利用改进截断奇异值分解法反演核磁共振弛豫时间

An improved TSVD algorithm to inverse NMR relaxation time

截断奇异值分解(TSVD)法已应用于核磁共振弛豫时间T2谱反演,而奇异值截止值的选取和非负约束的实现是其关键。本文提出一种新的确定奇异值截止值方法,同时利用联合迭代反演法(SIRT)实现非负约束,使本文的改进TSVD法适用于低信噪比资料;该方法具有只需进行一次奇异值分解、计算速度快、保持T2谱分布连续等优点。数值模拟结果表明,改进TSVD法对信噪比仅为5的测量数据依然可得到优于其他方法的较好反演结果;实际岩心资料反演结果进一步证明该方法适用于页岩核磁共振岩心分析和核磁共振测井。

Truncated singular value decomposition(TSVD)algorithm is widely used for nuclear magnetic resonance(NMR)relaxation(T2)inversion.Truncated singular value and non-negative restriction are critical to this algorithm.In this article,we propose a new method to determine the truncated singular value,and use simultaneous iterative reconstruction technique(SIRT)algorithm to non-negative restriction.Thus,the improved TSVD algorithm suits to low SNR echo trains.In this new algorithm,we just decompose the singular value once.So the algorithm is faster than the old one,and keeps the T2 spectrum continuity.Digital simulations show that the inversions by the proposed algorithm match very well with the model,and better than the inversions by other algorithms when SNR=5.The inversion of real core data shows that the proposed algorithm works very well for shale reservoir NMR core analysis and NMR logging.