核磁共振T_2谱M-P广义逆反演研究  

Study on the Inversion of NMR T_2 Spectrum with M-P Generalized Inversion

作　　者：李鹏举[1] 姜大鹏[1] 李鹏飞[2] 宋延杰[1] 

机构地区：[1]东北石油大学地球科学学院,黑龙江大庆163318 [2]东北石油大学计算机与信息技术学院,黑龙江大庆163318

出　　处：《吉林大学学报（地球科学版）》2011年第2期579-585,共7页Journal of Jilin University：Earth Science Edition

基　　金：中海油股份有限公司项目(JSKF2009YJ0007)

摘　　要：基于广义逆和奇异值分解理论,研究核磁共振T2谱反演的截断法和阻尼法。首先给出反演问题的M-P广义逆解;然后对系数矩阵进行奇异值分解求其M-P广义逆,对奇异值进行截断或者加阻尼,保证解的稳定性兼顾其分辨率;最后利用迭代技术实现解的非负约束。数值仿真实验和岩心T2谱反演表明:对于双峰谱,在信噪比SNR≥10时,截断法和阻尼法反演T2谱的分辨率和稳定性都很高;截断法截断因子选择范围小,在SNR<10时解的分辨率和稳定性差;阻尼法阻尼因子选择范围大,在SNR<10时解的稳定性好,但短组分分辨率低,长组分分辨率高。对于三峰谱,当SNR≥20时,截断法和阻尼法反演的T2谱光滑连续,具有三峰结构;当SNR<20时两者均不能反演出与构造谱接近的三峰谱。因此,2种方法可应用于SNR≥10的双峰谱和SNR≥20的三峰谱反演;从分辨率和稳定性、平滑噪声及截断和阻尼因子的选取上,阻尼法略优于截断法。The authors discussed both the cutoff method and damping method for NMR T2 spectrum inversion,which are based on the theory of generalized inverse and singular value decomposition.At first,the solution of M-P generalized inverse of the inversion problem is presented.Then M-P generalized inverse of coefficient matrix is obtained by means of singular value decomposition.The stability and resolution of the solution are ensured by discarding some small singular values or adding damping term.Finally,the non-negativity constraint of solution is realized by iterative technique.Numerical simulation and practical application of core demonstrates：As to bimodal spectrum,when the signal to noise ratio（SNR）≥10,T2 spectra inverted have high resolution and stability.Cutoff factors have a small range of option while damping factors have a large range of option.When SNR〈10,the resolution and stability of solution are poor in cutoff method while stability is well though low resolution of short-components,high resolution of long-components in damping method.As to trimodal spectrum,when SNR≥20,T2 spectra inverted with both methods has trimodal feature with good continuity and smoothness.When SNR〈20,both methods cannot invert trimodal spectrum close to the artificial spectrum.As a result,both of the methods can be applied to the T2 spectrum inversion of bimodal spectrum when SNR≥10 and of trimodal spectrum when SNR≥20.Taking the resolution and stability of solution,ability of smoothing noise,difficulty of selecting cutoff and damping factors into account,the damping method is a little better than cutoff method.

关 键 词：则井 核磁共振 M—P广义逆 奇异值分解 疋谱 反演 

分 类 号：P631.8[天文地球—地质矿产勘探]