Stress drop is the stress that is effectively available to drive fault motion. It is a key parameter in predicting peak ground acceleration (PGA), since , and it is very important in estimating ground motion. However, it is difficult to get an accurate estimation of stress drop. In order to get a more stable measurement of stress drop, we test two methods in this thesis: the first one is the Brune stress drop, which is more commonly applied, and the second one is the stress drop, which less applied before and theoretically should have less uncertainty. By comparing these two methods we would like to test the feasibility and stability of the method. We applied these two methods to data of earthquakes M3-5.5 in California and Oklahoma. We found that, taking Oklahoma results as an example, the mean value of Brune stress drop is 0.38 MPa, with a multiplicative uncertainty of 3.12, and the mean value of stress drop is 1.04, with a multiplicative uncertainty of 1.79. Therefore we concluded that the method is a good estimator of stress drop, with a smaller uncertainty. We determine the path attenuation so that we can increase the source-station distance of events studied to be as much as 76 km. The path seismic attenuation is a critical parameter that must be included in the analysis.

We show that both the slip distribution and the peak ground acceleration (PGA) for the 1999 Chi Chi earthquake can be described by Levy laws. Furthermore, we found that the tails of the probability density functions (PDF) characterizing the slip and the PGA are governed by a parameter, the Levy index, with almost the same values as predicted by the Central Limit theorem. The PDF tail controls the frequency at which extreme large events can occur. These events are the large stress drops-asperities distributed over the fault surface and the large PGA observed in the ground motion. Our results suggest that the frequency of these events is coupled; the PDF of the PGA is a direct consequence of the PDF of the asperities. The physical rationale responsible for the coupling is the principle of superposition of wave signals characterized by random properties that are governed by the Central Limit theorem.

We model the two most recent Mw~6 Parkfield, California, earthquakes, which occurred in 1966 and 2004, from a nonlinear global inversion of near-fault strong motion seismograms. Our rupture models are characterized by spatially variable slip amplitude and rake, rupture velocity, and risetime. The rupture models indicate that the two earthquakes generated slip in regions of the fault that are not identical, as earlier suggested. Given the sparse seismic data set available for the 1966 earthquake, we conduct a series of tests to verify our results: (1) we perform synthetic tests in order to study the resolution of the 1966 seismic data set; (2) we perform an inversion of the 2004 earthquake using a data set equivalent to the 1966 earthquake; and (3) we model the 1966 data set under the a priori assumption that it was similar to the 2004 earthquake. All of the tests, as well as independent observations, indicate that slip during the 1966 and 2004 Parkfield earthquakes occurred in different regions of the fault. This result implies that regions of a fault that are frictionally locked may remain locked even during a main shock (moderate-size earthquake). In this scenario, large earthquakes occur when all the locked regions of a fault are “synchronized” and ready to slip at the same time.

On 28 September 2004, the M(w)6.0 Parkfield earthquake became the most densely recorded earthquake for near-source ground-motion. To infer the kinematic nature of this event we invert the strong-motion data. The non-linear global inversion yields slip amplitude, slip rake, average rupture velocity, and rise time over the fault. By using subsets of the data, we study the dependence of the kinematic solutions on data input. The inversions reveal that the slip amplitude was less than 0.65 m and outline two major areas of slip; one that laterally surrounds the hypocenter, preferentially extending to its SE; the other 10 to 20 km NW of the hypocenter, at a depth between 2 and 8 km. The slip amplitude we obtain for each point on the fault varies less than 0.15 m depending on data set used; the rake angle variability is less than 40 degrees.