In finite-fault modeling of earthquake ground motions, a large fault is divided into N subfaults, where each subfault is considered as a small point source. The ground motions contributed by each subfault can be calculated by the stochastic point-source method and then summed at the observation point, with a proper time delay, to obtain the ground motion from the entire fault. A new variation of this approach is introduced based on a “dynamic corner frequency.” In this model, the corner frequency is a function of time, and the rupture history controls the frequency content of the simulated time series of each subfault. The rupture begins with a high corner frequency and progresses to lower corner frequencies as the ruptured area grows. Limiting the number of active subfaults in the calculation of dynamic corner frequency can control the amplitude of lower frequencies.
Our dynamic corner frequency approach has several advantages over previous formulations of the stochastic finite-fault method, including conservation of radiated energy at high frequencies regardless of subfault size, application to a broader magnitude range, and control of the relative amplitude of higher versus lower frequencies. The model parameters of the new approach are calibrated by finding the best overall fit to a ground-motion database from 27 well-recorded earthquakes in California. The lowest average residuals are obtained for a dynamic corner frequency model with a stress drop of 60 bars and with 25% of the fault actively slipping at any time in the rupture.
As an additional tool to allow the stochastic modeling to generate the impulsive long-period velocity pulses that can be caused by forward directivity of the source, the analytical approach proposed by Mavroeidis and Papageorgiou (2003) has been included in our program. This novel mathematical model of near-fault ground motions is based on a few additional input parameters that have an unambiguous physical meaning; the method has been shown by Mavroeidis and Papageorgiou to simulate the entire set of available near-fault displacement and velocity records, as well as the corresponding deformation, velocity, and acceleration response spectra. The inclusion of this analytical model of long-period pulses substantially increases the power of the stochastic finite-fault simulation method to model broadband time histories over a wide range of distances, magnitudes, and frequencies.