由於複雜為災害的基本特徵，因而採用複雜性科學方法為目前常見解析災害系統的工具之ㄧ。本研究以複雜科學為出發點，著重於災害時、空序列之特性探討及估測方法建立與應用，其中有六個主題為文中所欲探究者，分別為：(1)模擬與真實災害序列之長期記憶性解析；(2) 短序列估測模式建立與災害時間序列之應用；(3) 災害發生時間之複雜性與自組織臨界探討；(4) 以空間複雜性探究地震發生之空間分布自組織與複雜性；(5) 複雜地形之非均向性參數與地質特性相關解析與分區；(6) 時空序列之雙向分解法建立及其應用。

　　在模擬與真實災害序列之長期記憶性解析方面：對模擬與自然序列進行Hurst指數分析，說明災害序列具長期記憶效應。且門檻值越高或災害越大者，其記憶特性越不明顯。又於模擬與實際地震災變資料之研究，發現Hurst指數於建模或預測前可提供相關前置訊息以得至較確切的結果。於災害發生時間之複雜性與自組織臨界探討方面：經複雜性參數之計算與分析，顯示規模越大或越極端之災害時間序列的複雜性較強，所形成的時序資料於時間軸上不均勻分布。而在異常事件發生前，產生自組織臨界特性，具有高度變異勢能與高複雜。只要有一小的變動或偶發事件，隨之產生大規模崩解效應或連鎖反應，即遽變產生。在以空間複雜性探究地震發生之空間分布自組織與複雜性方面：地震空間複雜性參數均以二維平面歷程加以計算，其結果傾向低維度，顯然台灣地震發生之空間分佈受到構造之影響甚鉅，此一特性時間序列分析結果相同。透過聚類分析，可發現自組織臨界蘊含有勢能差異之特性，可區分高、低勢能不同之地震，並可驗證複雜系統之脆性組織過程。又複雜地形之非均向性參數與地質特性相關解析方面：由研究中參數之計算結果，顯示台灣地形系統似乎並不如想像中複雜，且此些參數分佈具六個不同方向的異向特性，每個方向似有其相擬合的地形與地質意義。渾沌吸子之分群顯示最少之解釋變數，亦合乎地形系統構成要素。以台灣地區構造線、岩性以及山脈分佈線等線形之分佈為東北─西南向，吸子為2；而70°至130°的剖面，反映出台灣受板塊運動之應力所推擠的方向，並垂直線形方向，吸子為4，此可視為渾沌動力學分區並與估測結果比對。在短序列估測模式建立與災害時間序列之應用方面：應用灰色預報過程於模擬災害序列，並推導R/S估測法，又為增加其估測效能，因而又導入灰色理論推得灰色結合R/S估測法。發現災害序列均顯示灰色結合R/S估測法較R/S估測或灰色預報為佳。此外，於時空序列之雙向分解法建立及其應用：所推演之雙向分解法對自組織與渾沌動力學分區的災害估測具相當的成效與適用性，且於選擇估測模式上可有較大彈性，若資料具多變量型態時可進行雙向修正。

　　由上結果可得知，災害序列之複雜特性分析可說明序列本身具記憶性與自組織特性。記憶性與自組織特性有利於估測過程，經模擬與自然災害序列估測均驗證灰色結合R/S估測法與雙向分解法的估測效能。

　It is the essential feature of the calamity to be complicated. Adopting the scientific method of complexity is one of the tools of common analysis for calamity system at present. Therefore, regarding complex science as the starting point and focusing on the characteristic discussion, model establishment and application of the spatial-temporal calamity series in this studying six topics are concerned and described as follows: (1) long term memories of simulation and true calamity series are analytic, (2) discussion of time takes place in the calamity by complexity and self-organization critical, (3) exploration of self-organized and complex distribution of earthquake by space complexity, (4) relational analysis and regionalization of anisotropic properties of complex parameters and geologic significance, (5) estimative modeling of shirt series and its application of calamity time series, (6) combination model establishment and its application of space-time series.
The study of long term memories of simulation and true calamity series, the Hurst exponent value of simulation and true calamity series are analyzed. The results show that the calamity series hold a strong long-term memory effect. The less obvious of the memory characteristic when the higher threshold value of series or the greater calamity are calculated. Furthermore, according to the case study of both simulated and real earthquakes, more accurate results could be acquired if Hurst exponent can provide relative leading information before the modeling and forecasting. On the discussion of time takes place in the calamity by complexity and self-organization critical, the complexity parematers are calculated and analyzed. It shows that the series of larger scale or grater calamity hold a strong complex feature. The higher threshold value represents the more extreme calamity, and the distribution of series is not uniform in time axis. Before the extraordinary events, it appeared self-organization critical with high variant entropy and complexity. The abrupt variation occurred when small change or sudden event, and a large scale avalanche or a chain reaction will follow. On the exploration of self-organized and complex distribution of earthquake by space complexity, the 2-D complex parameters of earthquake in space are calculated. The lower dimension represents that the tectonic influence in space distribution of earthquake of Taiwan is very great. The result is the same as time series analysis. According to clustering analysis, the self-organization critical represents the feature of different entropy of earthquake, and it will be use to separate earthquake. It shows that the variant complexity represent the change of entropy. The higher entropy and complexity occur in extremely critical events and demonstrate the brittle process of complex system. On the relational analysis of anisotropic properties of complex parameters and geologic significance, the results show that the topographic system does not reveal a high complexity. Different anisotropic characters in complexity parameters are observed along 6 different directions, and it seems that causing by a specific geologic process and/or geomorphologic process. The grouping of chaotic attractor represents the variance required for the interpretation of the elements of topographic system. From the geologic point of view, the linear distribution in structure, lithology and mountain ranges is the direction of NE-SW, and the attractor is 2. The sectors between 70° and 130° have an interpreting variance of 4, the highest value in Taiwan area, reflects the complexity caused by the tectonic movements. On estimative modeling of short series and its application of calamity time series, using gray theory and forecasting simulated calamity series. The R/S forecast method is developed, furthermore, it combining with gray theory to increase the potency of forecasting. The combination of gray theory and R/S method shows an even higher adaptability than R/S and gray method in the forecasting of simulated and natural calamity series. Furthermore, on the two-way decomposition analytical method establishment and application of disaster series, the results show that the effectiveness and suitability are proved by the forecasting of space-time series from the two-way decomposition process, and there is more flexible in choosing model for forecasting. It can be revised two-way when data are the type of multivariable.

　Concluding, the calamity series hold long-term memory and self-organization critically that analyze by complex analyses and contribute the results to data forecasting. According to the forecasting, modeling and natural data, the results show that the effectiveness and suitability are proved from the combination of gray theory and R/S method and the the two-way decomposition process.

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