| my country is a country with a shortage of fresh water resources,and per capita fresh water resources are only 1/4 of the world average.In order to solve the problem of the shortage of freshwater resources,in recent years,a non-invasive water exploration technology-Surface Nuclear Magnetic Resonance(SNMR)has been widely used in groundwater exploration in arid and water-deficient areas in my country.However,the traditional MRI data inversion method is susceptible to the influence of the initial model,easy to fall into the local optimal solution,and it is difficult to evaluate the reliability of the inversion result,which restricts the development of NMR water exploration technology.In order to solve these problems,this paper first studies the ground magnetic resonance data inversion method based on the fixed-dimensional Markov Chain Monte Carlo(MCMC)algorithm,which presets the number of inversion layers to a fixed value.From the point of view of probability statistics,each inversion parameter is regarded as a random variable,which changes randomly in each parameter space.Based on the Bayesian principle,this paper derives the expression of the posterior probability distribution function,searches the entire model space by generating Markov chains,generates candidate models from the proposed distribution,and completes the screening of candidate models according to the acceptance probability.The MCMC inversion method can generate a large number of samples that meet the accuracy of the data error.Probability and statistical analysis of the samples can obtain the maximum probability value and uncertainty information of each inversion parameter.Since the objective function used by the algorithm is not a single optimal solution function,the inversion process can jump out of the local optimal solution.During the inversion process,the selection of candidate models is only related to the current model,so the inversion result does not depend on the initial model.select.However,due to the complexity of the actual geological conditions,it is difficult to directly obtain the prior information of the number of layers in the underground water-bearing model.Therefore,it is difficult to obtain accurate inversion results for fixed-dimensional MCMC.On this basis,the inversion method is improved,and the optimized variable-dimensional MCMC inversion method is studied.In the inversion process,the sampling step is optimized and the number of layers is brought into the inversion process as an unknown parameter to improve the MCMC.The accuracy and computational efficiency of the inversion method.The main research work includes:The basic principles of magnetic resonance groundwater detection technology are studied,the forward modeling method of magnetic resonance is introduced,the calculation formula of magnetic resonance induction signal is deduced,and the change process of the macroscopic magnetization of hydrogen proton under the excitation current is introduced in detail.In addition,the finite element physics simulation software Comsol Multiphysics is used to subdivide the underground space,solve the underground three-dimensional space magnetic field intensity distribution,and calculate the sensitivity kernel function required for forward and inversion.The basic principle of the MCMC inversion method is studied,and the expression of the posterior probability distribution function of the inversion result is derived.Based on the Bayes theorem,the concept of the prior distribution and the likelihood function is introduced in detail,and the update of the Markov chain is defined.Method,discussed several common candidate model sampling methods,deduced the calculation formula of model acceptance probability,and verified the convergence of the algorithm.Traditional MCMC inversion methods have problems such as low accuracy and low inversion efficiency,which severely restrict the development of MCMC methods in inversion problems.This paper studies the optimized variable-dimensional MCMC inversion methods for the problems of inversion accuracy and efficiency..On the basis of the traditional MCMC inversion method,by adjusting the suggested distribution,step transformation is performed,that is,the search step is adjusted in the distance between the candidate model and the real model.When the distance is farther from the true value,the sampling step is increased.The step size is reduced when it is close to the true value,which effectively improves the calculation accuracy and efficiency of the MCMC inversion method.Taking into account the complexity of the geological conditions,the basic principle of the variable-dimensional MCMC inversion method is studied.The number of layers is regarded as a random variable and varies randomly with the inversion parameters,which further improves the calculation accuracy of the inversion method.Two sets of theoretical water-bearing models are designed,and the deterministic inversion method(genetic algorithm),the fixed-dimensional MCMC inversion method under different layer parameters,and the variable-dimensional MCMC inversion method are used to explain the theoretical data,verifying the variable-dimensionality The superiority of MCMC method.Using the measured magnetic resonance data collected in Shaoguo Town,Changchun City,the traditional fixed-dimensional MCMC and variable-dimensional MCMC inversion methods were used for data interpretation and the consistency comparison with actual geological data further verified the practicality of the variable-dimensional MCMC inversion method.In summary,this article has completed the study of the magnetic resonance inversion method based on the variable-dimensional MCMC algorithm.Through theoretical simulation data and measured data inversion interpretation,it is verified that the inversion method is improving the inversion accuracy and efficiency and evaluating the inversion results.The superiority and practicability of the reliability of MRI are of great significance to the application and development of magnetic resonance groundwater exploration. |
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