Equivalence between ωn Source Time Functions and Those Proposed from Dynamic Finite-Source Modeling

Abstract

ABSTRACT There is far-reaching equivalence between the source time functions inferred from dynamic rupture simulations and those corresponding to the kinematic models of slip radiating the generalized omega-n spectrum, in which the power n is allowed to take on noninteger values. First, the same two physical parameters of faulting—the final-fault displacement U and the peak rate of slip vm—govern the slip law in both cases. Second, in both models, the widths of the radiated far-field velocity pulses follow close analytical forms. Third, the full variety of temporal shapes of the dynamic source time functions, spanning the entire parameter space, closely corresponds to the variation in the omega-n shapes with n changing from 1.5 to 3.5, approximately. Smaller n lead to the source time functions that reach the maximum value of slip velocity faster: they cause greater asymmetry of the resulting far-field ground-displacement pulse and shorter duration of the positive velocity pulse. Fourth, in the frequency domain, the ωn spectrum, in which n changes in a narrower range from approximately 2 to 2.5, similarly includes nearly the entire range of possible dynamic Fourier spectra. The narrower range in n found in the frequency domain is explained by the constraints on the spectral slope imposed by the specific triangular shape of the dynamic functions. Fifth, in both dynamic and ωn models, the peak rate of slip vm is the parameter exerting dominant effect on the strength of fault’s high-frequency radiation, in the identical quantitative manner. It follows that the omega-n model of slip, in which n is allowed to vary, correctly captures the underlying physics of rupture.