Comparison of stabiliser functions for surface NMR inversions

Surface nuclear magnetic resonance is a geophysical technique providing non-invasive aquifer characterization. Two approaches are commonly used to invert surface nuclear magnetic resonance data: (1) inversions involving many depth layers of fixed thickness and (2) few-layer inversions without predetermined layer thicknesses. The advantage of the many-layer approach is that it requires little a priori knowledge. However, the many-layer inversion is extremely ill-posed and regularisation must be used to produce a reliable result. For optimal performance, the selected regularisation scheme must reflect all available a priori information. The standard regularisation scheme for many-layer surface nuclear magnetic resonance inversions employs an L2 smoothness stabiliser, which results in subsurface models with smoothly varying parameters. Such a stabiliser struggles to reproduce sharp contrasts in subsurface properties, like those present in a layered subsurface (a common near-surface hydrogeological environment). To investigate if alternative stabilisers can be used to improve the performance of the many-layer inversion in layered environments, the performance of the standard smoothness stabiliser is compared against two alternative stabilisers: (1) a stabiliser employing the L1-norm and (2) a minimum gradient support stabiliser. Synthetic results are presented to compare the performance of the many-layer inversion for different stabiliser functions. The minimum gradient support stabiliser is observed to improve the performance of the many-layer inversion for a layered subsurface, being able to reproduce both smooth and sharp vertical variations of the model parameters. Implementation of the alternative stabilisers into existing surface nuclear magnetic resonance inversion software is straightforward and requires little modification to existing codes.