Perturbation theory for a spectrum of normal modes in a stratified inhomogeneous medium

A perturbation theory is proposed for open systems whose eigenvalue spectrum is complex and whose eigenfunctions become limitlessly large at infinity. For the case of the stratified inhomogeneous troposphere, an analysis is made of the spectrum of wave-propagation constants and the corrections to height functions in the case of weak refraction, when the height dependence of the refractive index differs only slightly from the dependence in the case of normal refraction.