本研究針對fLm碎形隨機非均勻場提出通用碎形水流及傳輸模式，並發展現地不規則分佈資料點分析方法，求取fLm碎形地質模式所需之模式參數，用以探討現地水文地質參數之空間分佈特性，最後以桃園龍潭核能研究所之現地資料為例。研究結果顯示fLm模式比傳統之fBm模式更適合描述該場址水力傳導係數場之高度非均勻性分佈，fLm模式為傳統fBm模式之通式，瞭解fLm模式之相關水流及傳輸行為將有助於序率理論在地下水水流與傳輸領域之發展。本研究針對fLm模式推導獲得具有上下界限之冪指數型變差函數，本冪指數型變差函數適用於Hurst係數介於(0,1/alpha)，在此alpha為Levy指數，本研究利用最小擾動法獲得速度場共變異函數、溶質位移場共變異函數及巨觀延散係數之一階近似解，最後針對穩態指數模式、非穩態fBm及fLm模式之結果進行分析與比較。在水流行為分析上，研究結果指出fLm模式在短距離時，縱向及橫向之速度場共變異函數具有最快之遞減速率，但隨著距離逐漸增大亦最慢趨近於0；在傳輸行為分析上，不論fBm或fLm模式，當分離距離達到極大時，縱向位移場共變異函數呈現一固定增加之速率，但橫向位移場共變異函數卻與分離距離呈現對數增加之趨勢，其中fLm模式之對數增加速率大於fBm模式。研究結果並指出當分離距離達極大時，fLm模式之縱向延散度成長與積分尺度之1+alpha*H次方成正比，小於fBm模式之1+2H次方，顯示使用fLm模式所獲得之污染團成長速率將小於fBm模式與穩態指數模式，意指在固定觀測時間下，使用fLm模式將會比fBm模式與穩態指數模式獲得分佈範圍較小但濃度較高之污染團分佈。因此，選擇合適之水文地質序率模式對於水流及傳輸行為預測之準確性與可靠性將具有關鍵性之影響。

This dissertation investigates flow and transport in heterogeneous random field with fractional Levy motion model. We proposed a method of site characterization using the fractional Levy motion (fLm) model for sites with irregularly spaced data. The method was applied to a potentially polluted site in Tao-Yuan, Taiwan. Results show that the fLm model describes the highly heterogeneity well in Tao-Yuan site. Then, a generalized fractal model of flow and transport in the fLm field was proposed. The fLm model is a generalized version of the traditional fractional Brownian motion (fBm) and is superior to describe a highly heterogeneous field. Understanding flow and transport in such fields expands the applicability of the stochastic theory. The authors derive the truncated power variogram in the fLm field. The variogram is valid for Hurst coefficient in the range of (0,1/alpha) where alpha is the Levy index of fLm. The first-order analytical solutions of velocity covariance, displacement covariance and macrodispersion coefficient in the fLm field are derived by using small perturbation method. The spatial correlation of log hydraulic conductivity and behavior of flow and transport are compared for the stationary exponential, non-stationary fBm and fLm fields. Both of the longitudinal and the transverse velocity covariances in the fLm fields show the fastest decreasing rate at short separation distance and diminish to zero slowest at largest separation distance. The longitudinal displacement covariance has a constant increasing rate at large separation distance for both the fBm and the fLm models. The logarithmic increasing rate of the transverse displacement covariance at large separation distance for the fLm model is faster than the fBm model. The longitudinal macrodispersivity in the fLm field is proportional to 1+alpha*H that is smaller than 1+2H in the fBm field at large separation distance. The asymptotic transport in the fLm field is reached slower than others in the fBm and the exponential fields. Predicting plume size will grow slowest but with the highest concentration for the fLm model than the fBm and the exponential models. The appropriate stochastic model is important toward to more accurate modeling results.

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