The estimation of potential strong ground motions at short epicentral distances (Δ = 10 to 25 km) resulting from large earthquakes, M ≧ 6.5, generally requires extrapolation of a limited data set. The goal of this project has been to quantify the extrapolation through a simulation technique that relies heavily upon the more extensive data set from smaller magnitude earthquakes. The simulation utilizes the smaller events as Green's functions for the elements of a larger fault. Comparison of the simulated peak acceleration and duration with the data from the Parkfield earthquake is very good. Simulation of three earthquakes, M = 5.5, 6.5, and 7.0 indicate that the slope of the peak acceleration versus distance curve (Δ = 5 to 25 km) flattens, for strike-slip earthquakes, as the magnitude increases.