應用克利金和貝氏法辨識非均質侷限含水層之參數結構

Identification of Parameter Structure for Confined Aquifer by Combining Kriging and Bayesian Approaches

吳呈懋(Cheng-Mau Wu) ； 徐年盛(Nien-Sheng Hsu) ； 李天浩(Tim-Hau Lee)

《中國土木水利工程學刊》 20卷1期 (2008/03) Pp. 45-56

https://doi.org/10.6652/JoCICHE.200803_20(1).0004

摘要

本文建立一套適用於二維、非穩定、異質侷限含水層系統參數結構的辨識方法。利用事先的參數訊息，以克利金法分析均值趨勢與空間分佈參數統計結構，求得一地質統計空間分佈參數結構，然後利用事後訊息（即觀測水頭），以優選模式修正參數結構之係數，求取最佳的空間分佈統計結構。數值實例以Yeh和Yoon(1983)的例子來辨識流通係數，結果顯示本方法只需要少量的事先參數訊息和事後訊息就能辨識出合理的參數空間分佈結構。文中亦探討事先參數訊息和事後訊息兩者數量與辨識度的關係，當事先參數訊息達到11.7%以上，對地質統計空間分佈參數結構模式，就能達到收斂的效果，參數辨識也得到很好的結果。

關鍵字

參數辨識方法 ； 克利金法 ； 貝氏估計法 ； 事先訊息 ； 事後訊息

並列摘要

A methodology is developed for parameter identification in an isotropic, inhomogeneous and confined aquifer system. The parameter chosen for identification is the spatially distributed transmissivity. We first use prior information of observed transmissivities at a limited number of locations to determine the transmissivity structure by the geo-statistical method of Kriging. That is, parameterization is achieved by Kriging and the inverse problem now seeks to identify the coefficients associated the geo-statistical parameter structure. We then use posterior information of observed heads to determine the coefficients. The proposed methodology can be considered as Bayesian estimation since it incorporates the prior and posterior information. The developed methodology is tested using the hypothetical aquifer of Yeh and Yoon (1983). The results obtained show that a better fit can be obtained if a polynomial drift function and an exponential type of semivariogram are used to characterize the random variable of transmissivity. A comparative analysis is made between the identified transmissivity and the true transmissivity distribution. The results indicate that the inverse solution captures the true transmissivity distribution using only the prior information and a limited number of head observations.

並列關鍵字

parameter identification ； Kriging ； Bayesian estimation ； prior information ； posterior information