Study On Inversion Of Nuclear Magnetic Resonance Signals For Fluid Identification In Porous Formations

The echo signal of nuclear magnetic resonance（NMR）logging needs to be inversed for fluid identification.In the transverse relaxation time（T₂）distribution spectrum inversion process of one-dimensional（1D）NMR logging,the condition number of kernel matrix is large,and the inversion problem is ill-posed,which will cause great uncertainty in the inversion result,while the conventional kernel matrix optimization method is inefficient.The transverse relaxation time-diffusion coefficient（T₂-D）spectrum inversion problem of two-dimensional（2D）NMR logging has a larger amount of data,a higher degree of ill-posedness,when the signal-to-noise ratio（SNR）of the echo data is extremely low,the inversion error of the conventional algorithm is large.Based on the above problems,the following works are carried out in this thesis:The kernel matrix is optimized by discrete binary particle swarm optimization（PSO）algorithm,which reduces the ill-posedness of 1D T₂ spectrum inversion problem.The key point of kernel matrix optimization is to optimize the T₂ distribution sequence.In order to improve the optimization efficiency,the method of excessive pre-assignment of points and vector dot product to obtain points is proposed,and the condition number of the kernel matrix can be greatly reduced with only a few particle search steps.In order to verify the optimization effect,each optimized kernel matrix is used to construct multiple low SNR analog echoes with random noise,and the inversion is performed based on truncated singular value decomposition method.The results indicate that in the range of 16～64points,the inversion error of the optimized kernel matrix is lower than that before optimization,and the optimization effect is hardly affected by the randomness of noise.Based on the L2 regularization method,a regularization factor update strategy of double decay continuity is proposed,and the Barzilai-Borwein gradient and momentum acceleration strategy are combined to optimize the inversion results of T₂-D spectrum.The improved algorithm can continuously and quickly solve the inversion spectrum corresponding to multiple regularization factors,which effectively reduces the difficulty of selecting regularization factors.In order to verify the effect of the modified algorithm,the constructed 2D analog signal and the measured signal of Cu SO₄ solution are used for inversion.The results show that the improved inversion algorithm can accurately identify the fluid composition when the SNR is extremely low.Compared with the traditional inversion algorithm,the improved algorithm has higher regularization factor update efficiency and smaller inversion error.