伊朗中部阿尔博尔兹地震的多重分形分析一个唯象的自组织临界模型
Multifractal analysis of Earthquakes in Central Alborz, Iran; A phenomenological self-organized critical Model
摘要：
本文对伊朗阿尔博尔兹中部地震进行了唯象研究。使用三个观测量，即权重函数，品质因数，和速度模型在这一地区，我们开发了一个唯象耗散沙堆模型，捕捉系统的主要特征，特别是在研究区域的平均活动场。该模型是基于外部刺激，其位置被随机选择（\textbf{I}），（\textbf{II}）的故障，（\textbf{III}）的高度活跃的点在该地区。我们分析了所有这些情况下，并显示了一些普遍的行为的系统略有依赖于外部刺激的方法。利用多重分形分析提取的Hurst指数的时间序列的频谱由这些方案。虽然平均赫斯特指数取决于方法的刺激（上述三种情况下），我们数值表明，在所有情况下，它是低于$0.5$，反映了反相关的系统的性质。最低的平均Hurst指数是针对情况（\textbf{III}）的，以这样的方式，刺激的地点越活跃，获得的平均Hurst指数的值越低，即，较大的地震与地震的相关性越大。然而，本研究中的不同活动场提供了基底的深度、基底的深度变化（地形）以及可以成为未来概率事件位置的区域。
英文摘要：
This paper is devoted to a phenomenological study of the earthquakes in central Alborz, Iran. Using three observational quantities, namely weight function, quality factor, and velocity model in this region, we develop a phenomenological dissipative sandpile-like model which captures the main features of the system, especially the average activity field over the region of study. The model is based on external stimuli, the location of which are chosen (\textbf{I}) randomly, (\textbf{II}) on the faults, (\textbf{III}) on the highly active points in the region. We analyze all these cases and show some universal behaviors of the system depending slightly on the method of external stimuli. The multi-fractal analysis is exploited to extract the spectrum of the Hurst exponent of time series obtained by each of these schemes. Although the average Hurst exponent depends on the method of stimuli (the three cases mentioned above), we numerically show that in all cases it is lower than $0.5$, reflecting the anti-correlated nature of the system. The lowest average Hurst exponent is for the case (\textbf{III}), in such a way that the more active the stimulated sites are the lower the value for the average Hurst exponent is obtained, i.e. the larger earthquakes are more anticorrelated. However, the different activity fields in this study provide the depth of the basement, the depth variation (topography) of the basement, and an area that can be the location of the future probability event.
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