Mathematical aspects of remote assessment of the radiation state of contaminated areas

Abstract

The use of radioactive materials is widespread in scientific investigations and various sectors of the economy. There are also extremely radiation-hazardous objects, for instance the well-known Chornobyl Exclusion Zone (Chornobyl, Ukraine) covering the large contaminated areas and the Shelter Object containing the materials of huge radioactivity of about 20 MCi. To safe handling with such objects and materials, the correct their monitoring, detection and characteristics evaluation are vital. The modern development of small flying machines, measurement equipment, and information technologies allow one to increase the amount of measurement data and their accuracy, and to reduce the processing time. On the other hand, the requirements to accuracy, quickness, and correctness of data interpretation increase as well. To solve these problems effectively, the mathematical tools of data processing should be improved. The main mathematical problem at the remote evaluation of radioactive fields relates to the solving the inverse problem for the Fredholm integral of the first kind. In this research, we consider the reconstruction of surface density of gamma radiation on the ground using the data of aerial shooting. We survey the methods for solving the inverse problem, their advantages and disadvantages. The adaptation of the methods to the reconstruction of nonstationary discontinuous radioactive fields is presented. We modify the numerical algorithms using the opportunities of modern calculating software. In particular, it is considered the task when the algorithm reconstructs the density distribution very well.