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The goal of a probabilistic seismic hazard analysis (PSHA) is the estimation of the expected rate of exceedance of a particular ground motion level A, (Y A), where Y is a ground motion intensity parameter such as peak ground acceleration or the response spectrum. This is achieved by combining probabilistic assumptions about earthquake occurrences (spatial and temporal), magnitudes and generated ground motions, which yields a so-called hazard curve that relates a ground motion level with its expected rate of exceedance. Any such analysis is accompanied by large uncertainties, both aleatory and epistemic in nature. It has been noted (Toro, 2006) that uncertainties in the estimation of ground motions, i.e. so-called ground motion models (GMMs), have the largest effect on the results of PSHA, in particular for very low rates of exceedance, which are important for critical facilities such as nuclear power plants.

In this work, several investigations are carried out with respect to GMMs. These investigations address different issues in the development and estimation of GMMs.

First, a polynomial GMM is developed, where the order of the polynomials is determined based on generalization capability. The model is rather complex and non-physical, but is optimized for predictive power. Partial dependence plots reveal the characteristical scaling of the ground motion parameter with the predictor variables. They also show ranges which are not well sampled by data. The polynomial model is converted into a physical stochastic model to make it physically interpretable. The results are in good agreement with other published models.

Going a step further, a Bayesian network is learned on roughly the same dataset as the polynomial model. The Bayesian network provides a multivariate model for the ground motion domain, where direct (in)dependencies between quantities are estimated. It can both be used as a powerful tool for reasoning under uncertainty, as well as to investigate which parameters are directly relevant for QH predicting ground motions. In particular, VS is not directly connected to PGA in the Bayesian network, but is mediated through the depth to the 2.5 km/s shear wave horizon. This is an indiQH cation that VS might not be the parameter characterizing site effects with the highest predictive power for ground motions. The Bayesian network is in reasonable agreement with regression models in regions of good data coverage.

Two Bayesian GMMs are developed to investigate parameter uncertainty. Prior distributions of the coefficients are determined by setting prior distributions on physical parameters, simulating a synthetic ground motion dataset and determining the coefficients by regression on the synthetic dataset. This provides a way to combine both physical knowledge (simulations) and data-driven models in a principled way. The parameters related to source scaling (magnitude and style-offaulting dependence) are generally associated with higher uncertainty than the ones related to path and site scaling. This is not surprising, since the latter ones are based on much more data – there are generally more records than earthquakes in a strong motion dataset.

The two Bayesian GMMs are similar in that they both comprise the same base model, which is expanded in different ways: The first model estimates directly the covariance (both between-event and within-event) between different ground motion intensity values during learning, which are usually considered independently. Strong correlations are found, the strength depending on the difference in period of the response spectrum. The between-event correlation is larger than the within-event correlation.

The second model takes into account possible regional differences in ground motion scaling.

Therefore, the global dataset is split into 10 regions, each of which is represented by an individual GMM. These regional GMMs are assumed to be sampled from a global distribution of GMMs, which are parameterized by global hyperparameters. Data from all regions is used to estimate the parameters of the regional GMMs, though autochthonous data is assigned more weight. This procedure makes it possible to estimate an individual GMM in regions with a sparse amount of data.

The analysis is not supposed to prove or disprove regional differences in ground motion scaling, but merely to present a methodology to take them into account in the light of large uncertainties.

Consequently, results regarding regional differences are inconclusive. It seems to be that regional differences in magnitude scaling of PGA are small – the model is developed for magnitudes between 5 and 7.9 – while differences regarding anelastic attenuation appear to be genuine. However, results may be obfuscated due to large differences in the amount of data between different regions.

Finally, a naive Bayes classifier to predict seismic intensities from peak ground acceleration or peak ground velocity is learned, based on an Italian dataset. Such a model is useful for the rapid generation of so-called ShakeMaps or for the selection of GMMs in regions where instrumental ground motion data is sparse. The naive Bayes classifier performs better than commonly employed regression models, judged by generalization error under 0-1 loss. It also provides a better representation of the uncertainty by estimating a (discrete) conditional distribution of intensity given €r(I P GA; P GV ), which makes a fully probabilistic the instrumental ground motion variables, treatment of the conversion possible.




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