地震破裂普遍被認為發生在極其異質的應力環境下並涉及摩擦滑移的不穩定性，其複雜與非線性的本質仍是現代地震學許多關鍵議題的核心。鑑於前人研究中所歸納的橫跨岩石剪切實驗與現地地震觀測的尺度不變性，我們將地震破裂視為隨機過程、建立控制此過程的隨機動力學方程式，並基於資訊理論對系統的無序程度進行量化。從一個以摩擦失效類比破裂的一維滑塊模型出發，我們基於朗之萬的方法將破裂過程中動量的傳遞簡化為一馬可夫過程，並使用代表性布朗粒子在速度空間中的軌跡對破裂前緣所發生之剪切滑移的動量狀態之隨機擾動進行描述。透過將代表性布朗粒子的受力拆分為決定性(古典)和隨機(熱動力學)力，多體系統中的力學問題變得實務上可解。我們根據所提出的朗之萬方程式生成大量的樣本路徑，並對相應的福克－普朗克方程式解析求解。結果顯示，系集統計分布的解析解與地震滑移分布的經驗性定律相吻合，而樣本路徑的分析結果則呈現一個在廣泛參數條件下通用且符合區域及全球範圍內地震統計的能量(矩)－持續時間尺度定律。資訊分析結果則顯示，樣本路徑的費雪－夏農表徵可有效區別不同的背景摩擦耗散機制，並能幫助解釋岩石摩擦學的滑動表面結構以及潤滑狀態。總結來說，本研究基於隨機動力學模型為地震斷層之摩擦耗散過程提出一個新的描述框架與相關見解，並展示資訊理論的分析工具在研究地震環境下的岩石磨耗之應用潛力。;Earthquake ruptures are generally considered to occur in extremely heterogeneous stress environments and involve the instability of frictional sliding.Their complex and nonlinear nature remains at the core of many key issues in modern seismology.Given the scale invariance summarized from previous studies across rock shear experiments and field earthquake observations, we regard earthquake rupture as a stochastic process, establish a stochastic dynamic equation governing this process, and quantify the disorder of the system based on information theory.Starting from a one-dimensional slider model that analogizes rupture as frictional failure, we employ the Langevin approach to simplify the momentum transfer at the rupture front as a Markov process. We use the trajectories of representative Brownian particles in velocity space to describe the fluctuation of the momentum of shear slip at the front where the rupture sweeps by. By decomposing the forces acting on the representative Brownian particle into deterministic (classical) and stochastic (thermodynamic) components, the mechanical problems in multi-body systems become practically solvable. We generate a large number of sample paths based on the proposed Langevin equation and solve the corresponding Fokker-Planck equation analytically. The results show that the analytical solutions of the ensemble statistical distribution coincide with the empirical laws of earthquake slip distribution, and the analysis of sample paths reveals a universal energy (moment)--duration scaling law that aligns with regional and global earthquake statistics under a wide range of parameter conditions. The results of informational analysis indicate that the Fisher-Shannon characterization of sample paths can effectively distinguish different background frictional dissipation mechanisms and help explain the structure and lubrication state of sliding surfaces in rock friction. In summary, our study proposes a stochastic dynamic model that offers a new descriptive framework and insights into the frictional dissipation processes in earthquake faulting, demonstrating the potential application of informational analysis in studying the behavior of rock shearing in seismogenic environments.
