The stochastic finite-fault ground-motion modeling technique is modified to simulate the effects of a variable-stress parameter on the fault. The radiated source spectrum of each subsource that comprises the fault plane is multiplied by a correction spectrum that leaves the low-frequency portion of the spectrum intact and multiplies the high-frequency end of the spectrum by a constant proportional to the stress parameter of each subfault raised to the power of 2/3; this scaling behavior follows from the Brune source model. The modification causes the response spectra and time series of simulated traces to be sensitive to the stress parameter distribution on the fault surface.
The approach is implemented using an inversion tool that effectively inverts observed response spectral data to derive the stress parameter distribution on the fault surface. It applies the Levenberg–Marquardt nonlinear inversion method to minimize differences of average (log) response spectra ordinates at high frequencies between observations and simulations at all stations.
We perform a number of experiments to study the effects of fault-dip angle, iterations per station, initial guess of the stress distribution, and station distribution on the capabilities of the inversion tool. We also evaluate the ability of the inversion tool to resolve the relative stress parameters of multiple asperities.
Application of the inversion tool to the data of the M 6 2004 Parkfield earthquake indicates that an asperity with a high stress parameter is located in the southeast end of the fault, at a depth greater than 4 km; another asperity is located in the center of the fault, but with a lower stress parameter. This distribution is in agreement with results by other researchers.