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研究生:施清芳
研究生(外文):Ching-Fang Shih
論文名稱:序率分析應用於地球科學研究
論文名稱(外文):Application of Stochastic Analysis to Geosciences
指導教授:吳逸民吳逸民引用關係
指導教授(外文):Yih-Min Wu
學位類別:博士
校院名稱:國立臺灣大學
系所名稱:地質科學研究所
學門:自然科學學門
學類:地球科學學類
論文種類:學術論文
論文出版年:2008
畢業學年度:96
語文別:英文
論文頁數:238
中文關鍵詞:地球科學序率頻譜分析不確定性迴歸分析地下水地震雷利波衛星定位二氧化碳深海隔離海底地形風場評估一階自由度振動
外文關鍵詞:geosciencesstochasticspectral analysisuncertaintyregressiongroundwaterearthquakeRayleigh waveGPSCO2 deep sea sequestrationseabed topographywind characterizationone-degree-of-freedom vibration
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在地球科學領域,我們常常發現觀測到的有趣現象都和時間與空間變化有關,序率問題的剖析自然成為解釋這些現象的關鍵,也成為必要的步驟之一。一般而言,與時間有關的序率問題,頻譜分析可以加以運用,並解釋大部份之週期性現象。對於某些問題因取樣方式不同造成之不確定性為地球科學領域另一個值得關切的序率問題。本研究主要在探討序率分析方法在地球科學領域的應用;以頻譜分析研究時間序列在頻率域的特性,並可以用頻譜表示法轉換時間域系統為頻率域系統並反求解系統之重要控制因子;微分分析法以變異數與均值解釋任何解析系統經由不同取樣方式造成之不確定性傳遞問題;以統計分析歸納地球科學觀測資料,迴歸分析解釋資料的可預測性。本研究展現九個應用案例以說明上述方法的運用,其中包含主要案例:地下水與地震雷利波之相關研究(四個案例),次要案例:水文地質溶質傳輸不確定性分析、衛星定位位移迴歸分析、海底空間迴歸分析運用於二氧化碳深海隔離之評估,風場之頻譜分析,及地震造成物體一維自由度振動特性之長期評估等,完成之具體成果值得地球科學研究進一步評價。

本研究第一部份在探討地下水水位受到外界擾動造成的現象,主要擾動來源為海水與地震,研究首先將時間域觀測到之擾動源轉換成頻率域以探討來源之週期性現象,根據地下水受壓水層之彈性理論與地震位移造成地層之擴張理論,結合頻率域之頻譜,反解受壓水層之貯水係數與比貯水係數。此外,根據地下水受壓水層之水理模式,建構地下水水位與海水擾動邊界之頻譜關係,並反解地下水水力擴散係數。最後,綜合上述研究評估研究區域之水力傳導係數。研究花蓮地震觀測站之地下水位,發現該站地下水與海水半日潮12.6 hr波動有極高相關性,運用南亞蘇門達臘地震(規模9,UT 2004/12/26 00:58:53.45)造成花蓮附近NACB地震寬頻觀測站之地表位移,經由頻譜分析,發現該站地下水之貯水係數與比貯水係數分別為10^-3與10^-4(m^-1),地下水水力擴散係數為2.886×10^5 m^2/h,估計水力傳導係數為0.1 cm/sec。

