Robust Lp-Norm Inversion for High-Resolution Fluid Contents from Nuclear Magnetic Resonance Measurements

Fluid content computed from nuclear magnetic resonance (NMR) has proved to be an accurate and reliable tool for petrophysical property estimation. To overcome the limitations of conventional NMR measurements, high spatial resolution NMR (HSR-NMR) has been introduced to achieve the desired resolution for cores of any size. However, inversion of fluid contents from HSR-NMR data suffers from nonreliable measurements at the ends of the detection coil due to the heterogeneities of the magnetic fields caused by the relatively small size of the coil. A robust L-p-norm inversion algorithm, developed for geophysical inverse problems, has been implemented and applied on the inversion of NMR measurements. The estimated fluid content from L-p inversion matches well with the kerogen content in the cores both visually and quantitively. The resolution of the inverted fluid contents is as high as 1 inch. Further testing on the raw data with large derivations demonstrated that reliable results can only be achieved by using L-p inversion with low p's values within the range of (1, 1.1).