This paper considers a class of low-order, range-dependent propagation models obtained from the normal mode decomposition of infrasounds in complex atmospheres. The classical normal mode method requires calculating eigenvalues for large matrices making the computation expensive even though some modes have little influence on the numerically obtained results. By decomposing atmospheric perturbations into a wavelet basis, it is shown that the most sensitive eigenvalues provide the best reduced model for infrasound propagation. These eigenvalues lie on specific curves in the complex plane that can be directly deduced from atmospheric data through a WKB approach. The computation cost can be reduced by computing the invariant subspace associated with the most sensitive eigenvalues. The reduction method is illustrated in the case of the Fukushima explosion (12 March 2011). The implicitly restarted Arnoldi algorithm is used to compute the three most sensitive modes, and the correct tropospheric arrival is found with a cost of 2% of the total run time. The cost can be further reduced by using a stationary phase technique. Finally, it is shown that adding uncertainties triggers a stratospheric arrival even though the classical criteria, based on the ratio of stratospheric sound speed to that at ground level, is not satisfied.

SUMMARY In low-seismicity areas such as Europe, seismic records do not cover the whole range of variable configurations required for seismic hazard analysis. Usually, a set of empirical models established in such context (the Mediterranean Basin, northeast U.S.A., Japan, etc.) is considered through a logic-tree-based selection process. This approach is mainly based on the scientist’s expertise and ignores the uncertainty in model selection. One important and potential consequence of neglecting model uncertainty is that we assign more precision to our inference than what is warranted by the data, and this leads to overly confident decisions and precision. In this paper, we investigate the Bayesian model averaging (BMA) approach, using nine ground-motion prediction equations (GMPEs) issued from several databases. The BMA method has become an important tool to deal with model uncertainty, especially in empirical settings with large number of potential models and relatively limited number of observations. Two numerical techniques, based on the Markov chain Monte Carlo method and the maximum likelihood estimation approach, for implementing BMA are presented and applied together with around 1000 records issued from the RESORCE-2013 database. In the example considered, it is shown that BMA provides both a hierarchy of GMPEs and an improved out-of-sample predictive performance.

The normal mode method provides a reduced basis that can decribe the long range propagation of infrasounds in the atmosphere. Using that technique, we study the infrasound signal recorded in Japan after the explosion of the first reactor of the Fukushima power plant. By applying small perturbations to the sound speed profile, we find highly sensitive structures that can radically impact the signal. Moreover, the main tendencies seem to change when considering different datasets for the meteorological profiles.

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