We present here the theory of the refraction inverse problem developed for the immersion geometry when either the receiver or a source change its position inside the atmosphere to be sounded. We consider the problem for the case when the refraction is set only within some portion of the entire altitude range studied. The inverse problem reduces to solution of integral equation of the 1st kind that is different inside and outside the altitude interval of sounding. We also present here analytical solutions obtained for the region inside the observation interval when assuming the receiving angle to be constant. Some results of numerical simulations are given in the paper as well.