Statistical Analyzes of Seismicity by Space-Time point process models

当几次地震开始发生时，它可能是大地震的前震序列，也可能是群震或简单的主震-余震序列。我们已经揭示了前震相对于其他类型的集群的一些区别特征，即除了第一次事件的地理位置外，事件在时间和空间上更接近，以及按时间顺序增加震级的趋势。这些特征使我们能够建立预测地震为前震概率的模型。并对预测结果进行了验证。分析了1971 ~ 1995年日本34次余震序列的统计模型特征参数，如Gutenberg-Richter关系的b值、修正Omori公式的p值、ETAS点过程模型的p值和α值以及震源分布的分形维数D之间的相关性。除了两对（b， D）和（alpha, p）具有相似的相关模式外，板内地震和板间地震的参数之间呈现出截然不同的相关模式。基于经典的聚类实证研究和一些推测性假设，构建了若干时空统计模型。我们还对该模型进行了进一步的实际扩展，以适应背景地震活动在空间上是非均匀的情况，以及集群是非各向同性的情况。在不同构造区域的两个高质量数据集上比较了模型的拟合优度。AIC允许澄清空间中集群结构的细节。模拟数据集的空间分布与真实数据集相似，但在时空聚类的一些特征上有所不同，为进一步的研究提供了有用的指示方向。

When a few earthquakes start to occur, it may be foreshock sequence to a larger earthquake, or it may be a swarm or simple mainshock-aftershock sequence. We have revealed some discriminating features of foreshocks relative to the other type of clusters, namely, the events' stronger proximity in time and space, and a tendency towards chronologically increasing magnitudes, in addition to the first event's geographic location. These features have led us to construct models which forecast the probability of the earthquakes being foreshocks. The validation of the forecast has been demonstrated.The correlation between characteristic parameters of statistical models, such as the b-value of the Gutenberg-Richter relation, the p-value of the modified Omori formula, the p- and alpha-value of the ETAS point process model, and the fractal dimension D of the hypocenter distribution, is analyzed for 34 aftershock sequences in Japan from 1971 to 1995. The contrasting correlation patters are revealed between the parameters for the intraplate and interplate earthquakes except the two pairs (b, D) and (alpha, p) where the similar correlation patterns are found.Several space-time statistical models are constructed based on both classical empirical studies of clustering and some more speculative hypothese. We also made further practical extensions of the model to sitations where the background seismicity is spatially non-homogeneous, and the clusters are non-isotropic. The goodness-of-fit of the models is compared for two high quality data sets, in different tectonic regions. AIC allows the details of the clustering structure in space to be clarified. The simulated data sets show the similar spatial distributions to the real ones, but differ from them in some features of space-time clustering which may provide useful indicators of directions for further study.