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描述了应用非参数局部线性回归对震级平均趋势空间结构的研究。如果推测特定区域的地震数据集有空间相关,则需要使用修正版本的广义交叉验证方法计算光滑参数,以获得平均震级估计量。这种方法允许我们将空间依赖考虑进去从而获得更好的光滑参数。而且,应用参数自助法(bootstrap)可以量化由非参数估计方法得出的空间图的变异,也可以计算在特定震中发生的地震观测的震级大于等于给定阈值的概率。这些方法应用于两个不同的地震数据集:伊比利亚半岛西北部历史地震目录和加利福尼亚1998年1月到2008年4月的地震。
Describes the study of the spatial structure of the mean trend of magnitude using nonparametric local linear regression. If it is speculated that the seismic data sets for a particular area are spatially correlated, a modified version of the generalized cross-validation method needs to be used to calculate smoothing parameters to obtain the average magnitude estimate. This method allows us to take space dependence into account for better smoothing parameters. Moreover, the bootstrap method can be used to quantify the variation of the spatial map obtained by the non-parametric estimation method and also to calculate the probability that the magnitude of the seismic observation that occurs in a particular epicenter is greater than or equal to a given threshold. These methods are applied to two different seismic data sets: the catalog of historical earthquakes in the northwestern Iberian Peninsula and the earthquakes in California from January 1998 to April 2008.