In this work a theoretical model has been developed to simulate the natural gamma-ray spectrometry responses in random media. The transport of gamma-rays is simulated by the finite-element method (FEM) for the scalar flux derived from the P1 approximation of the Boltzmann transport equation for radially symmetric media. The spectral response concerned with the random distributions of potassium-40, uranium-238 and thorium-232 enables us to determine the concentrations by weight of these nuclides using the Monte Carlo method. The physical parameters of the formations, i.e., diffusion coefficient and total and scattering cross-sections, are determinated by Klein-Nishina distributions and multiple linear regression of the experimental data. This method is used to generate synthetic well logs and also shows the usefulness of the FEM technique in extracting important information from the nuclear logs run in a complex geological environment.
Well-logging; Gamma-ray spectrometry; Random sources
