A computationally efficient framework is presented for modification of stochastic ground motion models to establish compatibility with the seismic hazard for specific seismicity scenarios and a given structure/site. The modification pertains to the probabilistic predictive models that relate the parameters of the ground motion model to seismicity/site characteristics. These predictive models are defined through a mean prediction and an associated variance, and both these properties are modified in the proposed framework. For a given seismicity scenario, defined for example by the moment magnitude and source-to-site distance, the conditional hazard is described through the mean and the dispersion of some structure-specific intensity measure(s). Therefore, for both the predictive models and the seismic hazard, a probabilistic description is considered, extending previous work of the authors that had examined description only through mean value characteristics. The proposed modification is defined as a bi-objective optimization. The first objective corresponds to comparison for a chosen seismicity scenario between the target hazard and the predictions established through the stochastic ground motion model. The second objective corresponds to comparison of the modified predictive relationships to the pre-existing ones that were developed considering regional data, and guarantees that the resultant ground motions will have features compatible with observed trends. The relative entropy is adopted to quantify both objectives, and a computational framework relying on kriging surrogate modeling is established for an efficient optimization. Computational discussions focus on the estimation of the various statistics of the stochastic ground motion model output needed for the entropy calculation.
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