Analytical Solution of Direct and Inverse Problems in the Internal Gravity Waves Studies by the Doppler Frequency Shift Method

Abstract

An analytical solution of direct and inverse problems arising in the study of the internal gravity waves (IGWs) dynamic via recording of the Doppler frequency shift, is presented. The direct problem is to determine the response of the Doppler shift to IGWs in the region of the radio wave reflection point; the inverse problem is the determination of IGW parameters from data on the Doppler frequency shift. Solutions were obtained in an approximation of the isothermal ionosphere for the heights of the F-region. They are presented in a form convenient for their practical use and can have a wide range of applications, including the detection of soliton-like wave structures in the F-region of the ionosphere.