Ray Tracing for Long Range Atmospheric Propagation of Infrasound

Abstract

In the framework of the Comprehensive Nuclear-Test-Ban Treaty, the long range propagation of infrasound through the atmosphere is modeled in the limits of linear geometrical acoustics. In this paper, ray tracing equations are provided to develop an operational computational code. Especially, ray trajectory equations and geodesic equations needed for amplitude calculation are expressed in spherical coordinates. Reection of rays on the Earth surface and their initialization for a motionless point source are given. A way to validate the code implementation is proposed and illustrated. The waveform evolution along rays takes account of caustics and atmospheric attenuation. The time evolution of the pressure at a receiver is the sum of eigenrays contributions. An operational eigenrays research method based on shooting method is proposed. After determination of eigenrays, an optimization method is used in order to rene eigenrays initial parameters. The propagation of infrasound emitted by a motionless point source in a realistic atmosphere illustrated the method. Ray tracing limits are argued too. I. Introduction In the framework of the Comprehensive Nuclear-Test-Ban Treaty (CTBT), the International Monitoring System (IMS) is developing a network of sixty barometric stations. These stations, which record infrasound, detect long range explosions, supersonic airplanes, meteors, oceanic swells, and volcano eruptions. For data analysis, the Analysis, Surveillance, and Environment Department of the French Atomics Energy Commissariat (CEA), in collaboration with the Laboratoire de M ecanique des Fluides et d’Acoustique (LMFA), have modeled long-range atmospheric infrasound propagation. The atmosphere is a windy inhomogeneous medium in which the infrasound propagation is a three dimensional phenomenon. The time variability of the atmosphere and the wind are the main specicities of the atmospheric propagation that dier from seismic and oceanic propagation. Atmospheric propagation can be modeled by the Euler equations. Direct resolution of these equations (ex. nite-dierence methods) is often limited to two dimensional problems because of computational cost. For three dimensional problems, asymptotic developments of acoustic equations are useful. The parabolic equation method, frequently used in oceanic propagation, is less convenient for windy media. These two methods are numerically limited to low frequencies relatively to the range of propagation. For three dimensional inhomogeneous windy medium, geometric acoustics appear interesting, particularly for operational applications. This paper sums up the equations needed to develop a computational ray tracing code in the goal to predict the receiver pressure signature. The initialization of these equations for a motionless point source is