為有效掌握空間變異的組成而提昇估計的準確度，以趨勢面分析區分出土壤中重金屬濃度空間變異的決定性變異，將趨勢面分析法結合克力金法來估計重金屬濃度的分佈，且與趨勢法、克力金法一同比較估計的準確度。另一方面，為避免了傳統地理統計法的平滑效應(Smooth effect)，也希望對土壤中重金屬分佈的不確定性加以測定。因此以序列高斯模擬(Sequential gaussian simulation, SGS)與序列指標模擬(Sequential indicator simulation, SIS)對土壤中重金屬濃度空間分佈進行模擬，且探討樣品數據、克力金估值、模擬估值三者的差異。
研究區域有二：A研究區位於新竹縣市境內面積約200平方公里，以間距1公里規則採取89個樣本，以0.1N HCl可抽取土壤鉛濃度資料進行趨勢結合克力金法之探討；B研究區位於A研究區內面積約2.5平方公里，以間距100公尺規則採取149個樣本，以0.1N HCl可抽取土壤鉛濃度資料進行序機模擬之探討。
經均值比較發現在A研究區中工廠或河流的存在與否對鉛濃度有顯著影響，因此工廠及河流的存在對鉛濃度造成趨勢效應，遂進行趨勢面分析。經交叉驗證發現三種估計方法所得鉛濃度的均方誤差而言，趨勢結合克力金法小於克力金法小於趨勢法，即趨勢克力金法有較佳的估計準確度。
序機模擬結果顯示B研究區鉛濃度數據不符合序列高斯模擬的雙高斯分佈的基本假設，而改以序列指標模擬繁衍鉛濃度模擬估值。樣本數據的平均值、變異數、偏歪值、峰度值四種統計介量與1000次聯合序列指標模擬估值的平均值、變異數、偏歪值、峰度值四種統計介量的平均值相近，但與克力金估值的統計介量有相當差異。比較樣本數據的分佈直方圖及1000次聯合模擬估值的平均分佈直方圖，發現兩者整體分佈類似，但聯合模擬估值在10 mg/kg到30 mg/kg出現的比率較樣本數據高，而克力金估值與其他兩者的分佈直方圖則有相當差異；比較樣本數據的標準化半變異圖與聯合模擬估值的平均標準化半變異圖，在短距離內，樣本數據的標準化半變異圖與聯合模擬估值的平均標準化半變異圖相當一致，唯隨距離的增加，模擬估值的半變異數逐漸超過樣本數據的半變異數；而克力金估值半變異圖的碎塊效應不明顯，半變異數有逐漸上昇的趨勢。

The spatial variability of heavy metal concentrations in soil consists of three components : systematic variation (i.e. trend), spatial dependence, and random variation. Understanding the conponents of total variability of the spatial variables is important for estimation. In the first part of this study, we extract the systematic variability from the total variability of soil heavy metal concentration by trend surface analysis.The spatial distribution of heavy metal concentrations estimated with kriging combined with trend surface analysis was compared with those estimated using kriging, and trend surface analysis. Mean square of error (MSE) of cross validation was used to evaluate the estimation accuracy of the three methods. In the second part of this study, we use a probability approach to model the uncertainty of the spatial distribution of soil heavy metal concentration in order to prevent smooth effect usually occurred in geostatistical interpolation algorithm. Sequential gaussian simulation (SGS) and sequential indicator simulation (SIS) were used to estimate the spatial distribution of soil heavy metal concentration.The simulated estimates by SIS were compared with kriging estimates and oringinal sample data.
There are two data sets used in this study：One data set from site A is in an area of 19600 ha in Hsing-Chu county ; the interval of sampling points are 1000 m and there are 89 soil samples collected at each sampling location to a depth of 0-15 cm. The 0.1N HCl extractable soil Pb concentrations in site A were used in the first part of this study. The other data set from site B in an area of 250 ha which is a subsite located in site A ; the interval of sampling points are 100 m and there are 149 soil samples collected at each sampling location to a depth of 0-15 cm. The 0.1N HCl extractable soil Pb concentrations in site B were used in the second part of this study.
In the first part of this study, the results showed that the existence of plants or rivers influences the soil Pb concentrations, so there was systematic variability existed in Pb concentrations. The results of cross validation showed that the MSE of kriging combined with trend surface analysis was smaller than those of kriging, and trend surface analysis. It indicated that kriging with trend surface analysis could estimate spatial distribution of soil Pb concentrations more accurately than the other two methods.
In the second part of this study, we found that Pb concentrations in site B were not corresponding to two-point Gaussian distribution, and therefore used SIS to estimate its distribution in stead of using SGS. The SIS simulated estimates were similar in mean, variance, skewness, and kurtosis to sample data, however, the statistic parameters of kriging estimates were not similar to those of the sample data. The simulated estimates were similar in histogram to sample data, and the frequency of SIS simulated estimates accurred in the range of 10 mg/kg to 30 mg/kg was higher than the sample data. The kriging estimates were not similar in histogram to sample data. The simulated estimates were similar in semivariance in short distance to sample data. The more increasing distance, the more increasing semivariance in SIS simulated estimates than in the sample data. The nugget effect of kriging estimates is smaller than that of the sample data and the semivariance of kriging estimates increases with distance.

第一章 緒論 1
第二章 原理 6
第一節 區域化變數理論 6
第二節 克力金法 11
第三節 指標克力金法 14
第四節 非定常性資料的分析 16
第五節 序機模擬 18
第六節 序列高斯模擬 23
第七節 序列指標模擬 31
第三章 材料與方法 34
第一節 研究材料 34
第二節 資料分析與研究方法 35
第四章 結果與討論 46
第一節 趨勢面分析結合克力金法之探討 46
第二節 序機模擬之探討 70
結論 108
參考文獻 110

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