A study on multi-exponential inversion of nuclear magnetic resonance relaxation data using deep learning

Nuclear magnetic resonance (NMR) is a powerful tool for formation evaluation in the oil industry to determine parameters, such as pore structure, fluid saturation, and permeability of porous materials, which are critical to reservoir engineering. The inversion of the measured relaxation data is an ill-posed problem and may lead to deviations of inversion results, which may degrade the accuracy of further data analysis and evaluation. This paper proposes a deep learning method for multi-exponential inversion of NMR relaxation data to improve accuracy. Simulated NMR data are first constructed using a priori knowledge based on the signal parameters and Gaussian distribution. These data are then used to train the neural network designed to consider noise characteristics, signal decay characteristics, signal energy variations, and non-negative features of the T₂ spectra. With the validation from simulated data, the models introduced by multi-scale convolutional neural network (CNN) and attention mechanism outperform other approaches in terms of denoising and T₂ inversion. Finally, NMR measurements of rock cores are used to compare the effectiveness of the attention multi-scale convolutional neural network (ATT-CNN) model in practical applications. The results demonstrate that the proposed method based on deep learning has better performance than the regularization method.