本研究第二部份在探討地球科學之相關研究。分析地下水一維溶質傳輸之不確定性發現地下水流速與延散係數之變異數分別與實驗空間尺度之二次方與四次方及伴隨之其他系統變異數與共變異數有關,由於實驗空間尺度是固有的(非人為因素或取樣方式)系統參數,在解釋地下水流速與延散係數時,除了人為因素或取樣方式的產生之變異外,要特別、謹慎考慮實驗空間尺度固有影響,即過大的實驗空間尺度會放大其他系統參數之變異性。迴歸分析長達8年之台灣東北方之蘇澳非等間隔之時序衛星定位位移記錄發現持續偏移量達0.625 m,隨著時間演變期間,有三個突增之線性增大趨勢,線性變化率(斜率)維持在10^-4 m/day,且變化率有增加現象。如果維持台灣目前二氧化碳之增長趨勢不變,預估在西元2010至2030間,產生之二氧化碳將高達6.473 Gt,從研究的角度考慮台灣東邊之深層海床,即初步觀察122°E 至 122.5°E、21.8°N至22.3°N,深度從-4554 m(區域內開始接觸到部份海底地形)開始,是一平坦且小幅封閉之適用海床,經由海底地形反推海洋儲存空間,發現Sigmoidal Weibull 4個參數之非線性廻歸可以預測海洋儲存空間與二氧化碳封存量對深度的變化。若從深度-4554 m開始往下,20年與100年之封存空間分別需要3 m與12 m之海洋厚度。若從深度-4900 m(區域內大部份的深度)開始往上,20年與100年之封存空間則分別需要40 m與60 m之海洋厚度。運用頻譜分析研究台灣主要之6個氣象觀測站之風場時間序列,發現中西部之梧棲站有50%之逐時風速與平均值超過4 m/sec,主要風向為東北風與北風,週期性風速的成分維持在半日與全日,且各測站與澎湖站之時間延遲皆小於1 hr。考慮一個長期以強震儀觀測之建築物,並視其為一階自由度振動系統,經由以地下室為振動輸入端,模擬計算頂樓振動輸出端,分析比較觀測記錄,獲得最佳振動週期與衰減係數。自1994年起,收集12年之172組顯著強震資料,並以921大地震為比較點,發現,經統計分析發現振動週期與衰減係數在921之後皆有增大現象,對震央距小於50 km之大部份強震記錄,亦發現振動週期與衰減係數隨著地震規模增大而增大。
The most commonly observed phenomena in nature, especially for geosciences, always demonstrate as the temporal and spatial dependent cases. Naturally, profiling the stochastic issues will be the key for addressing the process in cases and be the necessary steps in analysis. In general, for time-dependent problems, spectral analysis can be stochastically utilized to investigate the periodic fluctuation in the most cases that interested period can be considered in time domain. On the other hand, it is apparently that sampling manner and ways frequently dominants the judgments for the major task of observation and analysis. The exploration in geosciences can not be averted from the sampling by mankind or automatic records; uncertainty will grow in abundance to the some degree of extent corresonding to the different cases. This research demonstrates stochastic analysis of time domain and observation in geosciences. Spectral analysis and representation are used to investigate periodical time series and inversely inspect dominant factors in the considered model, respectively; differential analysis is manipulated to demonstrate the uncertainty assessment for the system. Descriptive statistics is generally used to summarize a crowd data; non-linear regression also cohere the stochastic data to the predictable level. There are nine applications associated with the major work for groundwater and seismic Rayleigh wave (four cases), and the secondary researches about hydrodispersive in hydrogeology, GPS observation for displacement, seabed marine volume assessment for CO2 deep sequestration, wind characterization, and long-term assessment of one-degree-freedom vibration for building have been completed. It shows that the methods can be well applied to the research in geosciences; the fruitful and consolidated results inspire one who is interested and concerns.
Table of Contents

Table of Contents I
List of Figures IV
List of Tables VIII

Chapter 1 Introduction 1-1
1.1 Purpose 1-1
1.2 Scope and structure of dissertation 1-5

Chapter 2 General methodology 2-1
2.1 Purpose 2-1
2.2 Spectral analysis 2-2
2.3 Spectral representation 2-6
2.4 Differential analysis 2-7
2.5 Descriptive statistics and regression 2-10

— PART I —

Chapter 3 Spectral decomposition of periodic groundwater fluctuation in an coastal aquifer 3-1
3.1 Purpose 3-1
3.2 Conceptual model of hydrogeology 3-4
3.3 Spectral analysis 3-6
3.4 Data analysis and discussion 3-6
3.5 Conclusion 3-9

