利用地震事件及長期地下水位變化推求水文地質參數

Evaluating hydrogeological parameters by using seismic events and long-term groundwater level variations

姚俊豪(Chun-Hao Yao)

指導教授 ： 徐年盛

國立臺灣大學/工學院/土木工程學研究所/博士(2021年)

https://doi.org/10.6342/NTU202100380

摘要

目前求得地下水參數之方法，主要仍以進行現地抽水試驗及採用數值模式推估等兩種方式，如何在前述方式之外，以新的概念來推估水文地質參數也是工程界不斷尋求的目標。本論文之研究目的即是分別採用地震事件及長期性兩種不同特性地下水位觀測資料，利用相關理論擬合Theis方程式以及建立分布式系統模式，然後建立優選模式以推估相關水文地質參數。
本論文第一個主題為「以地震事件引致地下水位變化推求水文地質參數」，由於921地震時，部分同震水位上升後接續退水地下水井，其退水曲線類似抽水試驗洩降般的情況，因此本主題最重要的假設即為地震會導致部分含水層(阻水層)破裂，在震後特定期間，上層含水層的水垂直向下轉移至下層相鄰含水層，可採用Theis方程式來模擬同震水位上升後，孔隙水壓消散的退水過程。此部分研究將分別應用多種時空頻率分析方法，包含主成分分析、小波轉換及小波去噪等訊號分析方法分析同震水位壅高後之退水曲線，以得到震後地層釋放超額孔隙水壓之退水歷線，並以雷曼積分及機率密度等理論，建立序率試驗優選模式，推估震後儲水係數S與導水係數T。
推估結果顯示，研究對象溪州(2)(SC2)儲水係數S的演化過程，從921地震前的0.00107，減低到民國88年921震後27小時推估的0.000826，再減到前人於民國93年進行現地抽水試驗的0.000578；導水係數T的演化過程，從921地震前的92.4(m2/hr)，增加到民國88年921震後27小時推估的98.6(m2/hr)，再增到前人於民國93年進行現地抽水試驗的147.6(m2/hr)。港後(3)(GH3)儲水係數S的演化過程，從921地震前的0.000149，減低到民國88年921震後27小時推估的0.000112；導水係數T的演化過程，從921地震前的28.8(m2/hr)，增加到民國88年921震後27小時推估的120.7(m2/hr)。由於溪州(2)(SC2)及港後(3)(GH3)觀測井在921地震時，均出現同震水位上升，震後儲水係數S推估值下降之現象，可以證實地震導致該區地層受到壓縮。而震後導水係數T推估值均出現大幅增加之現象，可以證實地震會導致部分含水層(阻水層)破裂，甚至使含水層結構可能受到永久的破壞。
本論文第二個主題為「以長期地下水位變化推求水文地質參數」，此部分研究將各地下水觀測井之影響範圍視為一地下水庫，採用地下水位、河川水位、雨量、人為抽水量等長期性觀測資料，以水流連續方程式建立地下水分布式系統優選模式來推估相關水文地質參數，包含水力傳導係數K、比出水量Sy、河川流量轉換係數λ，降雨入滲轉換係數γ、人為抽水轉換係數σ，及其他影響地下水位之因素C。由於人為抽水量之推估缺乏確切調查資料，然而根據Theis方程式，抽水量與洩降或是水位呈現線性關係，因此似可以水位來推估抽水量。依前人以頻譜分析方法針對台灣中部地區地下水位變動的研究顯示，人為抽用地下水之主要影響頻率為1天1次，因此採用時頻分析方法，分析地下水位觀測資料，進而以抽補強度(PRS)推估人為抽水量。
水位擬合結果顯示，研究區域整體RMSE值約為0.96(m)，研究區域北邊豐洲與潭子之RMSE較其他站為高，北邊RMSE介於0.63~1.63(m)之間，主要是研究區域內觀測水位變動範圍呈現北往南遞減，因此北邊地下水觀測站水位擬合結果一旦稍有偏差，RMSE值即會顯著呈現，然而研究區域北邊測站之模擬水位仍能反映峰值變化趨勢。研究區域南邊RMSE介於0.65~0.92(m)之間，然而模擬結果較無法反映部分峰值變化趨勢，初步推測研究區域南邊在烏日及霧峰地區，地質分層現象較複雜，有明顯的阻水層分隔。整體而言，研究區域內除南邊烏日(1)與霧峰(1)外，其餘模擬結果尚符合水位變化趨勢。研究區域內水力傳導係數K值約介於3~16(m/hr)之間，比出水量Sy值約介於0.11~0.27之間，與歷史試驗資料及前人研究相去不遠，推估範圍也符合礫石的物理特性。

