In this paper we propose a nonparametric method, based on locally variable band- widths kernel estimators, to describe the space-time variation of seismic activity of a region of Southern California. The flexible estimation approach is introduced together with a diagnostic method for space-time point process, based on the interpretation of some second-order statistics, to analyze the dependence structure of observed data and suggest directions for fit improvement. In this paper we review a diagnostic method for space-time point processes based on the interpretation of the transformed version of some second-order statistics. The method is useful to analyze dependence structures of observed data and suggests directions for fit improvement also when a more flexible estimator of the conditional intensity function is used, such as the kernel one. In particular locally variable bandwidths kernel estimators are used to describe space-time variations of seismic activity of a region of Southern California.