Evolutionary properties of stochastic models of earthquake accelerograms: Their dependence on magnitude and distance

An approach to generate artificial earthquake accelerograms on hard soil sites is presented. Each time-history of accelerations is considered as a realization of a non-stationary gaussian stochastic process, with statistical parameters depending on magnitude and source-to-site distance. In order to link the values of these parameters for each ground motion record with the corresponding magnitude and source-to-site distance, semi-empirical functional relations called generalized attenuation functions are determined. The set of real ground-motion time histories used to obtain these functions correspond to shocks generated at different sources and recorded at different sites in the vicinity of the southern coast of Mexico. The results show significant dispersion in the parameters of the model adopted, which reflect that associated with the real earthquakes included in the sample employed. The problem of conditional simulation of artificial acceleration time histories for prescribed intensities is briefly presented, but its detailed study is left for a companion paper. The criteria and models proposed are applied to generate two families of artificial acceleration records for recurrence intervals of 100 and 200 years at a specific site located in the region under study. The results shown in this article correspond to acceleration time histories recorded on firm ground for earthquakes generated at the subduction zone that runs along the southern coast of Mexico, and cannot be generalized to cases of earthquakes generated at other sources or recorded at other types of local conditions. This means that the methods and functional forms presented here are applicable to these other cases, but the values of the parameters that characterize those functions may differ from those presented here.