Introductory theory for upper atmosphere wind and sonic velocity determination by sound propagation

Abstract

The problem is considered of deriving the mean values of the horizontal wind velocity components u( z), v( z) and the velocity of sound c( z), averaged with respect to height z along a sound-ray travelling between two known points in the atmosphere, from measurements of the time of travel of the ray between these points and the co-ordinates of the ray. It is shown that, for a ray which does not suffer total reflection, expressions can be derived for u(z) , v(z) , and c(z) in terms of the measured quantities, and the mean value of the vertical component of wind velocity w( z), provided the variations in u( z), v( z), w( z), and c( z) with height are sufficiently small. The theory is carried further by working out in detail the second order contributions to u(z) , v(z) , and c(z) which arise from the variations in u( z), v( z), w( z), and c( z). Using typical atmospheric data, the more important of these second-order terms are evaluated numerically for the case of a sound-ray received at an observation point on the ground from a source at any height up to 90 km. It is shown that the contributions from these terms to u(Z) , v(z) , and c(z) are less than 0.8 m/sec when the ray lies near the vertical. For a ray which departs appreciably from the vertical (inelination about 45°), the contributions amount to a few metres per second, but are unlikely to exceed about 8 m/sec unless exceptionally large wind velocities are present.