PI (pattern informatics)為Rundle及Tiampo等人於2002年發表之計算方法，用以評估區域地震活動異常，並已應用於地球上地震活動最活躍的數個區域，如美國加州及日本中部地區。由PI方法所評估的地震活動異常分布其有效性主要奠基於兩個統計穩定的前提: (1)研究區域內的長期平均地震總數維持近乎定值，而僅有微幅振盪(2)將研究區域等分為若干格子並分別計算每一格子中單位時間內的地震個數(地震發生率, seismic rate)，則此地震發生率-格子數的統計分布需維持穩定，意謂分布的平均數及標準差需維持近乎定值。然而，在先前的研究中(Rundle et al.,2002; Tiampo et al., 2002; Nanjo et al., 2006)未曾探討過上述兩個前提是否成立，因此無法判斷所提出的地震活動異常是否來自統計振盪的影響，進而損害評估結果的可靠度與客觀性。
另一方面，分析真實地震活動即可發現其統計分布為顯著的右偏分布。右偏分布的特性為平均及標準差的值非常容易受到離群值的加入而產生顯著變動，而此統計特性顯然與PI的計算的基本前提相悖。有鑑於此本研究使用Thirumalai-Mountain (TM) metric探討台灣中央氣象局(Central Weather Bureau, CWB)地震目錄中存在具實質遍歷性(effective ergodicity)的時間段的可能性。根據統計力學的定義，遍歷性為統計平衡系統的特性之一。一旦系統證實達到統計遍歷性，此系統中特定物理量的統計分布可維持長時間穩定，並不因系統隨時間的演化而顯著改變其統計分布的形式及相對應的平均及標準差值。本研究發現使用1973~1986年的地震目錄於TM metric的計算中會使TM metric的倒數值產生巨幅振盪，顯示此時間段內的地震資料並不具有穩定的統計分布。當TM metric的計算中僅使用1987年之後的地震資料，本研究發現台灣地震目錄中存在數個於具統計穩定性的時間段。若使用PI評估這些時間段中的地震活動異常，其評估結果可合理排除統計擾動的影響，而視為肇因於純粹的地震活動變化。
本研究實踐此概念於PI計算中並發現，在1996/10~1999/8之間，1999年台灣集集地震的主震及較大餘震發生區域內地震活動呈現顯著的異常。另一方面，若使用不具統計穩定性的時間段(1994/7~1999/8)評估地震活動異常，則相同區域內的地震活動並未呈現顯著的異常。此活動異常的改變顯示，使用原版的PI評估的地震活動異常確實明顯受到統計分布的振盪影響。地震活動固有的右偏分布所產生的統計不穩定並無法藉由TM metric的協助得到全然的改善。
有鑒於原版PI極易受到統計振盪的顯著影響，本研究進一步修改原有PI的計算步驟，主要包括: (1)使用地震發生率變化(change of seismic rate)作為統計量，其統計分布通常以0為中心呈現約略對稱，(2)導入空間標準記分以消除不同構造所產生的地震活動程度差異。針對1999年台灣集集地震的研究，陳建志(2003)發現在集集地震發生前台灣地區的全區域地震活動具有地震活化假說(Rundle et al., 2000)的特徵，中等規模的地震(M≧5.0)其發生頻率隨時間接近集集主震而逐漸增加。本研究利用修改版PI評估發生於中等規模地震頻率增加最顯著的時間段，1993/11~1999/6之間的地震活動異常分布，發現地震活動異常最顯著的區域涵蓋了集集地震的主震及多數的大規模餘震。此一結果顯示地震活化可能是集集地震前可能的前兆現象之一。
為進一步克服主觀選擇重要參數及預先辨識前兆現象的困難，本研究中也提出了結合修改版PI及基因演算法(GA)的策略，希望在不進行任何人為的選擇、調整及測試之下，客觀地檢驗大地震前是否確實存在前兆性的地震活動異常，如地震活化或地震寧靜。一旦經由PI辨識出與目標地震的主餘震分布相似的地震活動異常，可更進一步的探討此異常是否具有任何已提出的前兆機制之特徵。結合PI及基因演算法的策略應用於2008年中國汶川地震發現，與1984/10~2001/9的地震活動相比，2001/10~2008/1之間地震活動異常較顯著的區域其空間分布與汶川地震的主餘震分布相似。進一步探討其特性發現，1984/10~2001/9與2001/10~2008/1的地震活動其Gutenberg-Richter規模-頻率曲線具有地震活化假說的特徵。本研究認為1999年台灣集集地震與2008年中國汶川地震皆可視為地震活化的範例。

Pattern informatics (PI) is developed by Rundle and Tiampo et al. in 2002 as a calculation method to evaluate seismic anomalies and is already applied in several researches to high seismicity regions, such as California and Japan. However, two fundamental premises of PI about statistical stability of seismicity are rarely concerned in previous researches. This disregard led to serious doubt about these published results. On the other hand, the contradiction between the fundamental premises of PI and real seismicity also results in further difficulty in applying PI to Taiwanese seismicity.
We applied Thirumalai-Mountain (TM) metric to identify the effectively ergodic intervals in Taiwanese seismicity. Seismicity in the identified effectively ergodic intervals are stable in statistical distribution and can be used to evaluate seismic anomalies disregarding statistical fluctuations. Through several tests we concluded that the original PI is very sensitive to statistical fluctuations and can’t be improved merely by the assistance of TM metric.
On the other hand, we modified the original PI by using average seismic rate change as statistical quantity and by introducing spatial normalization to cease the inherent difference of seismicity due to tectonic environment. A seismic activation process before the 1999 Chichi earthquake is proposed by Chen in 2003. We used the modified PI to identify the distribution of seismic anomalies corresponding to the seismic activation. The identified seismic anomalies marked most of the locations of the Chichi main shock and big aftershocks.
To overcome the difficulty of identifying precursory phenomenon and parametric selection, we used a combination of modified PI and genetic algorithms (GA) to objectively confirm the existence of precursory seismic anomalies before big earthquakes without any manual selection, tuning, or tests. Once the seismic anomalies are obtained, we can further explore which underlying forecasting mechanisms result in these anomalies. This strategy is successfully applied to the research for the 2008 Wenchuan, China, earthquake and identified this catastrophic earthquake as another example of seismic activation.

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