地震次数预测测试
Earthquake Number Forecasts Testing
摘要：
我们研究了两个全球目录中的地震数分布：全球质心矩张量和震中的初步确定。这些分布是发展未来地震活动率预测的数字检验所必需的。一个常见的假设是这些数字由泊松分布描述。与单参数泊松分布不同，负二项分布（NBD）有两个参数。第二个参数表征过程的聚类或过度分散。我们调查这两个分布的参数的依赖性上的目录震级阈值和目录持续时间的时间细分。我们发现，对于大多数感兴趣的情况下，泊松分布可以拒绝统计在一个高的显着性水平，有利于NBD。因此，我们调查这些分布是否符合观测到的地震活动性分布。为此，我们研究了地震数的上统计矩（偏度和峰度），并将它们与两种分布的理论值进行了比较。偏度和峰度的经验值增加较小的震级阈值，并增加更大的强度为小的时间细分目录。NBD偏度和峰度水平的计算表明这些高阶矩水平迅速增加。然而，偏度和峰度的观测值上升得更快。这意味着，对于小时间间隔，地震次数分布比NBD预测的更加重尾。因此，对于小的时间间隔，我们建议使用经验数分布适当平滑的测试预测地震数。
英文摘要：
We study the distributions of earthquake numbers in two global catalogs: Global Centroid-Moment Tensor and Preliminary Determinations of Epicenters. These distributions are required to develop the number test for forecasts of future seismic activity rate. A common assumption is that the numbers are described by the Poisson distribution. In contrast to the one-parameter Poisson distribution, the negative-binomial distribution (NBD) has two parameters. The second parameter characterizes the clustering or over-dispersion of a process. We investigate the dependence of parameters for both distributions on the catalog magnitude threshold and on temporal subdivision of catalog duration. We find that for most cases of interest the Poisson distribution can be rejected statistically at a high significance level in favor of the NBD. Therefore we investigate whether these distributions fit the observed distributions of seismicity. For this purpose we study upper statistical moments of earthquake numbers (skewness and kurtosis) and compare them to the theoretical values for both distributions. Empirical values for the skewness and the kurtosis increase for the smaller magnitude threshold and increase with even greater intensity for small temporal subdivision of catalogs. A calculation of the NBD skewness and kurtosis levels shows rapid increase of these upper moments levels. However, the observed catalog values of skewness and kurtosis are rising even faster. This means that for small time intervals the earthquake number distribution is even more heavy-tailed than the NBD predicts. Therefore for small time intervals we propose using empirical number distributions appropriately smoothed for testing forecasted earthquake numbers.
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