結合卡曼率波及伴隨狀態之序 率方法反推估含水層特性

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阮黃俠(Nguyen Hoang Hiep) 查詢紙本館藏

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應用地質研究所

論文名稱

結合卡曼率波及伴隨狀態之序率方法反推估含水層特性
(Stochastic Inversion of Aquifer Properties based on Integrated Kalman Filter and Adjoint State Methods)

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至系統瀏覽論文 (2027-1-9以後開放)

摘要(中)

本研究提出一基於序率方法之反推估模式，能夠以高解析度推估水力傳導係數及比儲水係數在一飽和異質性孔隙含水層中的分佈狀況。透過結合卡曼率波及伴隨狀態之序率方法，本研究提出EnKF-AS (Ensemble Kalman Filter - Adjoint State)模式，其參考跨孔抽注試驗中所觀測的水頭變化，計算暫態水流的敏感度。透過兩個合成案例，包含一維的適定性、非適定性案例，以及垂直二維剖面反推估問題，以評估本研究所提模式推估孔隙介質含水層中水力傳導係數及比儲水係數分布狀況。數值試驗顯示出良好結果，本研究所提出之模式在明確定義狀態下，能透過相對少量的觀測數據，有效描述飽和受壓的異質性孔隙介質含水層中參數分佈狀況。本研究提出之模式表現優於於傳統方法如MCS及EnKF，在二維合成案例中EnKF-AS相關係數為0.80，而MCS及EnKF分別為0.70及0.71。在計算資源上，EnKF-AS計算速度分別為MCS及EnKF的2倍及4倍。

摘要(英)

This study presents a stochastic inversion model of aquifer properties that is capable of estimating the distributions of hydraulic conductivity and specific storage with high resolution in heterogeneous saturated porous media. Based on the concept of the Kalman Filter technique and the Adjoint State method, we successfully developed an EnKF-AS (Ensemble Kalman Filter - Adjoint State) model that accounts for the sensitivities of transient flows using the hydraulic head measurements from cross-hole hydraulic pumping or injection tests. Two synthetic cases, including a one-dimensional well-posed and an ill-posed case and a vertical profile of aquifer in two-dimensional problems, are used to evaluate the developed model in estimating the distributions of hydraulic conductivity and specific storage in saturated porous media. The results of the numerical experiments are promising. The developed stochastic inversion model can reconstruct the property (i.e., hydraulic conductivity and specific storage) fields if well-defined conditions are met. With a relatively small number of available measurements, the proposed model can accurately capture the patterns and the magnitudes of estimated properties in the saturated zone, confined aquifer, and heterogeneous porous media. In comparison, this model outperformed better than conventional methods in the field, such as Monte Carlo Simulation (MCS) and Ensemble Kalman Filter (EnKF) in two-dimensional synthetic aquifer cases with high correlation at 0.80 while MCS and EnKF are 0.70 and 0.71, respectively. Furthermore, the computational costs of the EnKF-AS model exhibited 2-fold and 4-fold speedups compared to MCS and EnKF, respectively.

關鍵字(中)

★ 序率反推估
★ 適定性
★ 非適定性

關鍵字(英)

★ Stochastic Inversion
★ Well-posed and ill-posed
★ EnKF-AS
★ EnKF
★ MCS

論文目次

Pages
Abstract .................................................................................................................... i
Acknowledgement ................................................................................................. iii
List of Contents ....................................................................................................... v
List of Figures .......................................................................................................... vii
List of Tables ............................................................................................................ ix
Chapter I. Introduction ......................................................................................... 1
1.1. Inverse problems .................................................................................... 2
1.2. Data assimilation in groundwater flow system ................................ 3
1.2.1. Kalman Filter .............................................................................. 4
1.2.2. Ensemble Kalman Filter ............................................................ 4
1.3. Adjoint State Method ............................................................................. 6
1.4. Research objectives and basic approaches .......................................... 7
1.5. Organization of dissertation ................................................................. 8
Chapter II. Methodologies ................................................................................... 9
2.1. Problems formualation .......................................................................... 10
2.2. Kalman Filter technique ........................................................................ 11
2.3. Ensemble Kalman Filter ........................................................................ 16
2.4. Adjoint State method for transient flow ............................................. 17
2.4. Performance evaluation metrics .......................................................... 19
Chapter III. Stochastic Inversion of Aquifer Properties ................................ 20
3.1. One-dimensional synthetic case example ........................................... 21
3.1.1. Numerical considerations and conceptual model ................ 21
3.1.2. Parameter estimation in well-posed synthetic case .............. 22
3.1.3. Parameter estimation in ill-posed synthetic case .................. 27
3.2. Two-dimensional synthetic case example .......................................... 30
3.2.1. Generation of synthetic aquifer ............................................... 30
3.2.2. Sampling of the syntheic observations ................................... 31
3.2.3. Parameter estimation of hydraulic conductivity ................... 32
3.2.4. Parameter estimation of specific storage ................................ 34
3.2.5. Computation efficiency in parameter estimation ................. 35
Chapter IV. Conclusions and contributions ..................................................... 41
References ............................................................................................................... 43
Bibliography ........................................................................................................... 52

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指導教授

倪春發(Ni Chuen Fa)

審核日期

2025-1-10

推文