottom part shows the results from the cross-correlation analysis.

**Figure 4.**(

**a**) Precipitation in Gyeongju and (

**b**) tide levels in nearby Ulsan for the month of September 2016.

**Figure 5.**Atmospheric pressure recordings for the month of September 2016 from a monitoring well barometer as well as the nearest weather station.

**Figure 6.**Groundwater level changes for well W1 during (

**a**) September 2016 and (

**b**) a closer inspection of the 3 days around the earthquake event.

**Figure 7.**Groundwater level changes for well W2 during (

**a**) September 2016 and (

**b**) a closer inspection of the 3 days around the earthquake event.

**Figure 8.**Groundwater level changes for well W3 during (

**a**) September 2016 and (

**b**) a closer inspection of the 3 days around the earthquake event.

**Figure 9.**Groundwater level changes for well W4 during (

**a**) September 2016 and (

**b**) a closer inspection of the 3 days around the earthquake event.

**Figure 10.**Groundwater level changes for well W5 during (

**a**) September 2016 and (

**b**) a closer inspection of the 3 days around the earthquake event.

**Figure 11.**Cross-correlation analysis between groundwater levels in wells (

**a**) W1, (

**b**) W2, (

**c**) W3, (

**d**) W4, and (

**e**) W5 against precipitation, tide, and earthquake, showing lag in days at 1 week before and after the main shock.

**Figure 12.**Cross-correlation analysis between groundwater levels in wells (

**a**) W1, (

**b**) W2, (

**c**) W3, (

**d**) W4, and (

**e**) W5 against precipitation, tide, and earthquake, showing lag in hours one day before and after the main shock.

**Figure 13.**Results from Granger causality tests on wells (

**a**) W1 and (

**b**) W2 with respect to precipitation.

**Figure 15.**Results from Granger causality tests on wells (

**a**) W1, (

**b**) W2, and (

**c**) W5 with respect to the earthquake.

**Figure 16.**Example plot of groundwater levels at W1 against precipitation at one-hour intervals for a window spanning one day before and after the earthquake, indicating a negative correlation. Data for lag = 0 and –18 is shown.

Well | I(0) | I(1) |
---|---|---|

W1 | No | Yes |

W2 | No | Yes |

W3 | Yes | Yes |

W4 | No | Yes |

W5 | Yes | Yes |

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**MDPI and ACS Style**

Yee, E.; Choi, M.
Influence of the Gyeongju Earthquake on Observed Groundwater Levels at a Power Plant. *Water* **2022**, *14*, 3229.
https://doi.org/10.3390/w14203229

**AMA Style**

Yee E, Choi M.
Influence of the Gyeongju Earthquake on Observed Groundwater Levels at a Power Plant. *Water*. 2022; 14(20):3229.
https://doi.org/10.3390/w14203229

**Chicago/Turabian Style**

Yee, Eric, and Minjune Choi.
2022. "Influence of the Gyeongju Earthquake on Observed Groundwater Levels at a Power Plant" *Water* 14, no. 20: 3229.
https://doi.org/10.3390/w14203229