Slip Velocity Parameterization for Broadband Ground Motion Simulation

Abstract

Slip velocity functions commonly used in kinematic inversions and forward simulations have a number of problems that affect the computation of high frequency ground motion. These problems include an imposed greater than omega square high frequency spectral decay rate, introduction of spectral holes from the use of temporally sharp functions such as boxcar and triangle functions, and the use of functions that are inconsistent with dynamic rupture models. We introduce a new analytic slip velocity function parameterization that has the favorable attributes of a smooth spectrum with an adjustable high frequency decay rate. This function has two parameters. One describes the rise time and corner frequency, and the other defines the sharpness of the onset of the time function and the high frequency decay rate. This function convolved with the finite rupture process yields a net source spectrum with an omega squared high frequency decay rate consistent with observations, and does not suffer from spectral holes that can bias frequency or period dependent ground motion parameters. We apply this function to published kinematic slip models for the 1979 Imperial Valley, 1989 Loma Prieta, 1992 Landers, 1994 Northridge, 1995 Kobe, and the 1999 Izmit earthquakes to document the range controlling parameters to fit the broadband (0.05 to 20 Hz) data. Observed and simulated spectral acceleration from 0.05 to 20 seconds period as well as time histories are compared. Finally, using a finite-difference method to solve the elastodynamic equations of motion given a kinematic slip model as a boundary condition, we relate the defining slip velocity function parameterization to the traction evolution on the fault and dynamic rupture parameters following the method of Tinti et al. (2005).