非负约束修正阻尼算法求解核磁共振测井T_(2)谱反演问题

Modified Non-Negative Constraint Damping Method for T_(2)Spectrum Inversion of Nuclear Magnetic Resonance

为了优化核磁共振测井技术,加快核磁共振测井数据处理速度,提出了一类非负约束修正阻尼算法求解核磁共振T_(2)谱反演问题。通过数学建模及理论推导,证明该算法可以更好地保留T_(2)谱的有效信息,同时也能更有效地减少反演问题的噪声对解的影响。数值算例表明新算法相较于修正的截断奇异值算法和阻尼算法具有更好、更稳定的反演效果,尤其是低信噪比情况下新算法的优势更加明显,可以进一步优化核磁共振测井技术。

In order to optimize nuclear magnetic resonance(NMR)logging technology and accelerate the processing speed of NMR logging data,a class of non-negative constraint modified damping algorithm is proposed to solve the NMR T_(2)spectral inversion problem.Through mathematical modeling and theoretical deduction,it is proved that the algorithm can retain the effective information of T_(2)spectrum better,and reduce the influence of noise on the solution of inversion problem more effectively.Numerical examples show that the new algorithm has better and more stable inversion effect than the modified truncated singular value decomposition method and damping method,especially in the case of low signal-to-noise ratio,the new algorithm has more obvious advantages,and can further optimize the NMR logging technology.