Earthquake potential at Parkfield, CA inferred from geodetic data spanning two earthquake cycles with assessment of model resolution and uncertainty

Although some models used in long-term earthquake forecasting treat earthquake occurrence as a time-independent process, it is generally accepted that an earthquake relieves accumulated stress on a fault and that time is required to rebuild stress before another large event. This idea is embodied in the time-predictable model for earthquake recurrence, which is used in hazard forecasting. The related slip-predictable model states that earthquake size is proportional to the time since the last event and the fault stressing rate. Geodetic data offer a means of measuring strain accumulation and release in the Earth's crust throughout the earthquake cycle. Inversion of these data can provide useful inputs, such as estimates of slip in earthquakes or the long-term slip rate, to recurrence models. However, the slip resolution of geodetic observations decreases with depth on the fault. If the results of geodetic modeling are to be properly incorporated into hazard forecasts, it is critical to assess which features of the models are robust by quantifying the model resolution and the uncertainties of estimated parameters. With geodetic measurements for the three most recent earthquakes (in 1934, 1966, and 2004), Parkfield, California is one of the few locales where geodetic data span multiple earthquake cycles. Sparse observations exist for the 1934 - 1966 time period, and geodetic monitoring steadily increased during the 1966 - 2004 interseismic period. Through joint inversion of the variety of Parkfield geodetic measurements (triangulation, trilateration, two-color laser, and GPS) we obtain the most detailed image yet of the evolution of slip on the fault since the 1934 earthquake. Obtaining the model resolution and model covariance matrices is straightforward for linear inversions. However, due to the inclusion of non-negativity constraints, the inversions of Parkfield data are nonlinear. We apply an alternative technique for calculating the model resolution and use the bootstrap resampling method to obtain confidence intervals on the slip estimates. The geodetically-inferred interseismic slip rate distribution is used to calculate the range of moments for the 2004 event expected based on the slip-predictable model. We find that the moment of the coseismic slip in the 2004 event plus that during the first 230 days of the postseismic period is below the slip-predictable range. Postseismic deformation is expected to continue for several years at Parkfield, but it is unlikely that the total moment release associated with the 2004 earthquake will ultimately fall within the slip predictable bounds. However, application of the slip-predictable model is complicated by its requirement of a clearly-defined fault segment. Using the lower 95% confidence limit on slip estimates, the 33 km of the San Andreas southeast of Gold Hill has an average slip deficit of 1.7 meters, and its moment deficit is equivalent to a Mw 6.8 earthquake. Even the portion of the fault between Middle Mountain and Gold Hill, which slipped in the 1966 and 1934 earthquakes, has an average slip deficit of 0.9 meter, and moment deficit equivalent to a Mw 6.5 earthquake.