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.
The solidification of the Earth's inner core shapes its texture and rheology, affecting the attenuation and scattering of seismic body waves transmitted through it. Applying attenuation tomography in a Bayesian framework to 398 high‐quality PKIKP waveforms, we invert for the apparent Qp for the uppermost 400 km below the inner core boundary at latitudes 45°S to 45°N. We use damping and smoothing for regularization of the inversion, and it seems that the smoothing regularization combined with the discrepancy principle works better for this particular problem of attenuation tomography. The results are consistent with a regional variation in inner core attenuation more complex than hemispherical, suggesting coupling between inner core solidification and the thermal structure of the lowermost mantle.
The variability in obtaining estimates of tsunami inundation and runup on a near‐real‐time tsunami hazard assessment setting is evaluated. To this end, 19 different source models of the Maule Earthquake were considered as if they represented the best available knowledge an early tsunami warning system could consider. Results show that large variability can be observed in both coseismic deformation and tsunami variables such as inundated area and maximum runup. This suggests that using single source model solutions might not be appropriate unless categorical thresholds are used. Nevertheless, the tsunami forecast obtained from aggregating all source models is in good agreement with observed quantities, suggesting that the development of seismic source inversion techniques in a Bayesian framework or generating stochastic finite fault models from a reference inversion solution could be a viable way of dealing with epistemic uncertainties in the framework of nearly‐real‐time tsunami hazard mapping.
Following a sequence of three Slow Slip Events (SSEs) on the northern Hikurangi Margin, between June 2015 and August 2016, a Mw 7.1 earthquake struck ~30 km offshore of the East Cape region in the North Island of New Zealand on the 2 September 2016 (NZ local time). The earthquake was also followed by a transient deformation event (SSE or afterslip) northeast of the North Island, closer to the earthquake source area. We use data from New Zealand's continuous Global Positioning System networks to invert for the SSE slip distribution and evolution on the Hikurangi subduction interface. Our slip inversion results show an increasing amplitude of the slow slip toward the Te Araroa earthquake foreshock and main shock area, suggesting a possible triggering of the Mw 7.1 earthquake by the later stage of the slow slip sequence. We also show that the transient deformation following the Te Araroa earthquake ruptured a portion of the Hikurangi Trench northeast of the North Island, farther north than any previously observed Hikurangi margin SSEs. Our slip inversion and the coulomb stress calculation suggest that this transient may have been induced as a response to the increase in the static coulomb stress change downdip of the rupture plane on the megathrust. These observations show the importance of considering the interaction between slow slip events, seismic, and aseismic events, not only on the same megathrust interface but also on faults within the surrounding crust.
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