ALBERT

Description: In geophysical inversion, inferences of Earth's properties from sparse data involve a trade-off between model complexity and the spatial resolving power. A recent Markov chain Monte Carlo (McMC) technique formalized by Green, the so-called trans-dimensional samplers, allows us to sample between these trade-offs and to parsimoniously arbitrate between the varying complexity of candidate models. Here we present a novel framework using trans-dimensional sampling over tree structures. This new class of McMC sampler can be applied to 1-D, 2-D and 3-D Cartesian and spherical geometries. In addition, the basis functions used by the algorithm are flexible and can include more advanced parametrizations such as wavelets, both in Cartesian and Spherical geometries, to permit Bayesian multiscale analysis. This new framework offers greater flexibility, performance and efficiency for geophysical imaging problems than previous sampling algorithms. Thereby increasing the range of applications and in particular allowing extension to trans-dimensional imaging in 3-D. Examples are presented of its application to 2-D seismic and 3-D teleseismic tomography including estimation of uncertainty.

Description: This paper develops a probabilistic Bayesian approach to the problem of inferring the spatiotemporal evolution of earthquake rupture on a fault surface from seismic data with rigorous uncertainty estimation. To date, uncertainties of rupture parameters are poorly understood, and the effect of choices such as fault discretization on uncertainties has not been studied. We show that model choice is fundamentally linked to uncertainty estimation and can have profound effects on results. The approach developed here is based on a trans-dimensional self-parametrization of the fault, avoids regularization constraints and provides rigorous uncertainty estimation that accounts for model-selection ambiguity associated with the fault discretization. In particular, the fault is parametrized using self-adapting irregular grids which intrinsically match the local resolving power of the data and provide parsimonious solutions requiring few parameters to capture complex rupture characteristics. Rupture causality is ensured by parametrizing rupture-onset time by a rupture-velocity field and obtaining first rupture times from the eikonal equation. The Bayesian sampling of the parameter space is implemented on a computer cluster with a highly efficient parallel tempering algorithm. The inversion is applied to simulated and observed W-phase waveforms from the 2010 Maule (Chile) earthquake. Simulation results show that our approach avoids both over- and underparametrization to ensure unbiased inversion results with uncertainty estimates that are consistent with data information. The simulation results also show the ability of W-phase data to resolve the spatial variability of slip magnitude and rake angles. In addition, sensitivity to spatially dependent rupture velocities exists for kinematic slip models. Application to the observed data indicates that residual errors are highly correlated and likely dominated by theory error, necessitating the iterative estimation of a non-stationary data covariance matrix. The moment magnitude for the Maule earthquake is estimated to be ~8.9, with slip concentrated in two zones updip 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 are higher than reported in previous studies, which we speculate may be due to the lack of bias caused by the regularization used in other studies.