Lippiello Eugenio, Corral Alvaro, Bottiglieri Milena, Godano Cataldo, de Arcangelis Lucilla
Department of Mathematics and Physics and CNISM, Second University of Naples, 81100 Caserta, Italy.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Dec;86(6 Pt 2):066119. doi: 10.1103/PhysRevE.86.066119. Epub 2012 Dec 28.
We present a study of the earthquake intertime distribution D(Δt) for a California catalog in temporal periods of short duration T. We compare experimental results with theoretical predictions and analytical approximate solutions. For the majority of intervals, rescaling intertimes by the average rate leads to collapse of the distributions D(Δt) on a universal curve, whose functional form is well fitted by a Gamma distribution. The remaining intervals, exhibiting a more complex D(Δt), are all characterized by the presence of large shocks. These results can be understood in terms of the relevance of the ratio between the characteristic time c in the Omori law and T: Intervals with Gamma-like behavior are indeed characterized by a vanishing c/T. The above features are also investigated by means of numerical simulations of the Epidemic Type Aftershock Sequence (ETAS) model. This study shows that collapse of D(Δt) is also observed in numerical catalogs; however, the fit with a Gamma distribution is possible only assuming that c depends on the main-shock magnitude m. This result confirms that the dependence of c on m, previously observed for m>6 main shocks, extends also to small m>2.
我们展示了一项针对加利福尼亚地震目录在短时间间隔(T)内的地震间隔时间分布(D(\Delta t))的研究。我们将实验结果与理论预测和解析近似解进行了比较。对于大多数时间间隔，通过平均速率对间隔时间进行重新标度会导致分布(D(\Delta t))在一条通用曲线上塌缩，其函数形式能很好地用伽马分布拟合。其余表现出更复杂的(D(\Delta t))的时间间隔，都以存在大震为特征。这些结果可以根据大森定律中的特征时间(c)与(T)的比值的相关性来理解：具有类似伽马行为的时间间隔确实以(c/T)趋近于零为特征。上述特征也通过对余震序列的流行病型（ETAS）模型的数值模拟进行了研究。这项研究表明，在数值目录中也观察到了(D(\Delta t))的塌缩；然而，只有假设(c)取决于主震震级(m)，才可能用伽马分布进行拟合。这一结果证实，先前在(m>6)的主震中观察到的(c)对(m)的依赖性，也延伸到了(m>2)的小震。
