Ground-motion models based on the Brune point-source approximation have an underlying ω2 spectrum, with a single corner frequency. These models over-predict observed spectral amplitudes at low to intermediate frequencies (∼0.1 to 2 Hz), for earthquakes with moment magnitudes M of 4 or greater. The empirical spectra of moderate to large events tend to sag at these frequencies, relative to the level suggested by the Brune point-source model.
A model that accounts for the finite extent of the fault plane correctly describes the observed spectral shapes. The model represents seismic radiation as a sum of contributions from several subfaults. Each subfault may be represented as a point source, and each subevent has an ω2 spectrum. When contributions to ground motion at an observation point are summed over all subfaults, the resulting spectral shape has two corner frequencies and more closely matches observed spectra. The more realistic spectral shape obtained through finite-fault modeling reflects the underlying reality that the radiation from real faults is formed by ruptures of their smaller parts, whose corner frequencies are higher than those implied by the full fault dimension. The two corners appear naturally as a result of subevent summation.
We use the stochastic finite-fault methodology to simulate the recorded ground-motion data from all significant earthquakes in eastern North America (ENA). These data include eight events of M > 4 recorded on modern digital instruments (regional seismographs and strong-motion instruments), and three historical events of M 5.8 to 7.3 recorded on analog instruments. The goodness of fit of synthetics to the data is defined as simulation bias, which is indicated by the difference between the logarithms of the observed and the simulated spectrum, averaged over all recordings of an earthquake. The finite-fault simulations provide an unbiased fit to the observational database over a broad frequency range (0.1 to 50 Hz), for all events.
A surprising conclusion of these simulations is that the subfault size that best fits the observed spectral shape increases linearly with moment magnitude, in an apparently deterministic manner. This strongly suggests that the subfault size can be unambiguously defined by the magnitude of the simulated earthquake. In this case, the radiation-strength factor(s), which is proportional to the square root of the high-frequency Fourier acceleration level, remains the only free parameter of the model. Its value is related to the maximum slip velocity on the fault. The strength factors for all modeled ENA events are within the range of 1.0 to 1.6, with the exception of the Saguenay mainshock (s = 2.2). This suggests a remarkable uniformity in earthquake slip processes.