For the past decade, the oil industry has used logging tools to understand the properties of the sub-surface. Water and hydrocarbons are contained in pores of sedimentary rocks beneath the sub-surface. The relaxation properties of the protons present in water and hydrocarbons as measured with nuclear magnetic resonance (NMR) can be used to determine both the rock and fluid properties adjacent to the borehole. The spin-spin relaxation (T2) is conventionally used for fluid typing in well logging. However, the distinction between relaxation times of water and oil is not always clear. The interpretation of the T2 distribution depends on a number of unknown factors such as viscosity of the hydrocarbon and wettability, relaxivity and pore geometry of the rock.
The study of spin-lattice (T1) and spin-spin (T2) correlation can provide us insights into the molecular processes of relaxation by providing an additional dimension for resolving the spin system. In this talk, I will first provide a brief introduction to the oil industy and the use of NMR in logging application. I will then present an experimental protocol to measure two-dimensional relaxation data. The measured two-dimensional data are related to to the density function of T1 and T2 by a Fredholm integral of the first kind. An algorithm to estimate the density function from the two-dimensional relaxation data will be described. Prior information about the smoothness of the desired solution is used to stabilize the problem.