This article presents a procedure that is meant for the generation of catalogs of synthetic inslab earthquake ground motions. The procedure is based on the Green’s function method, an empirical method that considers an improved two‐stage summation scheme of the basic signals emitted by the source. The proposed procedure takes into account that rise time and the acceleration spectrum of a signal originated at a known source S(ω) is more precisely described by an empirical source spectrum characterized by two corner frequencies ωa and ωb than it would be by the usual method where it is described by a single corner frequency. For the formulation of the probability density function of the rupture time, delays of the N cells in which the source of the simulated signal are discretized, and the definition of the empirical source spectrum is implemented using the aforementioned summation scheme. It is assumed that the extended area of the source is concentrated at a point and that the rupture duration is defined in accordance with its size. To illustrate the application of this procedure, the simulation of synthetic records of three different earthquakes events for several sites in Mexico is carried out. The results are validated via a statistical comparison of the response and Fourier acceleration spectra of the synthetic ground motions with the actual spectra of the real earthquake records from the three events considered as targets. Also, a comparison of the response spectra for the SCT station located in the lakebed zone of Mexico City with the single‐stage and the enhanced two‐stage procedure is presented. The latter comparison shows that signals simulated with the proposed procedure reproduce the amplification effects in the 1.4–5 s range in their response spectra in a better manner; this is also observed on real records, such as the east–west (E‐W) component, which was registered at the SCT station during the 19 September 1985 Michoácan earthquake.

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