斷層嵌塊的自我相似性

Abstract

若地震具備自我相似性，則不同大小的地震表現出來的物理性質會保持一定的比例關係，這對震源物理的了解和災害的評估有很大的幫助。地震的自我相似性被很多研究證實，但也存在著爭議。自我相似性的指標之一為靜態應力降不隨地震矩或規模改變。本論文針對地震斷層面上的嵌塊，而非地震本身，進行應力降分析。因為斷層嵌塊主導著破裂過程，而且其形狀更接近常用的理論圓形破裂，研究斷層嵌塊別有意義。 本論文搜集了28個規模大於5、震源深度淺於50公里的地震之震源破裂模型，以高斯函數來近似嵌塊上的滑移量分佈以定義嵌塊的位置與大小，共得到70個嵌塊，再由滑移量與面積計算每個嵌塊的地震矩與應力降。另外也使用矩形模擬嵌塊，應力降分佈趨勢與圓形並無明顯差異。 本研究發現，在地震矩10^15∼10^23 N-m的範圍內，應力降的分佈雖然紛亂，但平均值約在14MPa而不隨規模改變，證實斷層嵌塊具備自我相似性。在地震矩< 10^20 N-m (規模<7)處，應力降散佈在0.5∼1000 MPa，當地震矩>1020 N-m，由幾個大地震得到的應力降趨於穩定在3∼10 MPa左右。從台灣地區的數據得知，同一個地震多個嵌塊的應力降彼此之間差異很小，而不同地震的應力降之間的差異隨地震相隔距離增加而增加。這個現象暗示小尺度的構造與力學變化在決定 時，可能扮演了重要的角色。

Every earthquake has a set of physical parameters and a unique rupture process. However, the macroscopic representation of an earthquake may follow a simple rule regardless of event magnitude and rupture dimension. Some studies suggested that a simple self-similarity relationship may exist for earthquakes of all size, i.e., energy for large earthquakes can be scaled from that of small earthquakes. Other studies argued against this simple rule. Self-similarity can be expressed in different forms, depending on the observations. In our study, we focus on two seismic parameters: seismic moment and static stress drop. Finite fault slip models show that the slip distribution over the fault plane is often heterogeneous with slip concentrated on asperities. Thus, identities of asperity should be an important role in fault rupture and closely linked with the whole source. We investigate scaling relations of asperities based on 28 finite fault slip models. We determine the location and dimension of 70 asperities by circular and rectangular approximation, and calculate the associated M0 and stress drop. We found that stress drop determined from asperities are overall constant with respect to moment, implying the self-similarity exists for asperities over an moment range of 10^15~10^23 N-m, especially in M0 > 10^20 N-m (Mw > 7). We infer that the scattered stress drop appears in M0 < 10^20 (Mw < 7) highly depends on local tectonics.