A TWO-STAGE METHOD FOR SOLVING A NONLINEAR ILL-POSED OPERATOR EQUATION AND ITS APPLICATION TO THE INVERSE PROBLEM OF THERMAL SOUNDING OF THE ATMOSPHERE

The inverse problem of reconstructing the vertical profiles of CO\(_2\) in the atmosphere by IR spectra of the solar light transmission is investigated. To solve this problem, we propose a two-stage method. At the first stage, we use the modified Tikhonov method. At the second stage, to approximate a solution of the regularized equation, we apply a nonlinear analogue of the modified steepest descent method. The convergence theorem is formulated and the results of numerical experiments for retrieving the concentration of carbon dioxide in the atmosphere from measured spectra are discussed.