| Surface Magnetometric Reistivity Method(surface MMR),is a non-inductive electrical prospecting method.The magnetic field is triggered by the artificial wire source of DC or pseudo-DC.Unlike the traditional resistivity method,in which the potential difference between two points on the ground is measured,surface MMR meadures the magnetic field at various points.The spatial variation of magnetic field is used to study the variation of the underground conductivity.The magnetic field singals obtained through surface MMR contain the wire magnetic field,the background magnetic field and the abnormal magnetic field.The background magnetic field and wire magnetic field are not related to the underground resistivity.In the non-1D condition,the abnormal magnetic field is generated by the current through the underground target body,which is the function of target body's geometric shape and the relative conductivity.As such,the abnormal magnetic field can reflect the inhomogeneity of the underground resistivity.The advantages of surface MMR are(1)no ground connection of measurement devices,(2)high measurement speed,(3)environmentally friendly(4)and high economic benefit.It is not only used in traditional geological survey and prospecting.,but also used in engineering investigation and pollotant monitoring in recent years.However,the 3D modeling and inversion technology of this method is not mature,and no 3D inversion research has been carried out in China by now.For this reason,the research of 3D surface MMR data non-linear inversion was conducted in this paper to realize the application of NLCG and L.-BFGS.At the same time,the impression method and iterative reconstruction method were used to improve the depth resolution of the surface MMR data.At last,detailed study on the3-D inversion of field data was carried out.The forward modeling of traditional MMR adopts the method thought of DC electric method,which starts with the Biot–Savart law or Electrostatic field Maxwell's equations.However,this can only establish a mathematic relation between the magnetic field and the rateof conductivity,and the inversion result is reflected by the ratio value.In this paper,the frequency domain Maxwell's equations are used in surface MMR modeling,which can directly establish a mathematic relation between the magnetic field and conductivity.With regard to the numerical calculation,at first the Helmholtz equation of the electric field is established.The electric field is divided into the primary field and the secondary field,in an effort to solve the Helmholtz equation of the secondary field.The virtual interface method is used to calculate the stratiform background field caused by the source item on the right hand side of the equation.The Helmholtz equation of the secondary field is solved using the staggered grid finite difference method.The magnetic field is obtained according to the Faraday's law based on the electric field.Considering that the ultra-low frequency is used to simulate the DC source,the divergence correction is introduced during solving of the matrix equation system to increase the precision and speed of solution.The numerical solution of 3D pseudo-sphere is compare with the analytical solution of sphere to verify the calculation precision.Simulation and comparison analysis are used for the x,y and z components of the total field and abnormal field.The results indicate that the total field value of y component(vertical source direction)is larger,and the abnormal field of y component can accurately reflect the position of the abnormal body without being subject to impact of the source wire.It is the best component for inversion.The 3D non-linear inversion of surface MMR data start from the regularization theory,and the gradient algorithm is used to constitute the optimization to the objective function through iteration.The NLCG and L-BFGS are used to realize inversion.In the sensitivity matrix is calculated in a non-displaying method in gradient calculation.The sufficient descent condition and curvature condition are used to determine the iteration step length of L-BFGS.The sufficient descent condition and converse tracing are used to determine the iteration step length of NLCG.Through NLCG and L-BFGS inversion of the synthetic model,it is found out that the horizontal resolution of surface MMR data is high and the depth resolution is low.To improve the depth resolution of surface MMR data,in this paper,the impression method used in 2D magnetotelluric inversion is introduced.During the application,the impression depth is quantified at first.The vertical interface of the non-0 area of the model variation in the last iteration is used as the impression depth.A new reference model reconstruction method is proposed,in which the part above the impression depth is replacedwith homogeneous half space and the part below the impression depth is the previous inversion result.The reconstructed model is the reference model of the next inversion.Secondly,the end condition of the iteration reconstruction is determined.Specifically,the model variation at the end of individual iteration reconstruction is 0,or the difference between the two model variations at the end of adjacent iteration reconstructions is less than the minimum threshold,then the iteration reconstruction can be stopped.The inversion results indicate that if the reference model of impression method is used for iteration reconstruction inversion,the resolution of surface MMR data inversion against abnormal bodies will be improved,and a more accurate buried depth can be determined.At the same time,the resolution of shallow abnormal bodies is not compromised.The NLCG and L-BFGS methods are used for 3D inversion study of the field data collected from Mons Cupri deposit.The results show that:(1)The impression method and iteration reconstruction can significantly improve the resolution ground field data and confirm the buried depth of target;(2)In the inversion of field data of surface MMR,the impact of resistive basement is significant,and will determine whether the inversion is successful.In this paper,the resistive basement layer is included in the expansion grid of the reference model,with satisfactory inversion effect obtained;(3)The detailed comparison of application effect of NLCG and L-BFGS in 3D inversion of field data.For the methods themselves,L-BFGS has better inversion effect than NLCG.However,there will be over-fitting of data in L-BFGS.If it is used in combination with impression method,NLCG method performs better,and the over-fitting of data will deteriorate with iteration construction for L-BFGS.Theoretically,the inversion speed of L-BFGS is faster than NLCG.However,the two are equivalent for surface MMR.The purpose of research in this paper aims to boost practice of surface MMR in China.I hope that the research findings in this paper will serve as a modest spur to induce someone to come forward with his valuable contributions for surface MMR data interpretation.Considering there is only a few examples of surface MMR study and application in China,the research findings in this paper can provide technical support for application and development of this method in China. |
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