Mathematical modeling problems connected with pulsed neutron-gamma logging

Abstract

The work is devoted to direct and inverse problems of the transport equation in the context of a nuclear geophysical technology based on pulsed neutron gamma logging of inelastic scattering (PNGL IS). In the first part of the paper we analyze the distribution of fast neutrons from a pulsed source of 14.1 MeV and study distributions of gamma quanta of inelastic scattering. The particle dis tributions are computed by the Monte Carlo methods. In the second part of the paper we consider the problem of evaluating the elemental composition of the rock from the PNGL IS measurement data. In its solution we use the method of successive approximations over characteristic interactions, which can be classified as a simple iteration; at each iteration step we solve the corresponding direct problem for the system of neutron and gamma quantum transport equations. The main aspects of the employed method and the results of the numerical experiments that prove the convergence to the exact solution are presented.Keywords: transport equation, pulsed neutron gamma log of inelastic scattering, direct and inverse problems, Monte Carlo methods, successive approximations by the characteristic interactions