Validating a Dynamic Earthquake Model to Produce Realistic Ground Motion

A dynamic earthquake model is validated by finding good agreement with an empirical ground‐motion prediction equation (GMPE). The model replaces complex detailed deterministic processes on the nonplanar fault with a stochastic emergent law of stress on a planar fault. Initial stress on the fault plane is heterogeneous with a power‐law spectrum that is self‐similar. Rupture extent and moment are determined primarily by the specified lowest Fourier mode of initial stress. Higher modes are random with a self‐similar spectrum that is tied to the amplitude of the lowest mode. Rupture stops naturally due to variation of initial stress. We calculate 10 random realizations with a velocity structure for a hard‐rock site. The calculated mean response spectrum for M w 7 at a distance of 10 km agrees with the GMPE of Boore et al. (2014) within 25% of one standard deviation at periods from 0.3 to 10 s. The agreement of the ground‐motion spectral response levels depends on the spatial stress spectrum being correctly related to the amplitude of the lowest mode, so that it is a consistent self‐similar model. There are no arbitrary parameters in the model other than those that determine moment and rupture length and width. The standard deviation of the calculated ground motion is a substantial fraction of that of the GMPE.