Seismic site characterization requires large numbers of ground‐motion records, and such datasets are rarely available. Seismological models are generally used to enrich the existent sets of earthquake records with artificial ground acceleration time histories. The specific barrier model (SBM) is an earthquake source model that, as an integrating part of a seismological model, produces spectral densities of the ground‐motion process as a function of the moment magnitude m and source‐to‐site distance r. It is calibrated to regional records and, therefore, may only provide partial information on the site seismic characteristics. We propose a statistical update of the seismological model, constructed with the SBM such that it accounts for the site observations. A parametric probabilistic model is sought for the SBM spectral densities, and a Bayesian framework is used to statistically update it to local records. This new, enhanced version of the seismological model is used to simulate any number of ground‐motion samples and perform site‐specific probabilistic seismic‐hazard analyses (PSHAs). A numerical example of the PSHA calculations using the statistically updated seismological model is shown for a site in southern California.