Statistical Analyzes of Seismicity by Space-Time point process models

当几次地震开始发生时，它可能是一次较大地震的前震序列，也可能是一个震群或简单的主震-余震序列。我们揭示了前震相对于其他类型震群的一些明显特征，即除第一次地震的地理位置外，这些事件在时间和空间上具有更强的相似性，并有按时间递增震级的趋势。这些特征使我们构建了预测地震成为前震的概率的模型。对日本1971~1995年34次余震序列的古登堡-里希特关系的b值、修正的大森公式的p值、ETAS点过程模型的p和α值以及震源分布的分维D等统计模型特征参数之间的相关性进行了分析。除了(b，D)和(α，p)这两对相似的相关模式外，板内地震和板间地震的参数之间存在着相反的相关模式。基于经典的集群经验研究和一些更具推测性的假设，构建了几个时空统计模型。我们还将该模型进一步实际推广到背景地震活动在空间上不均匀、震群各向同性的情况。在不同构造区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相似，但时空聚类的某些特征有所不同，这可能为进一步研究提供有用的方向指标。

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.