Research Of Inversion Method In MRS Based On The Cubic Spline Interpolation

Surface nuclear magnetic resonance(Surface-NMR)technology applies to the nondestructive detection of groundwater directly with the property of the groundwater in hydrogen proton spin.Surface-NMR has even became the primary modern geophysical exploration methods because of its high efficiency and evaluate the result accurately.In recent years,with the further study of Surface-NMR technology,Surface-NMR detection by 1 D to the 2 D and 3 D development.The 2 D Surface-NMR detection usually adopt measure array coil which detects by magnetic resonance instruments with laying a transmitter coil and multiple receiver coils on the same measuring line,receiver coils adopt edge to edge or half covered embedded inside the transmitter coil.This method can achieve 2 D imaging with groundwater,but still cannot detect accurately for underground complex aquifer structure.Due to the ground measure points are limited,the inversion results of accuracy and image smoothness are yet to be improved.We can improve the accuracy of the results by laying more detecting coils,but it will increase the detection work,reduce the work efficiency in the meantime.For the above problem,this paper proposes the inversion method based on the cubic spline interpolation which will improve the inversion precision and imaging smoothness,reduce the workload of coils laying when conduct field detection at the same time.Firstly,this paper make a mesh dissection of 3 D to calculate the magnetic field intensity around the space distribution of receiver and transmitter coils,to calculate the kernel function required by forward and inversion.This paper establish underground water model to gain E0-q calculated by forward method.Then,we use the cubic spline interpolation to calculate the initial amplitude E0 and get a new data matrix which will be put into 2 D initial value inversion(IVI)to image 2 D water content.And we use dichotomy to calculation and look for the optimal regularization factor in order to improve the efficiency of the inversion algorithm.Finally,verify the applicability of this inversion method according to forward simulation and inversion calculation with different underground water model.In this paper,the cubic spline interpolation method is proposed for calculate the initial amplitude E0,expand the data matrix.Then in order to correspond the new data matrix,we recalculate the kernel function which can be carry out SVD decomposition and get resolution matrix.Through contrast before and after the interpolation model resolution information,we can verify the forward method based on cubic spline interpolation which is conducive to get high resolution on shallow area.Aim at the problem of data matrix and kernel function matrix increases because of using the cubic spline interpolation method for each detection coil's initial amplitude,which resulted in increased inversion calculation,this paper proposes the method using the dichotomy to calculation and look for optimal regularization factor ?.We can calculate each value of the objective function,improve the efficiency of the inversion algorithm with not bring each ? to calculate objective function.This paper has carried out the error analysis of the initial amplitude of interpolation results and water content inversion results to test the accuracy of the inversion results with proposed method in this paper.The initial amplitude of interpolation results RMS error is less than 7 n V in an ideal situation.When add 20 n V noise,interpolation results maximum RMS error is 13.475 n V.In terms of inversion results,inversion method based on cubic spline interpolation can reduce the RMS error of 4% overall.Finally,make the inversion interpretation which verify the effectiveness of the proposed method by yield measurements in the town of Shaoguo and village of Yangtai.Through the above studies,this paper drew the conclusion that the inversion method of Surface-NMR which based on the cubic spline interpolation can reduce the number of measurement coils,improve accuracy of inversion results and image smoothness of the underground water at the same time.It can effectively reduce the workload in practice and improve the work efficiency.Besides,the method proposed in the article has practical significance in 3 D measurement and data interpretation.That five coils were used to measure with half covered from four horizontal directions has often adopted in 3 D measurement.And moving the coils along the diagonal in the measurement area,the amount of measurement coils was increased according to square.Therefore,the inversion method of Surface-NMR which based on the cubic spline interpolation can significantly reduce the workload of coils laying in 3 D measurement,and will get the smooth and precise imaging results of groundwater.