Linearized inversion for fault rupture behavior: Application to the 1984 Morgan Hill, California, earthquake

We present a technique to infer the rupture history of an earthquake from near‐source records of ground motion. Unlike most previous studies, each point on the fault is assumed to slip only once, when the rupture front passes, with a spatially variable slip intensity. In this parameterization the data are linearly related to slip intensity but nonlinearly related to rupture time. We perform a linearized inversion for slip intensity and rupture time by iteratively perturbing an assumed starting model. The inverse problem for the model perturbation is solved using a tomographic back projection technique. Smoothing and inequality constraints are applied to ensure that the resulting solution is stable and feasible. Asymptotic ray theory is used to calculate theoretical seismograms and partial derivatives with respect to model parameters. In test cases with noisy synthetic data sets we found that it is possible to distinguish between rupture models having variable slip amplitude and models having variable rupture velocity, provided the station coverage is adequate. We apply the technique to recordings of the April 24, 1984, Morgan Hill earthquake. The results indicate that slip amplitude on the fault plane was extremely variable and that the rupture front did not propagate uniformly away from the hypocenter. In particular, rupture was delayed on a 12 km 2 section of the fault approximately 14 km to the southeast of the hypocenter. The rupture front surrounded the region, which subsequently failed with a component of rupture propagation back toward the hypocenter. Similar behavior has been observed in dynamic rupture models with stress or strength inhomogeneities. This segment of the fault ruptured with a large slip amplitude, releasing 12% of the total seismic moment from 4% of the total area of the aftershock zone. The surface trace of this section of the fault is characterized by a complex left step that could act to increase the normal stress acting across the fault. However, the distribution of aftershocks suggests that the fault at depth is simpler and that it may bend to the right. In either case, our rupture model suggests that this segment of the fault represents an asperity, which initially resisted rupture but eventually ruptured massively. We estimate the shear fracture energy for this earthquake to be 2×10 6 J/m 2 .