THE PHYSICAL FOUNDATIONS OF FORMATION DENSITY LOGGING (GAMMA‐GAMMA)

Abstract

The principal modes of interaction between gamma rays and atoms are reviewed. Special attention is paid to the need for using only Compton scattering in order to determine the electron density of a sample or earth formation and for eliminating chemical composition effects arising from low‐energy photoelectric absorption. The nature of the so‐called Z/A effect is discussed in relation to the conversion of electron density, the immediately measured quantity, into bulk density. Since gamma‐ray diffusion results from repeated scattering in the formation, the Boltzmann transport equation is used as the framework for understanding empirical observations. The method‐of‐moments solution provides both an understanding of the spatial variation of the gamma‐ray energy spectrum and also a basis for reducing the Boltzmann equation to the simple diffusion equation. A discussion is presented comparing experimental results with the diffusion solution for the point‐source‐at‐plane‐interface problem. The comparison confirms the validity of the mathematical and physical approximations made.