Research On Stretched-exponential Inversion Method Of MRS In Pre-polarization Field

Magnetic resonance sounding technology is a new geophysical exploration method.It uses paramagnetism of hydrogen protons in water to directly detect and quantitative evaluate groundwater.In recent years,it has been extensively used in analysis of near surface hydrological characteristics.Background field of traditional magnetic resonance sounding technology is the natural geomagnetic field.Signal collected is only nanovolt level,which is easily submerged by noise and has a low signal-to-noise ratio.In order to fundamentally solve the problem of low signal-to-noise ratio,this paper proposes the pre-polarization field magnetic resonance sounding technology,which greatly improves the amplitude of magnetic resonance signal in shallow underground layer.In addition,for porous groundwater with complex occurrence state,the magnetic resonance signal exists in the form of a multi-exponential free induction decay signal.At present,the existing single-exponential inversion method is relatively stable,but for the inversion of a complex water-bearing structure,there is a problem of insufficient accuracy.Multi-exponential inversion method considers multi-exponential phenomenon of complex pore water magnetic resonance signal,which can achieve accurate groundwater imaging.However its data set is too large and inversion efficiency is low.Aiming at this problem,this paper combines fractal dimension and the pore distribution of aquifer to describe pore size.Stretched-exponential C is introduced as fractal dimension of pore to accurately simulate magnetic resonance signal.Based on single-exponential inversion,this method adds a stretched-exponential C to approximate the attenuation of multi-exponential signal.Its advantages are small amount of inversion data,fast calculation speed and high inversion accuracy.In summary,this paper has carried out the research on inversion method of stretched-exponential based on pre-polarization field,which is of great significance to field engineering application.This paper has completed the following research contents and innovative achievements:1.Forward calculation of pre-polarization magnetic resonance sounding is realized.By studying basic principle of magnetic resonance sounding method of pre-polarization field,three-dimension mesh of model space is generated by using COMSOL multiphysics simulation software,and the value of pre-polarization field,emission magnetic field and induction magnetic field are calculated.Background field of magnetic resonance sounding in pre-polarization is the combined field of pre-polarization field and geomagnetic field,but the relationship between them is complex in space.In this paper,rotation matrix is used to simplify this problem.Then according to the principle of pre-polarization magnetic resonance sounding,the expression of sensitivity kernel function and forward signal of pre-polarization magnetic resonance are deduced.Finally the calculation method and meaning of resolution matrix are expounded.Resolution matrix is used to compare the central loop configuration with the traditional overlapping loop configuration.It is proved that the central loop configuration is superior.2.Aiming at the problem of insufficient accuracy of single-exponential inversion,a stretched-exponential inversion method is proposed and deduced,which uses all magnetic resonance signal waveforms and considers the multi-exponential characteristics of magnetic resonance signal of complex aquifer with multiple pores.The distribution of groundwater content w,average relaxation time T₂^*and stretched-exponential C are obtained by using the method of Tikhonov regularization and Gauss-Newton iteration method.For the selection of regularization parameters in inversion process,difference principle and dichotomy method are used to search the optimal regularization parameters.High precision imaging of underground water content is realized.3.Three water-bearing models are constructed.Under the two configurations of the overlapping loop and the central loop,stretched-exponential inversion and QT single-exponential inversion of the three models are carried out by numerical simulation,and RMSE is calculated.Stretched-exponential inversion method can realize the three parameter imaging of water content w,average relaxation time T₂^*and stretched-exponential C,considering the multi-exponential characteristics of magnetic resonance signals.QT single-exponential inversion method can only realize the two parameter imaging of water content w and average relaxation time T₂^*,without considering the multi-exponential characteristics of magnetic resonance signals.Comprehensive comparison shows that stretched-exponential inversion has a better inversion effect on water content and average relaxation time.The accuracy and effectiveness of stretched-exponential inversion method are verified.