3D Forward And Inversion Of Nuclear Magnetic Resonance With Complex Electric Structure

Nuclear Magnetic Resonance(NMR)is an effective geophysical method for direct water investigation.This paper is aimed at the three dimensional(3D)forward and inversion of nuclear magnetic resonance to solve the water investigation with complex geoelectric resistivity.According to the basic principle of NMR,3D forward modeling of NMR is established with the finite element method.Considering the influence of resistivity on the NMR,the electric distribution is deduced from the perspective of apparent resistivity in transient electromagnetic.The initial value of water content is determined by the electrical characteristics and the nonlinear inverse problem of NMR is solved using the trust region method.The accuracy and effectiveness of 3D NMR inversions is improved by the fusion interpretation of NMR and transient electromagetic data.Considering the influence of conductive medium on the excitation field,the magnetic field distribution in the layered conductive medium is calculated based on the typical horizontal layered medium model.Then the influence of layered resistivity distribution on magnetic field components is investigated by numerical simulation.The results show that the distribution characteristics of resistivity must be considered in the NMR response especially in the medium with low resistivity.For the problem that one-dimensional model is difficult to accurately describe the electrical distribution with the complex structure of the underground water,the 3D NMR response model is established and the distribution equations and boundary conditions of 3D magnetic field are derived from the Maxwell equations.The effective is verified by the comparision of numerical calculation results and the digital filtering results.The sensitivity of NMR response to homogeneous space,water content,cover layer resistivity and background resistivity are discussed using the forward algorithm.The influence of water depth,thickness,location,resistivity and water content parameter information on NMR response are analyzed and the NMR response characteristics with different coil attitude,size and shape are studied.The simulation results of the NMR response for oil,water,oil and water show that the NMR responses vary obvious for the medium with different hydrogen.With the same pulse moment,the isomers of pure water can mostly reflect the NMR signal.The study on the response of 3D NMR provides an important reference for the inversion of NMR in the complex environment.The purpose of NMR inversion is to calculate the parameter information related with moisture content by the observed NMR response.In view of the influence of complex electric structure on NMR response,we can obtain the geoelectric model by using the transient electromagnetic information and determine the initial water content together with the special distribution of resistivity.The improvement of inversion of NMR and the reducing of inversion iterations show that the effectiveness is enhanced.Due to the influence of resitivity on NMR,the relationship between NMR response and medium water content should be nonlinear.Then the NMR inversion is equivalent to solving the optimization problem which is solved by the trust region method in this paper.The calculation procedure of the algorithm is explained and selection of the trust region radius and step length is determined.The terrain model,tunnel model and well logging model are used to further verify the validity of the proposed algorithm.The numerical simulation results of water detection model in different environments and tunnel advanced prediction model show that the water distribution characteristics can be determined by 3D NMR together with the well logging information.The accuracy of NMR inversion is improved by the joint interpretation of three dimensional inversion NMR and transient electromagetic data.The forward and inversion algorithm of 3D NMR with electrical structure is carried out in this paper which provides an effective way for the NMR detection with complex geological condition.The method is not only suitable for the half space but also to the full space exploration.Therefore it has practical significance for solving the water detection in different environments.