From kinematic to dynamic inversion: The case study of the rupture process of the 2004 Parkfield earthquake

We explore a recently developed method for carrying out kinematic inversions. It is based on an elliptical sub-fault approximation, where the slip history is modelled using a small set of elliptical patches. We use it to invert near-field strong ground motion to obtain the rupture history of the 2004 September 28, Mw6.0, Parkfield, California, earthquake. We perform 12 kinematic inversions in order to explore the variability of plausible rupture models. The preferred rupture model has a final seismic moment of 1.21x10^18 Nm, distributed on two distinct ellipses. The average rupture speed is ~2.7 km/s. This model shows a good agreement with the location of large earthquakes (Mw > 3) that have occurred prior to the 2004 Parkfield earthquake, surrounding the two slip patches. Similar behaviour is also observed for the aftershocks. After considering kinematic inversion, we present a full dynamic inversion for the Parkfield earthquake using also elliptical sub-fault approximation. The best fitting model has a final seismic moment of 1.18 x 10^18 Nm, distributed on one ellipse. The rupture speed is ~2.8 km/s. In addition to the inversion, we explore the dynamic parameter-space using a Monte-Carlo method. Inside the parameter-space, we show that the rupture models are distributed according the rupture speed and final seismic moment, defining a optimal region where models fit correctly the data. We finally investigate the transition between kinematic models and dynamic models. To make the preferred kinematic model both dynamically correct while fitting the data, we show it is necessary to connect the two ellipses. This is done by adopting a new approach that uses b-spline curves.