The inversion of nuclear magnetic resonance (NMR) relaxometry data based on the first kind of Fredholm equation is an ill-posed problem. The accurate transverse relaxation time (T₂) distribution is of great significance to improve the application of NMR. The T₂ distribution from the norm smoothing method for low signal-to-noise ratio (SNR) data is inaccurate owing to a large penalty term of the objective function. It is therefore important to improve the inaccuracy of the regularized solution. A two-step inversion method for NMR relaxometry data using norm smoothing and artificial fish swarm algorithm (AFSA) is proposed to improve the accuracy of inversion results. First, the raw NMR echo data are compressed using a simplified singular value decomposition method to reduce the inversion time. The regularized inversion solution from the norm smoothing method is taken as the initial values of the AFSA. Through the uncertainty analysis of the regularized inversion solution, the boundary of the fish swarm is determined. A more accurate solution is obtained by the iteration of the AFSA. The results show that the AFSA-optimized T₂ distribution is closer to the T₂ distribution of model than the regularized inversion solution in terms of the relaxation time and intensity of signal, and thus calculating the formation porosity more accurately. The proposed method shows good performance for processing NMR core data.

基于第一类 Fredholm 方程的核磁共振 (NMR) 弛豫数据的反演是一个不适定问题。准确的横向弛豫时间（T ₂）分布对于提高核磁共振的应用具有重要意义。的Ť ₂由于目标函数的惩罚项很大，来自低信噪比 (SNR) 数据的范数平滑方法的分布不准确。因此，重要的是改善正则化解的不准确性。提出了一种使用范数平滑和人工鱼群算法（AFSA）的核磁共振弛豫数据的两步反演方法，以提高反演结果的准确性。首先，使用简化的奇异值分解方法压缩原始 NMR 回波数据以减少反演时间。取范数平滑方法的正则化反演解作为 AFSA 的初始值。通过正则化反演解的不确定性分析，确定了鱼群的边界。通过 AFSA 的迭代获得更准确的解。T ₂分布在弛豫时间和信号强度方面比正则化反演解更接近模型的T ₂分布，从而更准确地计算地层孔隙度。所提出的方法在处理核磁共振岩心数据方面表现出良好的性能。