Chapter 4 Spectral responses and coherence of groundwater head to seismic Rayleigh wave 4-1
4.1 Purpose 4-1
4.2 Conceptual model of hydrogeology 4-3
4.3 Spectral analysis 4-6
4.4 Data analysis and discussion 4-6
4.5 Conclusion 4-12

Chapter 5 Storage of confined aquifer: Spectral analysis of groundwater head responses to seismic Rayleigh wave 5-1
5.1 Purpose 5-1
5.2 Conceptual model of hydrogeology 5-2
5.3 Theory and approach 5-4
5.4 Data analysis and discussion 5-12
5.5 Conclusion 5-15

Chapter 6 Hydraulic diffusivity in confined aquifer: spectral analysis of groundwater responses to fluctuated and no-flow boundary 6-1
6.1 Purpose 6-1
6.2 Conceptual model of hydrogeology 6-2
6.3 Spectral representation for one-dimensional confined groundwater flow 6-4
6.4 Spectral analysis 6-8
6.5 Data analysis and discussion 6-8
6.6 Conclusion 6-12

— PART II —

Chapter 7 Uncertainty propagation of hydrodispersive transfer in an aquifer: An illustration of one-dimensional contaminant transport with slug injection 7-1
7.1 Purpose 7-1
7.2 Analytical system of contaminant transport 7-4
7.3 Differential analysis for uncertainty assessment 7-8
7.4 Uncertainty analysis 7-8
7.5 Discussion 7-12
7.6 Conclusion 7-13

Chapter 8 Assessment of long-term variation in displacement for a GPS site adjacent to a transition zone between collision and subduction 8-1
8.1 Purpose 8-1
8.2 Conceptual model of studied site 8-4
8.3 Quantitative analysis. 8-5
8.4 Discussion 8-6
8.5 Conclusion 8-9

Chapter 9 Potential volume for CO2 deep ocean sequestration: Assessment of the area located Western Pacific Ocean 9-1
9.1 Purpose 9-1
9.2 Conceptual model and data manipulation 9-5
9.3 Result and discussion 9-5
9.4 Conclusion 9-8

Chapter 10 Wind characterization and potential assessment using spectral analysis 10-1
10.1 Purpose 10-1
10.2 Spectral analysis 10-4
10.3 Data analysis 10-5
10.4 Discussion 10-7
10.5 Conclusion 10-8

Chapter 11 Long-term assessment of construction vibration: On the dynamics of a base-excited one degree of freedom system using strong motion of seismometer records……………………………………………………...11-1
11.1 Purpose 11-1
11.2 Methodology 11-3
11.3 Data analysis 11-5
11.4 Result and Discussion 11-6
11.5 Conclusion 11-8

