利用耦合馬可夫鏈率定沉積物之水平側向延伸參數 -以臺北盆地兩處研究區為例

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潘啟平(Chi-Ping Pan) 查詢紙本館藏

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應用地質研究所

論文名稱

利用耦合馬可夫鏈率定沉積物之水平側向延伸參數 -以臺北盆地兩處研究區為例

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★ 折射震測法之盲層P波與水平層界不確定性分析

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摘要(中)

地質模型是大地工程、地下環境及地質災害分析、模擬及評估的基礎。在建立地質模型時有許多原因會導致不確定性：鑽井中地質材料邊界解釋的不確定性、鑽井之間材料邊界與材料側向延伸解釋的不確定性及關於地質構造之知識不足導致的不確定性…等，這些原因所導致的不確定性，將會影響應用之分析成果與可靠度。本研究將會著重討論在鑽井之間地質材料邊界解釋的不確定性。其中，利用隨機場建立地質模型時地質材料在垂直與水平方向上之延伸長度比值為重要參數，若能利用既有鑽井資料加以率定垂直與水平向延伸長度之比例關係將可以更合理地使用沉積學學理，以降低地質模型建立時之不確定性。　
　　垂直的延伸長度可以由鑽井資料取得；而水平方向上的延伸長度常因資料點的不足而難以取得。耦合馬可夫鏈(coupled Markov chain)是一建模方法可根據調查鑽孔內在垂直向及水平向材料的變換機率，進行場地內各處材料的條件機率計算，進一步得到各材料在空間的出現機率，並根據計算出的材料機率模擬出潛在的地質模型。利用沉積學之韋氏定律 (Walther’s law)假設垂直方向與水平方向延伸之間的關係，以垂直向材料的變換機率來推得水平向材料的變換機率。藉由比較觀測井中材料的似然性(likelihood)可獲得最合適的垂直與水平向地質材料延伸長度的比例，作為建立模型時之沉積物垂直與水平延伸參數。
　　本研究已成功重現過去文獻中耦合馬可夫鏈率定參數之方法。並嘗試對臺北盆地中鑽井密集處之松山層內材料進行垂直與水平延伸長度參數之率定。以甲研究區進一步針對不同的耦合馬可夫鏈分析次序即演算方向組合進行研究，以探討分析次序對率定結果之影響。「由左而右由上而下」、「由右而左由上而下」、「由左而右由下而上」、「由右而左由下而上」的分析次序分別率定得到的參數值為13.0、12.5、15.5及11.5，表示以不同方向組合進行率定將會得到不同之結果。而其中，在材料邊界高程變化較大處尤為明顯。
　　以乙研究區，選定一組平行之東西向剖面及垂直兩剖面之垂直向剖面，檢視土壤取樣紀錄將土壤依據粒徑分布與塑性之有無重新分類土壤種類，進行參數之率定並建立地質剖面。同時比較依據統一土壤分類法建立之剖面及依據本研究之分類法建立之剖面之差異。「由左而右由上而下」的分析次序在東西向的兩剖面分別率定得到的參數值為40及65，南北向剖面率定得到的參數值為57；「由左而右由上而下」的分析次序在東西向的兩剖面分別率定得到的參數值為44及37，南北向剖面率定得到的參數值為33。結果顯示無論東西向與南北向剖面，率定之沉積物延伸比例參數皆位在相似之區間，表示率定結果受剖面方向性影響甚小，且水平向延伸遠大於垂直向之延伸。表現在臺北市龍門國民中學之校址內沉積層為近水平分布。表示基於率定結果之參數建立模型，能使模型符合地質知識，建立合理之地質模型。

摘要(英)

