Abstract

This article describes an application of nonparametric local linear regression to study the spatial structure of the mean trend of earthquake magnitudes. If spatial correlation is suspected in a data set of earthquakes in a particular geographic area, the smoothing parameter needed to obtain the estimator of the mean magnitude will be computed using a corrected version of a generalized cross-validation method. This procedure allows us to take the spatial dependence into account to obtain better smoothing parameters. Additionally, a parametric bootstrap technique is used to quantify the variability of the spatial maps produced with the nonparametric estimation method and to compute the probability of observing a magnitude larger than or equal to a given threshold for an earthquake occurring in a specific epicenter. These techniques are applied to two different earthquake data sets: the historic catalog of the northwest Iberian Peninsula and the earthquakes in California from January 1998 to April 2008.

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