This paper deals with mathematical models of reconstructing the fields of poly-dispersive impurities falls from instant sources as applied to traces of nuclear explosions and accidents. In approximation of a semi-kinematics model of aerosol impurities sedimentation in the atmosphere, the relations to evaluate the fields of impurity concentrations were obtained. Based on observational data of radioactive contamination of territories, the proposed evaluation model was tested as applied to a ground nuclear explosion set off on August 29, 1949 on the Semipalatinsk test site. With the help of asymptotic relations, the traces of the underground nuclear explosion "Chegan" were numerically analyzed. The observational data of contamination in the area of the East-Ural radioactive trace were interpreted. Using the obtained estimations of parameters, it is possibile to predict the radioactivity levels for the central part of the trace.