關鍵字

主成分分析 ； 小波轉換 ； 小波去噪 ； Theis方程式 ； 序率試驗優選模式 ； 抽補強度 ； 分布式系統模式

並列摘要

At present, there are mainly two methods for obtaining groundwater parameters, i.e., on-site pumping test and numerical model simulation. How to estimate hydrogeological parameters based on novel concepts has been a constant goal in the engineering field. This thesis contains two purposes. One uses the groundwater level observation data caused by earthquake events to fit Theis equation and then develops an optimal model to evaluate the relevant hydrogeological parameters. The other uses long-term groundwater level observation data to develop a distributed system model and then establishes an optimal model to evaluate relevant hydrogeological parameters.
The first topic of this paper is evaluating the relevant hydrogeological parameters by using seismic events. During the 1999 Chi-Chi earthquake, part of wells revealed co-seismic uplift and post-seismic drawdown in groundwater heads, whose drawdown curves are similar to the drawdown curve of a pumping test. Therefore, the most important assumption in this topic is that the earthquake will cause part of the aquifer (aquitard) to rupture. During a certain period after the earthquake, the water in the upper aquifer vertically transfers down to the adjacent aquifer. Theis equation could be used to simulate the post-seismic groundwater head drawdown during pore-water pressure release process. To find out the post-seismic drawdowns that are associated with the crustal strain followed by the relaxation process of excess pore-water pressure, this study applies multi-rank principal component analysis, multi-frequency wavelet transform, and multi-level wavelet de-noising to decompose the groundwater head fluctuation into a series of intrinsic mode functions. In addition, based on the Riemann integral and the probability density theory, a stochastic optimization model is established to estimate storage coefficient S and transmissivity T after the earthquake.
According to the estimation results for SC2, the evolving storage coefficient S reduced from pre-seismic on-site pumping test value 0.00107, and post-seismic 27th-hour value 0.000826 to post-seismic pumping test value 0.000578 in 2004; and the evolving transmissivity T increased from pre-seismic on-site pumping test value 92.4(m2/hr), and post-seismic 27th-hour value 98.6(m2/hr) to post-seismic value 147.6(m2/hr) in 2004. For GH3, the evolving storage coefficient S reduced from pre-seismic on-site pumping test value 0.000149 to post-seismic 27th-hour value 0.000112; and the evolving transmissivity T increased from pre-seismic on-site pumping test value 28.8(m2/hr) to post-seismic 27th-hour value 120.7(m2/hr). Since the observation wells of SC2 and GH3 both experienced rising co-seismic water levels during the earthquake and decreasing in the estimated value of storage coefficient S after the earthquake, these events could prove that the earthquake caused compression of the crust in these areas. In addition, the sharp increase in the estimated value of the transmissivity T after the earthquake could prove that the earthquake caused part of the aquifer(aquitard) to rupture, and the structure of the aquifer may even be permanently damaged.
The second topic of this paper is evaluating the relevant hydrogeological parameters by using long-term groundwater level variations. In this part of the study, the area controlled by a well is regarded as an underground reservoir, long-term observation data such as groundwater level, river water level, rainfall, and artificial pumping volume are used to establish an optimization model of distributed groundwater system based on the continuity equation to estimate relevant hydrogeological parameters. These parameters include hydraulic conductivity K, specific storage Sy, river discharge conversion coefficient λ, rainfall infiltration conversion coefficient γ, artificial pumping conversion coefficient σ, and other factors C that affect the groundwater level. Although there is a lack of accurate survey data for the estimation of artificial pumping volume, the pumping volume has a linear relationship with the discharge or water level, according to Theis equation. Thus, it seems that the water level could be used to estimate the pumping volume. In addition, according to previous studies, the frequency of artificial pumping is mainly once a day. Therefore, the time-frequency analysis method is used to analyze the groundwater level observation data, and then the artificial pumping volume is estimated based on the pumping recovery strength (PRS).
The water level fitting results show that the overall RMSE value of the study area is about 0.96(m). The RMSE of the water level at FJ and TZ in the north of the study area is higher than at other stations, which between 0.63~1.63(m). This is mainly because the observed water level in the study area is decreasing from north to south. Therefore, once the water level fitting results at the groundwater observation stations in the north slightly deviate, the RMSE value will change significantly. Nevertheless, the simulated water level of the stations in the north of the study area can still reflect the trend of peak change. The RMSE of the water level in the south of the study area is between 0.65~0.92(m). However, the simulation results are not able to reflect the trend how some peaks change. It is speculated preliminarily that the south of the study area is the WR and WF areas, where the geological stratification is more complicated, and there exist obvious aquitards. In general, except for WR(1) and WF(1) in the south of the study area, the other simulation results are still in line with the trend of water level changes. The hydraulic conductivity K in the study area is between 3 ~16 (m/hr), and the specific storage Sy is between 0.11~ 0.27, which is not far from historical experimental data and data from previous studies, which is also in line with the physical properties of gravel.

並列關鍵字

principal components analysis ； wavelet transform ； wavelet de-noising ； Theis equation ； stochastic experimental optimization model ； pumping recovery strength ； distributed system model

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