Bayesian Trans-Dimensional Finite Fault Inversion for the 2010 Maule (Chile) Earthquake

This work develops a non-linear Bayesian inversion to infer the spatio-temporal evolution of earthquake rupture on a fault surface from seismic data with rigorous uncertainty estimation. The fundamental problem of estimating slip on an unknown fault surface from incomplete and noisy data is highly non-linear, non-unique, and challenging to address without making substantial assumptions about some of the unknowns. To date, uncertainties of rupture parameters are poorly understood, and the effect of choices such as fault discretisation on uncertainties has not been studied. We show that model choice is closely linked to uncertainty estimation and can have profound effects on results.

The inversion is based on a trans-dimensional fault model, avoids regularization, and provides rigorous uncertainty estimation that accounts for model-selection ambiguity associated with the fault discretisation. In particular, the fault is parametrized using irregular grids which match the local resolving power of the data and provide simple solutions requiring few parameters to capture complex rupture characteristics. Causal first rupture times are obtained by solving the Eikonal equation for a spatially variable rupture-velocity field. The inversion is applied to W-phase waveforms (vertical components) from the 2010 Maule (Chile) earthquake. Residual errors are highly correlated and likely dominated by theory error, necessitating iterative estimation of a non-stationary data covariance matrix. Slip is concentrated in two zones up-dip of and north and south of the hypocentre, respectively. While this aspect of the slip distribution is similar to previous studies, we show that the slip maximum in the southern zone is poorly resolved compared to the northern zone. Both slip maxima show larger slip than reported in previous studies, which we speculate may be due to the lack of bias caused by the regularization used in other studies.