核磁共振共轭梯度解谱方法研究

核磁共振（NMR）解谱技术是核磁共振资料应用的基础和关键.本文将核磁共振解谱的混定线性反演问题转化为求目标函数极小值的最优化问题，然后利用共轭梯度算法具有二次终止性、收敛速度快的特点解决上述最优化问题.将该方法应用于无噪声和不同信噪比的理论数据解谱以及岩心NMR实验解谱并与真谱及实验室国外软件解谱结果对比表明：在信噪比SNR≥5时解谱结果和真谱符合得很好，谱线光滑连续；随着信噪比的降低对初始点的要求随之提高；两块岩心解谱结果与实验室结果符合得很好，利用解谱结果计算的核磁孔隙度与实验室氦孔隙度绝对误差分别为0.78%和0.57%.因此，本文方法有效、实用，具有较强的抗噪能力，对初始点的要求不高，能够应用于生产和科研实践中.

Method of T2 spectrum inversion with conjugate gradient algorithm from NMR data

The technology of T₂ spectrum inversion is the key to the applications of NMR data. Based on the optimization techniques, the T₂ spectrum inversion method of conjugate gradient is proposed in this paper. The method transforms the linear mixed-determined problem of T2 spectrum inversion into the typical optimization problem of searching the minimum of objective function by building up the inversion objective function according to the basic idea of geophysics modelling. The optimization problem above is solved with the conjugate gradient algorithm that has quick convergence rate and quadratic termination. The method has been applied to the inversion of noise free echo train generated from artificial spectrum, artificial echo trains with various signal-to-noise ratio(SNR) and NMR experimental data of drilling core. The comparison between the inversion results of this paper and artificial spectrum or the results of NMR laboratory shows that the method can correctly invert T₂ spectrum with good continuity and smooth from NMR relaxation data such as core or logging with low signal-to-noise ratio even though SNR=5.The T₂ spectra of two cores inverted with this method accord perfectly with those with imported software of laboratory, and moreover, the absolute error between the NMR porosity computed from T₂ spectra and helium(He) porosity in laboratory is 0.78% and 0.57%, respectively. Hence the T₂ spectrum inversion method is effective and practical for NMR data processing. It has strong anti-noise ability and doesn′t require elaborating initial point at the same time and can be applied to field production and scientific research.