Simplified normal mode treatment of long-period acoustic-gravity waves in the atmosphere

This paper deals primarily with the effects of geometric dispersion on low-frequnncy mechanical waves generated by nuclear explosions. This dispersion is the result of the stratification of the atmosphere (to be distinguished from dispersion due to changes in physical characteristics due to changing frequency). It is found that the pressure signal can be divided naturally into an early-arriving acoustic-gravity portion (treated in this report) and a later--by about five percent of the travel time--acoustic portion. In general, both portions of the signal are inversely proportional to the range (geometric spreading included), although, at very great ranges, portions of the gravity wave fall off faster by r^1/6; the effect of dispersion is to reduce the signal by r^-1/2. Most of the signal is composed of many propagating modes which, at a given time and range, will each demonstrate a characteristic frequency. A simplified treatment of this complicated model picture is presented here. It is argued that a ray treatment for the higher-frequency portion is appropriate. It is shown that the frequency of the long-period signal increases with time. So long as the frequency of the received signal is less than the characteristic frequency of the initiating explosive impulse, it is found that the signal has a universal form for the fundamental mode. Such characteristics as yield, range, and phase velocity merely change the scaling of the signal. It is concluded that attenuation is probably not important for the low-frequency signals (below one c/s) usually observed.