Earthquake ground motion prediction in Iceland where strong-motion data is scarce poses a challenge as empirical ground motion models (GMM) developed from data in other regions systematically fail to capture the consistently large near-fault peak amplitudes and their rapid attenuation with distance from the earthquake source. Therefore, regional GMMs must be constructed but due to the limited data, and none above Mw6.5, earthquake source scaling is unconstrained at larger magnitudes. Instead, physics-based GMMs should be applied based on realistic earthquake source modeling. For that purpose, a seismological model constructed around the specific barrier model (SBM) has been calibrated in the context of the stochastic method using random vibration theory, to earthquake high-frequency strong-motions in the South Iceland Seismic Zone. The SBM is used as it provides a physically consistent and efficient description of the heterogeneous faulting processes that are responsible for the generation of high-frequency waves. On the basis of the concise point-source representation of radiated spectra from N subevents of the SBM the pseudo-spectral accelerations were modeled and compared with that of data in the spectral domain. Backwards model selection was then carried out using Bayesian inference with Monte Carlo simulations and Markov Chains. The number of parameters in the model inference was reduced to obtain stable Markov chains and posterior probability density functions for each parameter, eliminating parametric cross-correlations to the extent possible. The seismological model has been shown to be unbiased with respect to strong-motions in the SISZ, with a total standard deviation of 0.216 (common logarithm), with only a minor contribution from inter-event variability, suggesting a relatively uniform character of SISZ earthquake strong-motions. We showcase the application of the SBM extended into a finite-fault and model the three Mw6.3-6.5 earthquakes in the dataset, allowing subevents of varying sizes to populate the fault plane and provide a more realistic earthquake source and acceleration ground motion time history modeling. The time domain results are shown to capture the essential characteristics of the ground motions of the three largest earthquakes in the dataset. We present therefore the SBM as a physically consistent source model of SISZ earthquakes for the generation of synthetic strong-motion time histories or peak parameters, with potential applications in scenario simulations and probabilistic or deterministic seismic hazard assessment.