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Asperity Model of an Earthquake: Dynamic Problem

¹ Center for Computational Seismology
Earth Sciences Division, 90-116
Lawrence Berkeley National Laboratory
One Cyclotron Road
Berkeley, California 94720
 (L.R.J.)

² Berkeley Seismological Laboratory
University of California
Berkeley, California 94720
 (R.M.N.)

A previous study that presented the static solution for an asperity model of an earthquake is extended to solve the dynamic problem that develops when failure occurs on the boundary of an asperity patch and then spreads over the surrounding displacement shadow region. The boundary integral equation method is coupled with basic constitutive equations for failure and friction to solve the dynamic problem, with different parameters used for the strong asperity patch and weak shadow region. No friction, displacement-weakening friction, and velocity-strengthening friction are all investigated. Depending on the type and amount of friction that is present, the dynamic solutions for slip on the fault exhibit a range of different features, including overshoot of the static solution and oscillation, rupture front velocities that may be greater than or less than the S velocity and change with position, and either total or partial release of the static moment. Common characteristics of the solutions are that failure on the asperity patch is almost independent of failure on the shadow region and that the displacement deficit on the shadow region is released by propagating slip pulses. The stress concentrations of the asperity model are sufficient to produce nonlinear elastic effects in a region extending outward from the fault to distances comparable with the dimensions of the shadow region. Beginning with the solutions for slip on the fault, waveforms are simulated for an earthquake of magnitude M_w 1.44 and compared with data recorded at a distance of 8.65 km. Simulations that contain both source and propagation effects are capable of explaining most of the basic features of the observational data, including general agreement with the shape of the waveforms in the time domain, the levels and slopes of the spectra at low frequencies (less than 10 Hz) and at high frequencies (greater than 100 Hz), and some of the interference effects present in both the time and frequency domains.