The geological model is the basis for analysis, simulation and evaluation of engineering, underground environment and geological disasters. The uncertainty within the geological model will highly influence the effectiveness of these applications. The relationship of extension length of the material (stone or soil) in vertical and horizontal direction is the critical parameter when building the geological model. If the parameter can be determined could make the model more reliable.
The extension length in the vertical direction can be obtained from the borehole data, while in the horizontal direction, due to the lack of information is hard to obtain the extension length directly. The coupled Markov chain modeling method using the transition probability to calculate the probability of the different materials occur in each position. Based on Walther’s law can describe the relationship between the extension length in vertical and horizontal direction, using the transition probability in the vertical direction to calculate the transition probability in the horizontal direction. By comparing the likelihood of the material in observed scenario can obtain the most reliable parameter value of the ratio of vertical and horizontal extension.
This research has reproduced the result of the parameter determination method and applied the method to the site in Taipei basin, which has high density of the borehole data to determine the ratio of the extension length in the horizontal direction to the vertical direction in SungShan Formation. In study area A, we used different simulated directions, “left to right, up to bottom”, “right to left, up to bottom”, “left to right, bottom to up”, “right to left, bottom to up”, and the determination results are 13, 12.5, 15.5 and 11.5, respectively. From these result we found that we got different values of parameter with different simulated directions, especially when the material boundary variety is enormous.
In study area B, we chose a pair of cross sections in direction East to West, and a cross section in North to South to determine the parameter and build the geological model. The types of soils have been reclassified by particle size distribution and soil plasticity. This research has also compared the geological models based on the reclassification with the geological model based on the unified soil classification system. We used the simulated direction in “left to right, up to bottom”, the determination results of the cross sections in direction East to West were 40 and 65, North to South was 57; In “right to left, up to bottom”, the determination results of the cross sections in direction East to West were 44 and 37, North to South was 33. From the determination results we can know that the influence from the cross sections direction is small, and the lateral extension length is much longer than vertical extension length in study area. The model which used the parameter shows that is easily to identify the sub layers in SungShan Formation. That is to say, the parameter makes geological model more reliable.

關鍵字(中)

★ 耦合馬可夫鏈
★ 最大似然估計
★ 韋氏定律
★ 臺北盆地
★ 松山層

關鍵字(英)

★ Coupled Markov chain
★ Maximum likelihood estimation
★ Walther′s law
★ Taipei basin
★ Songshan Formation

論文目次

摘要 ……………………………………………………………… i
Abstract ……………………………………………………………… ii
圖目錄 ……………………………………………………………… iv
表目錄 ……………………………………………………………… vii
一、緒論………………………………………………………… 1
1-1 研究動機與目的…………………………………………… 1
1-2 文獻回顧…………………………………………………… 3
1-2-1 台北盆地之沉積環境……………………………………… 3
1-2-2 對空間相關性之研究……………………………………… 8
1-2-3 機率性建模方法…………………………………………… 10
1-3 研究流程…………………………………………………… 13
二、研究方法…………………………………………………… 15
2-1 建立耦合馬可夫鏈模型…………………………………… 15
2-1-1 耦合馬可夫鏈……………………………………………… 15
2-1-2 轉換機率矩陣……………………………………………… 18
2-1-3 加入遠方邊界資訊之耦合馬可夫鏈……………………… 21
2-2 以最大似然估計評估沉積物延伸比例…………………… 24
2-3 土壤種類再分類…………………………………………… 26
2-4 建立機率地質模型………………………………………… 28
2-5 利用資訊熵量化地質模型之不確定性…………………… 30
三、臺北盆地研究區內松山層之建模………………………… 32
3-1 選定研究區域……………………………………………… 32
3-2 乙研究區土壤種類再分類………………………………… 40
四、結果與討論………………………………………………… 47
4-1 前人文獻分析結果再現…………………………………… 47
4-2 甲研究區－分析次序對模擬結果之影響………………… 50
4-3 乙研究區剖面率定成果…………………………………… 54
4-4 乙研究區本研究之分類法與統一土壤分類法之比較…… 62
五、結論與建議………………………………………………… 65
5-1 結論………………………………………………………… 65
5-2 建議………………………………………………………… 66
參考文獻 ……………………………………………………………… 67

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指導教授

董家鈞涂家輝(Jia-Jyun Dong Chia-Huei Tu)

審核日期

2022-8-3

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