Chapter 12 Summary 12-1

Reference R-1

List of Figures

Figure 3-1 Well location for Huakang Shan site 3-15
Figure 3-2 Geological map for Huakang Shan site 3-16
Figure 3-3 Hydrogeological profile for Huakang Shan site 3-17
Figure 3-4 Time series for the studied parameters 3-18
Figure 3-5 Time series zoomed in time domain 3-19
Figure 3-6 Autospectral density of the observed time series 3-20
Figure 3-7 Cross-spectral density for parameter pairs 3-21
Figure 3-8 Semidiurnal component of time series using Doodson bandpass filter 3-22
Figure 4-1 Seismograms at NACB and time series of groundwater head at GWH/HWA. 4-18
Figure 4-2 Map shows spatial locations for SAIE, groundwater monitoring well (GWH/HWA) and seismological station (NACB) 4-19
Figure 4-3 Sketched map shows coordinates, propagation and active plane between the source and receiver 4-20
Figure 4-4 Seismogram decomposed into vertical (Z), radial (x; horizontal) and transverse (y) components to characterize Rayleigh wave 4-21
Figure 4-5 Zoomed seismogram in time to characterize vertical (Z), radial (x; horizontal) and transverse (y) components for Rayleigh wave 4-22
Figure 4-6 Radial and vertical (x and Z) trajectory for the sections (I, II and III) selected from decomposed seismogram 4-23
Figure 4-7 Histogram summarize the first view of sample density for h, Z, x, and y components 4-24
Figure 4-8 Autospectral density in frequency (period) domain 4-25
Figure 4-9 Cross-spectral density in frequency (period) domain 4-26
Figure 4-10 Phase and time lag derived from cross-spectral density 4-27
Figure 4-11 Bandpass filter utilized for passing 0.047445 - 0.051095 Hz component of time series sampled from 1767 sec 4-28
Figure 4-12 Bandpass filter utilized for passing 0.047445 - 0.051095 Hz component of time series sampled from 1767 sec; zoomed for the time from 1800 sec to 2200 sec 4-29
Figure 4-13 Bandpass filter utilized for passing 0.32847- 0.33577 Hz conponent of time series sampled from 1767 sec 4-30
Figure 5-1 Vertical component in seismogram and time series of groundwater head are observed at NACB (Broadband Array in Taiwan for Seismology, BATS) and GWH/HWA, respectively 5-18
Figure 5-2 Map showing the conceptual model of the well-aquifer system in a confined layer of groundwater and displacement in the x-z plane 5-19
Figure 5-3 Autospectral density in frequency (period) domain 5-20
Figure 5-4 Cross-spectral density in frequency (period) domain 5-21
Figure 5-5 Phase and time lag derived from cross-spectral density for groundwater head and vertical displacement pair 5-22
Figure 5-6 Bandpass filter utilized for passing 0.047445 - 0.051095 Hz (nearly the period of 20 sec), the component of time series sampled from 1767 sec 5-23
Figure 5-7 The lower and higher band related to the period of 20 sec are inspected using the bandpass filter for the frequency 0.03~0.04 Hz and 0.065~0.075 Hz, respectively 5-24
Figure 5-8 Matrix bulk modulus estimated using porosity in the range of 0.1~0.5 and for standard water modulus, Ew taken as 2.2×109 Pa 5-25
Figure 6-1 Location of Huakang Shan groundwater monitoring well 6-15
Figure 6-2 Conceptualized profile of well log and nearby coastal boundary 6-16
Figure 6-3 Conceptual model designated with mathematical boundary conditions at both two ends 6-17
Figure 6-4 Plot show the time series for groundwater head and tidal seawater level 6-18
Figure 6-5 Autospectral density for groundwater head and tidal sea level 6-19
Figure 6-6 Cross-spectral density for groundwater head and tidal seawater level 6-20
Figure 6-7 Bandpass time series for semidiurnal component at frequency 0.075~0.0917 cph 6-21
Figure 7-1 Conceptual model of a one-dimensional flow field and solute transport using slug injection 7-17
Figure 7-2 Dimensionless curve for a one-dimensional flow field and solute transport using slug injection 7-18
Figure 7-3 Breakthrough curve versus dimensionless curve of one-dimensional flow field and solute transport using slug injection 7-19
Figure 7-4 Breakthrough curve versus dimensionless curve of one-dimensional flow field and solute transport (zoomed view for total curve) 7-20
Figure 7-5 Breakthrough curve versus dimensionless curve of one-dimensional flow field and solute transport (zoomed view for peak value) 7-21
Figure 7-6 CV of the input parameters comparing different sampling manner 7-22
Figure 8-1 Map showing studied GPS site and schematic tectonic boundaries 8-14
Figure 8-2 Schematic model showing continent-arc collision and plate tectonic setting of Taiwan 8-15
Figure 8-3 Active and extent plate boundaries in Taiwan-Luzon region 8-16
Figure 8-4 Seismicity activities near the studied site 8-17
Figure 8-5 Position obtained from GPS for SUAO station 8-18
Figure 8-6 Time series of position components and displacement at SUAO station 8-19
Figure 8-7 Histogram of position components and displacement at SUAO station 8-20
Figure 8-8 Histogram of the positioning error derived from GPS at SUAO station 8-21
Figure 8-9 Analysis of linear regression for the displacement at SUAO station 8-22
Figure 8-10 Comparison for the time series of displacement and seismicity activities shown on Figure 8-4 8-23
Figure 8-11 Vertical and horizontal angle of displacement demonstrated in the observed trends 8-24
Figure 9-1 Projected CO2 emission in Taiwan for the different purposes 9-10
Figure 9-2 Map shows topography around Taiwan and west Pacific Ocean 9-11
Figure 9-3 Conceptual model, topographic volume and ocean volume in the target area 9-12
Figure 9-4 Regression of ocean volume and estimated potential CO2 storage quantity 9-13
Figure 10-1 Map shows application area and weather stations KL, AB, PH, WC, HC, and HL in Taiwan 10-13
Figure 10-2 Time series of wind speed 10-14
Figure 10-3 Wind rose diagram 10-15
Figure 10-4 Autospectral density of wind speed for each station 10-16
Figure 10-5 Cross-spectra of wind speed for each pairs of station using PH station as reference 10-17
Figure 10-6 Phase angle and time lag estimated from the cross-spectral density 10-18
Figure 11-1 Vertical profiles in two directions of the building. 11-12
Figure 11-2 Top views of the building. 11-13
Figure 11-3 Top views of the structure. 11-14
Figure 11-4 Estimated best period and damping for channel 1 vs. 19. 11-15
Figure 11-5 Estimated best period and damping for channel 2 vs. 20. 11-16
Figure 11-6 Simulated response related to channel 19 for the event 921. 11-17
Figure 11-7 Simulated response related to channel 20 for the event 921. 11-18
Figure 11-8 Scatter of estimated best period and damping to earthquake magnitude and distance between earthquake source and target construction, after 921. 11-19
Figure 11-9 Regression for estimated best period and damping to PGA. 11-20


