摘要
The method of regularization factor selection determines stability and accuracy of the regularization method. A formula of regularization factor was proposed by analyzing the relationship between the improved SVD and regularization method. The improved SVD algorithm and regularization method could adapt to low SNR. The regularization method is better than the improved SVD in the case that SNR is below 30 and the improved SVD is better than the regularization method when SNR is higher than 30. The regularization method with the regularization factor proposed in this paper can be better applied into low SNR （5〈SNR） NMR logging. The numerical simulations and real NMR data process results indicated that the improved SVD algorithm and regularization method could adapt to the low signal to noise ratio and reduce the amount of computation greatly. These algorithms can be applied in NMR logging.
正则化因子的选择方法决定了正则化方法的稳定性和准确度。在分析改进的奇异值分解法与正则化方法的关系的基础上,给出一个正则因子计算公式。数值模拟试验表明改进的奇异值分解法和正则化方法适应低信噪比。当信噪比低于30时正则化方法比奇异值分解法结果更好,当信噪比高于30时奇异值分解法更优。采用本文提出的正则因子的正则化方法可以适用于实际核磁测井的低信噪比(5<SNR)情况。数值模拟及实际资料的计算实验表明,改进的SVD反演算法与正则化方法都具有适应低信噪比、求解速度快等优点,可以满足核磁共振测井工作的需求。
