A sensitivity-based Bayesian hierarchical process for calibrating reduced-order wave-propagation models

Model calibration is viewed in the sense of adapting the full set of model parameters in order to get better ressemblance between observations and major end-predictions. In this study, we present a new probabilistic method to calibrate normal-mode-based propagation models using some observed data and sources of uncertainties. The unknown parameters are estimated using a multiple parallel Markov Chain Monte-Carlo (MCMC) method. Using a few normal modes allows to rapidly estimate the statistical distributions of the arrival characteristics, on a mode-by-mode basis. In a sense, the unknown inputs "propagate" through the plausible waveguides with each mode and alters its amplitude and phase structure. The resulting waveform is obtained as a combination of individual wavepackets so that the likelihood is a continuous function of input parameters. Further, once the maximum likelihood has been identified, the reduced model can be extended to higher dimensions to better refine the calibration process. Numerical results are obtained using a spectral numerical method and realistic representations of atmospheric disturbances. The method is used to revisit the infrasound signals recorded during campaigns of ammunition destruction explosions.