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

Based on the optimization techniques, the T2 spectrum inversion method of conjugate gradient that is easy to realize non-negativity constraint of T2 spectrum is proposed. 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 objective function according to the basic idea of geophysics modeling. 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 train with signal-to-noise ratio (SNR)=25 and NMR experimental data of drilling core. The comparison between the inversion results of this paper and artificial spectrum or the result of software imported in NMR laboratory shows that the method can correctly invert T2 spectrum from artificial NMR relaxation data even though SNR=25 and that inversion T2 spectrum with good continuity and smoothness from core NMR experimental data accords perfectly with that of laboratory software imported, and moreover,the absolute error between the NMR porosity computed from T2 spectrum and helium (He) porosity in laboratory is 0.65%. (authors)