NMR T₂ Spectroscopy Inversion Based On Genetic Algorithm

Nuclear magnetic resonance is a new technique which developed from the last century later. By now, it has been widely used in medical, biological, chemical and geological fields and so on and NMR logging is a new type logging method based on the technology. The method reflects formation porosity, permeability, saturation and other information by studying the hydrogen's relaxation mechanism and the hydrogen widely exists in the external magnetic field. It overcomes the vulnerability of other conventional logging method that affected by the borehole, lithology and formation salinity ,and it can provide us the information of porosity that have noting to do with the rock lithology and bulk water saturation, free water saturation, permeability and the information of moving fluid oil, gas content. Meanwhile, the NMR logging is a effective mean to solve the problem of complex lithology, low resistance and low permeability reservoir.The direct measuring data of NMR logging is echo string, which is the response of different porosity and different nature of the fluid's relaxation. Echo string gets together of formation porosity, permeability, saturation and oil and gas information. It is the coding collecting of all the information. We can't get the information we want directly from the echo string. We should decode it and convert it into an intuitive way and the process is spectrum unfolding.The fluid relaxation mechanism is mainly transverse relaxation T2 and longitudinal relaxation T1 . Longitudinal relaxation process is long and it affects the efficiency of observation, so our spectrum process is mainly on T2 spectrum unfolding. The experimental analysis shows that the relaxation of a single pore fluid is a single-exponential decay process, and the main target of NMR logging - the strata around the bore is formed by porous, so the process of spectrum unfolding is a process of solution of a multi-exponential decay. By now, there have been various solutions of spectral methods, such as: single and double exponential fitting, least squares, non-negative least square method, penalty method, the regularization parameter method, combined iterative method and singular value decomposition. Because the formation of the pore structure is comparatively complicated, single and double exponential fitting can not fully explain the problem; Although variants based on least squares method are more commonly used method of exponential fitting, but the practical issues facing the penalty factorα's selection and adaptation of low signal to noise ratio limit the method's development; Combined iterative method has a strong ability to adapt to any signal to noise ratio, and even in low SNR we can get a good solution spectrum, but the method has a huge of computation and solution spectrum is inefficient; Regularization method is the main method to ensure that the value is non-negative solutions, but the selection of regularization parameter still very arbitrary; Singular value decomposition and improved methods based on this are many and the method is an important method to solve multi-exponential fitting, but because of problem of discontinuity of spectrum caused by reducing the morbidity of equation and problem that the method can not adapt to low SNR are still being studied.This article is based on Principles of nuclear magnetic resonance logging and the experience of the original method. It puts forward a new method of spectrum unfolding and that is the genetic algorithm. The method is based on theory of biological evolution and "survival of the fittest" natural criteria and it is a organized and intelligent adaptive search method with strong robust. Although the method can not be completely explained by a mathematical formula, but the optimization process basing on the mechanisms of biological evolution is undeniable. The paper synthetically utilizes and improves the method that gives us the GA'various parameters and we get the algorithm parameters and constraints of the actual problem base on the constraints in the spectrum unfolding .By constructing the forward model, the fitting results of the algorithm was tested. At the same time, we do a simple comparison with other spectrum unfolding algorithms. Through different structural spectra's fitting and comparison at different signal to noise ratio, we find that the method is highly adaptive and the method's effect is good. There is no line discontinuity, and its adaptability to the low signal to noise ratio's environment is significantly. On that basis, we verify the method with actual logging data and compare the result with NMR processing software DPP. We find that the result fitted by GA can nearly coincide with the DPP.Genetic algorithm has been widely used in the solution of large-scale equations, and it has good results in the solution of many practical problems. Through the combination of genetic algorithm and the spectrum solution we find that we can set the variable range to meet the constraints that relaxation components are non-negative. We can give the non-negative possible scope of the relaxation component which is based on past NMR work experience and the genetic algorithm can process through its own searching to find the optimal non-negative solution. Meanwhile, the rationality level of combination of different parameters determines the algorithm efficiency and solution quality. The algorithm involves a number of operators and parameters and these factors are largely linked with the practical problems and we can maximize performance of the algorithm only by selecting the best combination.Genetic algorithm has a very strong sense of organization. In previous studies, in order to strengthen the treatment effect of the algorithm, we constantly combine it with other optimization methods, such as neural networks, simulated annealing, etc, and the combination of methods proves that has a continuous improvement. In the solution process , we can also try to combine the algorithm with other algorithms, such as singular value decomposition method and neural network to maximum the quality of spectra solution.It is a new idea to introduce the genetic algorithm to the solution of NMR spectrum. We could make the method more suitable for spectrum solution by optimizing the algorithm parameters and operators of its own. Meanwhile, we can try to combine genetic algorithm with other optimization method to improve the spectral solution. In short, the genetic algorithm expands the research's space for the spectrum solution, and if we can form a stable regional parameters, the algorithm into the practical application stage will be possible.