A low-order reduced model for the long range propagation of infrasounds in the atmosphere

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.