核磁共振测井数据高分辨率反演方法研究

On High Resolution Inversion of NMR Logging Data.

将核磁共振测井回波数据反演为弛豫谱时通常采用梭状函数抽样方法。为了提高弛豫谱反演的分辨率 ,采用了阶梯函数对弛豫谱进行抽样离散 ,获得了与常规方法一样的线性方程组 ,并采用奇异值分解与投影迭代方法求解对应的非负约束的正则化问题。系数矩阵条件数与参数分辨率矩阵分析表明 ,阶梯函数抽样形成的线性方程组具有更高的稳定性和更好的参数分辨率。

Traditionally, comb function sampling method is used to get a linear equation set for T 2 distribution at discrete T 2 points when transforming NMR logging data into T 2 distribution. In the inversion technique presented here, to form a linear system of equations, T 2 distribution is parameterized by piecewise function over continuous sampling intervals. The elements of the coefficient matrix of the new linear system are calculated with Legendre-Gauss quadrature rule. And the linear system of equations, under the nonnegative and minimum energy constrains, is then solved by introducing a projection operator and singular value decomposition technique. Numerical results show that the new system is much more stable than traditional method. And the analysis of parameter resolution matrix of the two methods shows that the new method is of higher resolution than the old one. Inversion results of synthetic and real data are consistent with the above theoretical analysis.