Nonexponential decay of the surface-NMR signal and implications for water content estimation

Abstract

Noninvasive surface nuclear magnetic resonance (SNMR) measurements can yield direct and quantitative estimates of water content in the near surface. A fundamental assumption that is always made in the analysis of SNMR data is that the measured signal exhibits an exponential decay. Although the assumption of exponential decay is frequently valid, it can be shown that in the presence of an inhomogeneous magnetic field, the decay may be nonexponential in form. Simulated SNMR data were used to explore how the decay shape will vary with certain environmental and measurement conditions and to assess how nonexponential decay will affect SNMR-based estimates of water content. Results derived from analytical and pore-scale modeling demonstrated that the shape of the decay depends strongly on both pore geometry and the statistics of the regional or pore-scale magnetic field. In particular, the decay is most likely to be nonexponential when pores are large and when a strongly inhomogeneous magnetic field is present. For conditions in which the SNMR signal cannot be accurately modeled as exponential, standard processing approaches were found to result in significant errors in estimated water content—specifically, water content tends to be overestimated. Analysis of data misfits suggests that, in practice, it will be difficult to directly identify errors associated with nonexponential decay based only on the measured signal. Therefore, a description of the conditions leading to nonexponential decay and the implications for water content estimates is useful to support improved interpretation of SNMR measurements.