Remote Gamma Ray Mapping of Ground Surface: Mathematical Issues

The amount of use of radioactive materials permanently increases and, together with this, it is grows the danger related to the uncontrolled action of ionizing radiation on environment. Nuclear weapon application and accidents at nuclear power plants (NPPs) have shown the scope of dangers we can encounter. In particular, it should be mentioned the especially radiation-hazardous Chornobyl Exclusion Zone (Chornobyl, Ukraine) containing highly radioactive spots and the Shelter Object with the remains of a destroyed reactor. It is evident that a vital necessity arises to develop the tools for the fast and effective local safety diagnoses. To do this, in last decades the small flying machines are actively involved. These devices perform remote monitoring the ground surface and its subsurface layers. While the modern development of small smart machines, measurement equipment, and information technologies increased the amount of measurement data and their accuracy, to reduce the processing time, we still require improving the accuracy, quickness, and correctness of data interpretation. To solve these problems effectively, the mathematical tools of data processing should be modified. The main mathematical problem at the remote evaluation of radioactive fields relates to the solving the integral problem. In this research, we consider the forward and inverse problems. The former relates to evaluation of the detector's readings when gamma radiation is known. The latter deals with the reconstruction of gamma radiation density at the specified detector's data. We modified the numerical algorithm using the opportunities of modern calculating software and considered the case when the algorithm reconstructs the density distribution very well.