Méthode des rayons complexes pour la propagation infrasonore. Application au bang sonique d’un météoroïde
Annie Zelias
PhD thesis (in French)
Most of high-energy atmospheric phenomena, either natural (meteoroids, earthquakes, volcanoes, etc.) or anthropogenic (aircraft, chemical or nuclear explosions, etc.) emit acoustic waves of frequencies lower than 20 Hz, called infrasound. These waves can spread over thousands of kilometers thanks to their low attenuation and to the atmosphere stratification that guides their propagation. These long distances allow observation of acoustic information at any time and any point of the Earth. Thus, infrasound constitutes one of the detection technologies used within the framework of the Compehensive Nuclear-Test-Ban Treaty (CTBT). Simulation of the infrasonic propagation is the topic of many studies, in particular by parabolic approaches, finite difference models, eigen modes summations or by asymptotic methods such as ray tracing. This last one is suitable at a low numerical cost for very long distances in an inhomogeneous and advected medium, in three dimensions and for nonlinear effects. However, this method remains limited by the presence of caustics and shadow zones for which it is singular. In order to predict the geometrical parameters and the pressure signatures in these zones, while keeping its efficiency, we adapt the complex ray tracing method to the atmospheric propagation of infrasound.
In a first step, the usual ray method is recalled and its extension to the complex plane is presented. An analytical application is treated, corresponding to a fold horizontal caustic above the ground which can be formed by a supersonic flight at low Mach. This case highlights the influence of complex rays reflection on the ground, depending on the caustic altitude. In a second step, we develop a two-dimensional numerical algorithm computing eigenrays (rays
directly connecting the source to the receivers) in the whole domain and for all arrivals formed by the atmospheric waveguides. A detailed study of the point source case, representative for an explosion, with a reference atmospheric profile complemented by a horizontal wind, allows us to validate the developed eigenray research algorithm, by comparison to the parabolic approximation. The application is extended to the case of a range dependent profile. The
neighborhood of caustics is treated by the asymptotic Uniform Theory of Diffraction. For realistic atmospheric profiles, sound speed and wind datas have to be fitted by analytical functions ; various ways of fitting are proposed and compared to one another. This is then applied to a simplified case, inspired by the Carancas meteorite observed on September 15, 2007 in Peru. The outputs of the complex ray theory are compared to the recorded datas at one infrasound station located in the shadow zone. This shows that the complex ray method is effective in determining the geometrical parameters in the shadow zones.
“Résumé : La plupart des phénomènes atmosphériques de forte énergie, qu’ils soient naturels ou anthropiques émettent des ondes de fréquence inférieure à 20Hz, appelées infrasons. Ces ondes peuvent se propager sur des milliers de kilomètres en bénéficiant de leur faible atténuation et de la structure de l’atmosphère qui guide leur propagation. Dans le but de prédire les paramètres géométriques et les signatures dans les zones d’ombres, nous avons adapté la méthode des rayons complexes à la propagation atmosphérique des infrasons. Pour cela nous avons développé une méthode numérique permettant de calculer les rayons propres dans tout le domaine. Une étude détaillée sur le cas d’une source ponctuelle, analogue à une explosion a permis de valider l’algorithme par une comparaison à une méthode d’approximation parabolique. Une méthodologie d’ajustement de données de vitesse du son et du vent par des fonctions analytiques a été mise en place, afin de permettre l’utilisation de profils atmosphériques réalistes adaptés à la méthode des rayons complexes. Cela a donné lieu à l’application à un cas simplifié de météorite (météorite de Carancas observée le 15 septembre 2007 au Pérou), dont les signatures ont été enregistrées par une station infrasonore localisée en zone d’ombre. Ce cas nous a permis de montrer l’efficacité de la méthode des rayons complexes. “
