Statistical Analysis of Ground Motion from Steady State Dynamic Rupture Pulses

Two-dimensional steady state dynamic rupture model is used to perform statistical analysis on both synthetic and field data. Given the medium and acquisition parameters, this model relates the fault-parallel and fault-perpendicular ground motion to the slipping zone length L, the slip weakening zone length R, total locked-in slip δ and rupture velocity V. Moreover, fault rotation and static time shift parameters are added to account for possible acquisition errors. The model is examined for sub-shear rupture velocities only. Although relatively simple, this model has several attractive features such as computational efficiency and limited number of parameters, which makes sophisticated and comprehensive statistical analysis feasible. Our main goal is to infer fracture energies G for larger earthquakes and analyzing the sensitivity of these energies to the model parameters. First, we create a synthetic dataset using the steady state model to analyze the objective function behavior around the correct solution. We perturb each parameter independently to estimate the convexity of the parameters as well as the data sensitivity to the parameters. Then, we estimate the correlation matrix between the parameters using the analytical solution. The correlation matrix indicates that the rupture velocity, locked-in slip and fracture energy are weakly correlated with the other parameters for both the fault-parallel and fault-perpendicular data. Next, we implement a Markov chain Monte Carlo algorithm to the data to obtain the probability distribution of the objective function. We analyze both the marginal and the complete probability distributions. The results indicate that the parameters widely vary in terms of sensitivity and resolution with respect to the fracture energy. Nonetheless, the fracture energy can be estimated with reasonable accuracy. Afterwards, we repeat our analysis using field datasets. The resulting probability densities have maximum likelihoods for fracture energy around 1-4 MJ/m/m. The analysis was done using single-receiver data. Further analysis is needed for using multi-receiver data, which can potentially increase the accuracy and robustness of the method.