利用Phillips-Twomey方法对核磁共振弛豫测量结果的反演及其效果分析

Inversion of NMR transverse relaxation time using Phillips-Twomey method

为解决横向弛豫时间多指数反演所面临的反演不适定性和非负约束的问题,利用在反演理论中解决不适定性问题常用的Phillips-Twomey光滑化方法反演横向弛豫时间,并给出了一种实现非负约束的方法.通过与常用的反演算法进行对比,发现Phillips-Twomey光滑化方法更适用于低信噪比反演.考察了Phillips-Twomey光滑化方法对信噪比的敏感程度,研究横向弛豫时间布点数、原始回波采集个数、回波串采集时间间隔等因素对反演结果的影响.研究表明Phillips-Twomey光滑化方法适用于横向弛豫时间的多指数反演,且容易实现非负约束,对信噪比要求比较低.

The ill-posedness and the non-negative restriction are critical to multi-exponential inversion of NMR transverse relaxation time.Phillips-Twomey method is used for solving the ill-posedness and the non-negative restriction in the inversion of NMR transverse relaxation time,and a method for realizing non-negative restriction is proposed.Compared with conventional inversion methods,Phillips-Twomey method is more suitable to the inversion of NMR logging signals with low SNR.Its sensitivity to SNR is investigated,and the influence of the point number of pre-assigned transverse relaxation time,the number of spin-echoes and the time between two spin-echoes on the inversion result are studied.It is shown that,to the model with two peaks,the inversion result of the method is stable when SMR is greater than 10;the effect of the point number of pre-assigned transverse relaxation time on inversion result is little;the number of spin-echoes should be more than 1 024;the time between two spin-echoes should be less than 1.2 ms.Phillips-Twomey method is suitable to multi-exponential inversion of NMR transverse relaxation time,non-negative restriction can also easily realize,and the method is suitable to the inversion of low SMR logging signals.