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臺北盆地淺層三維速度構造模型與驗證 Modelling and Validation of 3-D Shallow Velocity Structure in the Taipei Basin

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臺北盆地淺層三維速度構造模型與驗證 Modelling and Validation of 3-D Shallow Velocity Structure in the Taipei Basin 國立臺灣師範大學 地理學系第三屆空間資訊碩士在職專班論文 臺北盆地淺層三維速度構造模型與驗證 Modelling and Validation of 3-D Shallow Velocity Structure in the Taipei Basin 指導教授：王聖鐸 博士 共同指導：林哲民 博士 研究生： 呂學敏 中華民國一○八年七月 Abstract The purposes of this study is to test and propose a method combining different existing geophysical survey data and build a three-dimensional S-wave velocity model for ground motion simulation. The inverse distance weighting (IDW) and the ordinary kriging methods were applied to interpolate the data obtained from the suspension P-S logging, the microtremor array, the horizontal-to-vertical spectral ratio (H/V) and the receiver function approaches. In regard to the ordinary kriging method, the test based on two types of setting, the first setting was to consider only the horizontal semivariogram to interpolate model. Conversely, the second was to consider both the horizontal and vertical semivariogram. Moreover, on the basis of the two major setting, the proposed confidence weight factor method was applied. Two set of the confidence weight factors calculated by the seismic H/V simulation result was tested, the first set based on the types of geophysical approaches. The second set based on considering the different approaches at each site. According to the spatial distribution of data, three depth scales were divided in this study. The parameters were tested by cross-validation and the fitness of models were verified by the seismic H/V simulation. The result showed that the simulation of IDW method do not fit the real geological condition well. The value of the ordinary kriging considering both the horizontal and vertical semivariogram varied stronger than the other. And the effect of confidence weight factors was stronger as well. Despite the cross-validation result was worse than the method only considering horizontal semivariogram. The fitness of simulation was higher than the latter. Keywords: Taipei Basin, S-wave Velocity, Ordinary Kriging i Chinese Abstract 摘要 本研究目的在測試並提出結合既有的地球物理探勘資料的方法，並建立可用 於地動模擬的臺北盆地三維速度構造模型。本研究結合了鑽探井測、微地動陣列、 微地動單站頻譜比法以及接收函數法等資料，利用反距離權重法與普通克利金法 分別進行測試。 在普通克利金法之中，測試了僅考量水平半變異函數的方法以及同時考量垂 直與水平半變異函數兩種主要設定，並分別對該兩種設定的普通克利金法分別加 入了所提出之信心權重因子方法進行測試結果。本研究測試了兩種信心權重因子， 其中，第一種權重因子以方法類別為基礎，利用各方法之強震站模擬之平均值作 為權重因子，第二種信心權重因子則以在相異場址之下，不同的方法模擬的個別 結果作為依據。 本研究依照資料的空間分布將內插模型分為三個部分進行內插，以交叉驗證 法驗證參數的結果，並以強震站單站頻譜法的模擬結果驗證模型用於模擬的適配 性。其結果顯示反距離權重法得到的速度不符合實際地質情況，普通克利金法僅 考量水平半變異函數使得內插數值變化較為緩慢，其交叉驗證的誤差略小於加入 垂直向半變異函數的方法，加入信心權重因子對於結果變化並不明顯。相反地， 考量垂直半變異數的方法對數值的影響變化較大，加入權重信心因子亦造成較大 的數值變化。對兩項空間內插模型進行強地動單站頻譜法模擬，其結果顯示後者 得到較好的適配性。 關鍵字：臺北盆地、剪力波速、普通克利金法 ii Acknowledgement First of all, I would like to express my sincere gratitude to my advisor Dr. Sendo Wang and co-advisor Dr. Che-Min Lin. They showed me a responsible, rigorous, organized scholar model. I learned not merely the knowledge and skills to solve academic problems but also the critical thinking to find problems. Besides, I appreciated the oral examination committee members Dr. Tzai-Hung Wen and Dr. Chun-Hsiang Kuo. They indicated many insufficient points in this dissertation and gave me some useful suggestions to improve it. Furthermore, I am really grateful to Dr. Kuo- Liang Wen, Dr. Jyun-Yan Huang, Dr. Zhe-Ming Chen, Dr. Teruo Hatakeyama and Dr. Yuuzi Tatuoka for leading me to the concerned fields. Finally, I have to thank the people who supported me during the two years. My family, friends, classmates and the seniors in research room 304, 315, 502 and 602. Thanks for your support. iii Index Abstract ........................................................................................................................... i Chinese Abstract ............................................................................................................ ii Acknowledgement ....................................................................................................... iii Index ............................................................................................................................. iv List of Tables ................................................................................................................ vii List of Figures ............................................................................................................ viii Chapter 1 Introduction ................................................................................................... 1 1.1 Motivation ........................................................................................................ 1 1.2 Literature Review............................................................................................. 3 1.2.1 Geophysical Survey Data ...................................................................... 3 1.2.2 Geostatistical Interpolation Method ...................................................... 8 Chapter 2 Study Area and Data .................................................................................... 12 2.1 Area of Interest ............................................................................................... 12 2.2 S-wave Velocity Data ..................................................................................... 14 Chapter 3 Methodology ............................................................................................... 18 iv 3.1 Inverse Distance Weighting ........................................................................... 18 3.2 Ordinary Kriging ............................................................................................ 21 3.2.1 Regionalized Variable Theory ............................................................. 22 3.2.2 Stationary ............................................................................................ 22 3.2.3 Semivariogram .................................................................................... 24 3.2.4 Effects in the semivariogram ....................................................... 33 3.2.5 Ordinary Kriging ................................................................................. 43 3.3 Confidence Weight factor .............................................................................. 48 3.4 Validation ....................................................................................................... 50 3.4.1 Cross-Validation .................................................................................. 50 3.4.2 Seismic H/V Simulation ..................................................................... 51 Chapter 4 Result and Discussion ................................................................................. 53 4.1 Study Process ................................................................................................. 53 4.1 Result of the IDW Method. ............................................................................ 56 4.2 Confidence Weight Factor Calculation .......................................................... 56 v 4.3 Semivariogram Analysis ................................................................................ 57 4.4 Cross-Validation ............................................................................................. 61 4.5 Simulation ...................................................................................................... 65 4.6 Discussion ...................................................................................................... 67 Chapter 5 Conclusion and Suggestion ......................................................................... 72 5.1 Conclusion ..................................................................................................... 72 5.2 Suggestion ...................................................................................................... 73 References .................................................................................................................... 74 Appendix A .................................................................................................................. 81 Appendix B .................................................................................................................. 92 Appendix C .................................................................................................................. 95 Appendix D .................................................................................................................. 98 Appendix E ................................................................................................................ 101 Appendix F................................................................................................................. 128 vi List of Tables Table 2.1 Data format in the study. .............................................................. 15 Table 3.1 Example of ordinary Kriging. ...................................................... 49 Table 3.2 Example of proposed method. ..................................................... 49 Table 4.1 data and methods of models. ........................................................ 61 Table 4.2 ME, MAE and MAPE result of model A. .................................... 62 Table 4.3 ME, MAE and MAPE result of model B. .................................... 62 Table 4.4 ME, MAE and MAPE result of model C. .................................... 63 Table 4.5 ME, MAE and MAPE result of model D. .................................... 63 Table 4.6 ME, MAE and MAPE result of model E. .................................... 64 Table 4.7 ME, MAE and MAPE result of model F. ....................................
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