List of Tables

Table 2-1 Statistics term 2-13
Table 3-1 Basic data for Huakang Shan site 3-11
Table 3-2 Abbreviation and unit of observed time series 3-11
Table 3-3 Descriptive statistics of observed time series 3-12
Table 3-4 Basic input and output parameters of spectral analysis 3-13
Table 3-5 Significant components evaluated by autospectral analysis 3-13
Table 3-6 Cross-spectral density for groundwater head and seawater tidal level (GWH/HWA-TID pair) 3-14
Table 4-1 Background information 4-14
Table 4-2 Abbreviation of the parameter 4-14
Table 4-3 Descriptive statistics for time series 4-15
Table 4-4 Phase and time lag derived from cross-spectral density for the period 20 4-16
Table 4-5 Relationship between wave variables 4-17
Table 5-1 Specific storage and storage coefficient estimated from spectral analysis 5-17
Table 6-1 Site location 6-14
Table 6-2 Hydraulic conductivity of sand in common cases 6-14
Table 6-3 Estimated hydraulic diffusivity and hydraulic conductivity 6-14
Table 7-1 Case 1: Parameter selection for Pe and tmax 7-15
Table 7-2 Case 1: Expected value, variance, and covariance based on the system parameter data in Table 7-1 7-15
Table 7-3 Case 1: CV of system parameters 7-15
Table 7-4 Case 2: Parameter selection for Pe and tmax .7-16
Table 7-5 Case 2: Expected value, variance, and covariance using the system parameter data from Table 7-4 7-16
Table 7-6 Case 2: CV of system parameters 7-16
Table 8-1 Descriptive statistics for the position displacement obtained from GPS 8-11
Table 8-2 Descriptive statistics for the error of GPS positioning 8-11
Table 8-3 Regression analysis for the position displacement 8-12
Table 8-4 Descriptive statistics for the orientation of position displacement 8-13
Table 10-1 Weather station 10-10
Table 10-2 Summary of prevailing direction for wind speed exceeding 4 m/sec 10-10
Table 10-3 Descriptive statistics of the wind speed 10-11
Table 10-4 Phase and time lag estimated from cross-spectral density function for peak wind speed 10-12
Table 11-1 Descriptive statistics for the best period and damping estimation 11-10
Table 11-2 Pearson product moment correlations and Spearman rank order correlations for the pair of period and damping estimation. 11-11
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