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假定地震是随机点过程的实现,并且全部地震的震级分布都遵从6为常数的古登堡一里克特定律,通过传染性模型,我们对地震的时空发生率密度进行了模拟。发生率密度是通过两项求和计算的,一项代表独立或者说自发的活动性,另一项代表由先前地震诱发的活动性。第一项只与空间有关,而第二项依赖于三个因素,包括已发生地震的震级、时间和位置。本文中,对时间项我们使用修正后的大森定律,重点研究震级和空间项。对于每一项,我们形成了两种不同的假设,并且根据1987年到2000年意大利仪器记录地震的目录,分别找出了各自的最大似然参数。对2001年纪录的地震活动性计算了各自的可能性并进行了比较,这为找到最佳模型提供了一个途径。对各种假设进行蒙特卡罗模拟,由此来评估我们选择的假设的可信度。我们的研究表明,对于空间分布,反向幂密度函数比正态密度函数更可靠,而余震发生对于震级的尺度不变性假设可以在高可信水平上被拒绝。最终的模型适宜于在真实环境中计算地震发生概率。
Assuming that the earthquake is a random point process, and the magnitude distribution of all the earthquakes follows the Gutenberg-Richter-Stiglitz law of 6, we model the spatiotemporal frequency of earthquakes through an infectivity model. The incidence density is calculated by two sums, one representing independent or spontaneous activity and the other representing activity induced by previous earthquakes. The first is space-related, while the second depends on three factors, including the magnitude, time and location of the earthquake that occurred. In this paper, we use the modified Otsu law for time items, focusing on magnitude and space items. For each one, we made two different assumptions, and based on the catalog of earthquakes recorded by Italian instruments from 1987 to 2000, we found the maximum likelihood parameters respectively. The possibility of each of the seismogenic events recorded in 2001 is calculated and compared, which provides a way to find the best model. Monte Carlo simulations of various hypotheses evaluate the credibility of our choice of assumptions. Our research shows that for spatial distribution, the inverse power density function is more reliable than the normal density function, while the scale invariance assumption for aftershock occurrences can be rejected with high confidence. The final model is suitable for calculating the probability of earthquakes in a real environment.