A class of kinematic rupture models for simple earthquakes is proposed; these models incorporate results from both theoretical and numerical solutions to the mixed boundary value problem of a three-dimensional frictional rupture. The analytic form for the slip velocity is divided into two phases: the rupture growth, during which the slip distribution is “self-similar” (Kostrov, 1964); and the healing, during which the slip velocity decreases monotonically to zero. The arrival of a P-wave stopping phase, propagating into the interior of the rupture area from the fault perimeter, initiates the healing. The duration of healing may be varied to produce a gradual or abrupt stopping of the rupture, which permits modeling a wide range of high-frequency spectral behavior.
These models are used to generate synthetics which are fit to the velocity and the velocity-squared pulse shapes obtained from strong motion accelerograms of the 0103 aftershock of the 1975 Oroville, California, earthquake. The aftershock (ML = 4.6) has a moment of 1.8 × 1023 dyne-cm and a total radiated energy of 2.7 × 1019 dyne-cm. The fitted source model propagates updip with a rupture velocity of 0.85β and a dynamic stress drop of 210 bars. The arrival times of five “stopping phases”, correlated across the suite of accelerograms, are used to determine the relative locations of the hypocenter and five stopping events. The description of rupture determined from these stopping events both corroborates the source model obtained from the waveform modeling and establishes an important counterpoint to the model by providing a dynamic interpretation of the unmodeled complexity of the waveforms.