Forward modeling and inversion of MRS relaxation signals using multi-exponential decomposition

The geophysical method of surface nuclear magnetic resonance (SNMR) or magnetic resonance sounding (MRS) allows a direct determination of the water-content (amplitudes) distribution in the subsurface. In addition, the MRS signal also contains information about the distribution of pore sizes (decay times) and electrical conductivity (phases) in the ground. So far, the inversion of MRS data has mainly concentrated on the interpretation of the water-content and decay-time distributions. The inversion is performed by fitting the recorded relaxation curve for each excitation pulse with a single initial amplitude value and relaxation constant, i.e. decay time (mono-exponential fit). However, MRS relaxation signals inherently exhibit a multi-exponential behaviour that arises due to the superposition of signal contribution originating from layers or volume fractions that feature different decay-time properties. Another geological situation that contributes to the multi-exponential behaviour of MRS relaxation data is given by a possible multimodal decay-time distribution within volume units or layers in the subsurface. This can be encountered in hard-rock material, e.g. sandstone, and occasionally in sediments. As a further consequence of the signal contribution from sources with different decay-time properties, the signal phase of MRS data is also affected. With the aim of a more quantitative and accurate aquifer characterization, in analogy with applications commonly used in borehole and laboratory NMR, we introduce a new approach to the inversion of MRS data taking into account the inherent multi-exponential behaviour of MRS relaxation data due to layering and non-uniform distribution of pores in the subsurface. Inversions carried out for synthetic data, i.e. the results of forward modelling, and MRS field data clearly show the advantages of such a comprehensive inversion (COIN) approach with respect to an improved determination of water content and decay times in the subsurface.