沙堆模型一直以來是探討地震孕育過程很重要的數值模型。原始的沙堆模型（Bak et al., 1987）考慮近距離傳遞能量的過程，表現系統「自組織臨界（self-organized criticality）」的特性。然而，真實世界中，大地震所釋放的能量極可能有遠距的影響，因此本研究以原始沙堆模型為基礎，利用1998年Watts and Strogatz提出的「小世界網路（small-word network）」理論，考慮遠距傳遞能量的過程，建立一個全新的沙堆模型，稱之為「遠距沙堆模型（Long range connective sandpile model）」。本研究利用該模型模擬數值地震B值（事件發生率與事件大小間冪律關係之斜率）的變化，並進一步探討地殼系統的巨觀統計行為。 Gutenberg-Richter law之斜率b值，為地震時間序列最常被探討的統計物理參數。b值可反應大地震與小地震之間其發生率的關係。經由前人研究發現，在大地震發生前，經常可以觀測到b值下降的前兆行為。本研究藉由遠距沙堆模型，同樣可以表現該前兆行為。此外，本研究亦探討遠距沙堆系統中「赫斯特指數」的漲落，該指數可表現時間序列的長程趨勢。研究結果發現遠距沙堆模型之赫斯特指數（H值）與B值呈現負相關的特性，且負相關的強度會依賴於「時間窗尺度」與沙堆模型大小的選取。B值下降與H值上升，均可視為遠距沙堆模型中大沙崩事件的前兆行為。同時，我們發現在真實地震目錄中，同樣可以表現類似的行為。 本研究進一步利用熱力學相變的概念，探討地震孕育的過程，並藉由遠距沙堆模型，對大震前b值下降的前兆行為，給予一個可能性的解釋。當地殼系統累積足夠的能量時，空間上的「相關長度（correlation length）」漸增，遠距傳遞能量的過程使得中型地震增多，小地震減少，因此在大震前可以得到b值下降的前兆行為。在大地震發生後，由於地殼系統瞬間釋放了大量的能量，「相關長度」瞬間縮短乃導致中大地震發生潛勢減低，能量多藉由小地震釋出，故b值漸增。b值的變化，則反應系統在穩態與非穩態間的轉變，表現了地震斷層系統的「陣發性臨界（Intermittent criticality）」行為。 過去研究發現，原始的沙堆模型可以表現類似地震的Gutenberg-Richter law特性，乃使許多物理學家相信，地殼是一種自組織臨界系統，當自組織臨界系統在累積能量的過程中，系統會穩定地存在於臨界狀態。但此模型難以表現出地震的前兆現象，其中大崩沙事件以隨機方式產生，導致許多研究學者認為「地震為不可預測之系統」。然而，遠距沙堆模型同樣表現了地震的Gutenberg-Richter law特性，但該模型的陣發性臨界性，則使系統在大崩沙發生前，出現了B值下降的前兆行為。本研究所建立的遠距沙堆模型，該模型存在與原始沙堆模型截然不同的物理特性。 The sandpile model (Bak et al., 1987) is very well known as the numerical earthquake model. The motivation of building the long-range connective sandpile model is earthquake triggering. Base on the concept of small-word network, we modify the original BTW sandpile model. We call it is long range connective sandpile model (LRCS model). The b values (from Gutenberg-Richter law) decay before big earthquake is an important precursor. We try to explain why we have such precursor before big earthquake. In this study, we simulate the behavior of the B values (the slope of the frequency-size power-law distribution by numerical model) decay before big event by LRCS model. In the other way, we also calculate another parameter "Hurst exponent". We can get the negative relation between B value and Hurst exponent in the LRCS model. When the size of sandpile model is larger, the negative relation between B value and Hurst exponent is more conspicuous. By the thermodynamic concept, we explain that the b value decay before big earthquake is caused by the correlation length increasing. When the system is up to meta-stable, longer correlation length makes more intermediate earthquakes occur. That's why we can get the precursor of b value decay before big earthquake. Further, the negative correlation between b value and Hurst exponent in the earthquake system means that the earthquake system will have persistence behavior when it is up to meta-stable. The original BTW sandpile model is characterized by the frequency-size power-law distribution. Earthquakes have been identified as an example of this phenomenon in nature (Bak and Tang, 1989; Sornette and Sornette, 1989; Ito and Matsuzaki, 1990) and the observation of the Gutenberg–Richter law has been suggested to be the manifestation of the self-organized critical (SOC) state of the dynamics of the earthquake faults. The state of the SOC system will keep staying in the meta-stable state. In this system, big events will occur randomly. So many researchers believe earthquake is unpredictable. Both of the original BTW sandpile model and LRCS model have frequency-size power-law distribution. But BTW sandpile model is difficult to show precursor before big event. The LRCS model can show the intermittent criticality behavior. The state of the system will change between meta-stable and non-meta-stable. Intermittent criticality system can have precursors before big event. This study supposes that the earthquake is an intermittent criticality system.
