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S U M M A R YDue to uncertainties in data and in forward modelling, the inherent limitations in data coverage and the non-linearity of the governing equation, earthquake source imaging is a problem with multiple solutions. The multiplicity of solutions can be conveniently expressed using a Bayesian approach, which allow to state inferences on model parameters in terms of probability density functions. The estimation of the posterior state of information, expressing the combination of the a priori knowledge on model parameters with the information contained in the data, is achieved in two steps. First, we explore the model space using an evolutionary algorithm to identify good data fitting regions. Secondly, using a neighbourhood algorithm and considering the entire ensemble of models found during the search stage, we compute a geometric approximation of the true posterior that is used to generate a second ensemble of models from which Bayesian inference can be performed. We apply this methodology to infer kinematic parameters of a synthetic fault rupture through fitting of strong motion data. We show how multiple rupture models are able to reproduce the observed waveforms within the same level of fit, suggesting therefore that the solution of the inversion cannot be expressed in terms of a single model but rather as a set of models which show certain statistical properties. For all model parameters we compute the posterior marginal distribution. We show how for some parameters the posterior do not follow a Gaussian distribution rendering the usual characterization in terms of mean value and standard deviation not correct. We compare the posterior marginal distributions with the 'raw' marginal distributions computed from the ensemble of models generated by the evolutionary algorithm. We show how they are systematically different proving therefore that the search algorithm we adopt cannot be directly used to estimate uncertainties. We also analyse the stability of our inferences comparing the posterior marginals computed by different independent ensembles. The solutions provided by independent explorations are similar but not identical because each ensemble searches the model space differently resulting in different reconstructed posteriors. Our study illustrates how uncertainty estimates derive from the topology of the objective function, and how accurate and reliable resolution analysis is limited by the intrinsic difficulty of mapping the 'true' structure of the objective function.

S U M M A R YWe image the rupture process of the 2000 Western Tottori earthquake (M w = 6.6) through fitting of strong motion and GPS data. We consider an observational network consisting of 18 strong motion and 16 GPS stations, located within three fault lengths from the epicentre. We assume a planar fault and compute Green's functions for a 1-D velocity model. The earthquake rupture is described as a shear dislocation parameterized in terms of peak slip velocity, rake angle, rupture time and rise time, defined on a regular grid of nodes on the fault surface and derived at inner points through bilinear interpolation.Our inversion procedure is based on a Bayesian approach. The solution of the inverse problem is stated in terms of a posterior probability density function (pdf), representing the conjunction of prior information with information contained in the data and in the physical law relating model parameters with data. Inferences on model parameters are thus expressed in terms of posterior marginal pdfs. Due to the non-linearity of the problem, we use a Markov Chain Monte Carlo (MCMC) method, based on the Metropolis algorithm, to compute posterior marginals.Except for a few cases posterior marginals do not show a Gaussian-like distribution. This prevents us from providing a mean model and from characterizing uncertainties in terms of standard deviations only. Resolution on each single parameter is analysed by looking at the difference between prior and posterior marginal pdfs.Posterior marginals indicate that the best resolved feature is a major slip patch (peak value of 311 ± 140 cm), located between the hypocentre and the top edge of the fault, centered at a depth of 4.5 km. This shallow slip patch is triggered about 3 s after the earthquake nucleated and required about 4 s to reach its final slip value. The presence of this shallow slip patch is common to all previous studies. In contrast to some previous studies, we do not identify any significant slip (>1 m) at the bottom of the fault.We also compare inferences from both strong motion and GPS data with inferences derived from strong motion data only. In both cases the shallow slip patch is identified. At other locations, the main effect of the GPS data is in reducing the probability associated with high values of slip. GPS data reduce the presence of spurious fault slip and therefore strongly influence the resulting final seismic moment.

In December 2018, at the conclusion of its second implementation phase, the Global Earthquake Model (GEM) Foundation released its first version of a map outlining the spatial distribution of seismic hazard at a global scale. The map is the result of an extensive, joint effort combining the results obtained from a collection of probabilistic seismic hazard models, called the GEM Mosaic. Together, the map and the underlying database of models provide an up-to-date view of the earthquake threat globally. In addition, using the Mosaic, a synopsis of the current state-of-practice in modeling probabilistic seismic hazard at national and regional scales is possible. The process adopted for the compilation of the Mosaic adhered to the maximum extent possible to GEM’s principles of collaboration, inclusiveness, transparency, and reproducibility. For each region, priority was given to seismic hazard models either developed by well-recognized national agencies or by large collaborative projects involving local scientists. The version of the GEM Mosaic presented herein contains 30 probabilistic seismic hazard models, 14 of which represent national or sub-national models; the remainder are regional-scale models. We discuss the general qualities of these models, the underlying framework of the database, and the outlook for the Mosaic’s utility and its future versions.