Title

序率分析應用於地球科學研究

Translated Titles

Application of Stochastic Analysis to Geosciences

DOI

10.6342/NTU.2008.00305

Authors

施清芳

Key Words

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 ; geosciences ; stochastic ; spectral analysis ; uncertainty ; regression ; groundwater ; earthquake ; Rayleigh wave ; GPS ; CO2 deep sea sequestration ; seabed topography ; wind characterization ; one-degree-of-freedom vibration

PublicationName

臺灣大學地質科學研究所學位論文

Volume or Term/Year and Month of Publication

2008年

Academic Degree Category

博士

Advisor

吳逸民

Content Language

英文

Chinese Abstract

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。

English Abstract

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.

Topic Category 基礎與應用科學 > 地球科學與地質學
理學院 > 地質科學研究所
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Times Cited
  1. 李躍斌(2016)。應用短時距傅立葉轉換於地下水位資料補遺。交通大學土木工程系所學位論文。2016。1-107。