A Lightweight Multi-scale Neural Network for Inversion of NMR Relaxation Measurements in Porous Media

Abstract

Nuclear magnetic resonance (NMR) can be used to find fluid type and pore size distribution in rocks. Low-field NMR employs Carr–Purcell–Meiboom–Gill pulse sequences to measure reservoir rock properties, where echo signals are inverted to determine T₂ relaxation times. Further analysis provides petrophysical parameters and fluid classification. However, noise and the ill-posed nature of inversion lead to low-resolution T₂ spectra, complicating fluid quantification. This study introduces LMsNN, a lightweight multi-scale neural network, to enhance the accuracy of T₂ spectrum inversion. By incorporating physical response equations and constraints, LMsNN reduces artifacts and enhances optimization robustness. We validate the method using numerical simulations and direct rock sample measurements, comparing it with two traditional inversion techniques. Results show that LMsNN effectively processes low signal-to-noise ratio, improving fluid identification across rock types. We further applied LMsNN to NMR well log data, where the porosity derived from the inverted T₂ spectra closely matched direct rock sample measurements. These findings demonstrate that LMsNN significantly improves NMR relaxation spectrum resolution, offering a more reliable and robust approach for fluid characterization.