Reconstruction Method Of Gravity And Magnetic Fields By Equivalent Sources

The characteristics and changes of gravity and geomagnetic field are very important for the exploration and research of potential field.Based on the constitutive relation and the limited observation data,the mathematical and physical methods can be used to reconstruct the gravity and geomagnetic field.These methods could be applied to spatial continuation,gradient calculation,component conversion,gridding and so on.So that,a richer and more complete three-dimensional information of the potential field can be obtained.Moreover,the reconstruction of data on discrete positions not only improve conversion accuracy,but also recove the characteristics of source accurately,which is helpful to the effective separation of superposition field.The reconstruction techniques of discrete potential field data has been widely utilized in many areas.However,with the improvement of observation technology and computer technique,new requirements have been put forward for the reconstruction of potential field.Therefore,it is of great academic significance and practical value to develop potential field reconstruction technique.The equivalent source technique is widely used for restoring potential field.Based on the equivalence principle of potential field,the equivalent(virtual)sources are constructed to replace the actual sources through fitting the observed data.Then anomaly data would be produced at any other points in passive region by forward calulation of these equivalent sources.With the advantages of concision,stabilization,precision and flexibility,equivalent source method has still been the interest of geoscientists.However,the current researches still have some deficiencies,i.e.,low-frequency signal “leak” during reconstruction processing and lacking pertinence in equivalent source construction schemes.In this thesis,through synthesis experiments and analysis,we research the optimal structure of equivalent source and inversion algorithms,for solving the problems of traditional equivalent source method.Based on the theory of equivalent source method,we discuss the parameters setting of equivalent sources,which could impact calculation results significantly.These parameters include depth,spatial distribution,magnetization direction,cell type and mesh spacing of equivalent source.By analyzing the causes of signal leakage,we hold the opinion that using multi-layer equivalent source can effectively suppress the leakage of signal.Furthermore,through comparison of reconstruction accuracy,low-frequency signal recovery and computational efficiency,the results of synthetic experiments show that three-layer equivalent source scheme has the best reconstruction effect.According to above research results,we propose a technical scheme of three-layer equivalent source.In this scheme,the first layer is located at the depth of 1~6 times average interval of discrete data;the depth of second layer is determined by source depth estimation method;and the third layer is set near the depth of substrate.The equivalent sources on the first and second layer can be distributed with terrain or horizontal plane;the equivalent sources of third layer is placed along a horizontal plane.Rectangular prism is selected as cell of equivalent source to better retain multi-frequency field information.And the geometry size of cell increases with its setting depth,so as to ensure corresponding sensitivity of each cells and control the total number of cells.The threelayer equivalent source constructed by this scheme is distributed in a trapezoidal region under observation surface,which effectively reduces the edge effect over the study region.We discuss inversion algorithms for density or susceptibility of equivalent sources.By comparing advantages of each inversion algorithms and combining the three-layer equivalent source scheme,we select the preconditioned conjugate gradient method for solving inverse problem to obtain equivalent source property distribution.This method could make deep equivalent sources contributing by setting preoptimization factor,and it can reduce the skin effect and improve computational efficiency.In addition,we introduce the error of gradient of reconstructed potential field as a parameter for evaluating reconstruction quality,to improve the computational accuracy.The results of 2D and 3D syntheic experiments show that the proposed method can not only reconstruct gravity and magnetic field with high precision,but also obtain high precision gradients and components of anomaly.Furthermore,the data gridding and multi-source data fusion can be implemented well.Therefore,there are significant advantages over traditional equivalent source method.Finally,real data examples are used to illustrate the stability and practicality of the three-layer equivalent source method.