A Spectral Approach of Multi-Scale Metamodelling Applied to Acoustic Propagation

There exists many numerical methods to simulate wave propagation through complex media with a very good precision. However, taking into account the fluctuations of the propagation medium necessitates a statistical approach implying a prohibitive numerical cost.To have those studies affordable, we propose the construction of a metamodel based on a polynomial chaos decomposition of normal modes. This approach presents the great advantage to give statistics of signals propagating in a random medium at an affordable numerical cost.Those results are illustrated with acoustic propagation in the atmosphere. In fact, meteorological fluctuations have a critical impact on the propagation, it is therefore essential to take them into account. The numerical cost of a simulation over thousands of kilometers fully justifies the use of a metamodel. An application to source localization is proposed to illustrate the joint use of a metamodel and a bayesian inversion. The bayesian framework allows a resolution of the inverse problem in a probabilistic context able to take into account the fluctuations of the medium and uncertainties due to unknown source localization.