Method of T2 spectrum inversion with conjugate gradient algorithm from NMR data
核磁共振共轭梯度解谱方法研究

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.