Choices of Slip Function and Simulated Ground Motions

Kinematic simulations of strong ground motions require representation of the temporal functional form of fault slip. There is a range of source time functions that are commonly used: those that are generalized from numerical simulations of crack dynamics or those that radiate the seismic spectra of the omega-n type. All are physical plausible, while the modern source-inversion studies are still unable to better constrain the choices available. The uncertainty in the kinematically simulated motions due to the ambiguity in assigning an underlining form of fault slip still requires rigorous quantification. The representation integral of elasticity is an appropriate analytical tool, providing the exact seismic field in the entire practically relevant frequency band and including all near- and far-field terms. The smooth dynamically compatible version of the source time function, in which the rise time is the governing parameter, has the drawback of implicitly leading to unreasonably high slip rates and, as a consequence, unrealistically extreme ground velocities and accelerations. On the other hand, the functions, both dynamic and of the omega-n type, in which the static offset U and peak rate of slip v_max are the two independent controlling parameters, all provide nearly the same peak-motion values that match the prescribed, realistically observed coseismic fault-slip rates. With U and v_max as the correctly prescribed slip parameters, respectively controlling the low- and high-frequency ends of the radiated spectra, the choice between a dynamic or omega-n function leads to insignificant differences in radiation, causing the uncertainty in peak motions not exceeding approximately 10%.