Research On Modeling And Inversion Of Three-dimensional Controlled Source Electromagnetic Method With Topography In Frequency-domain

In controlled source electromagnetic method, receivers in far fields receive the total EM(electromagnetic) fields produced by the anomalous body underground and a long wire that can produce EM fields in different frequencies. The total fields in far field can be used as data to illustrate the rock properties underground. This method has various benefits when we want to detect the near surface structure, such as high resolution as well as signal to noise ratio and less measuring time. As a consequence, it is widely used in the field work. However, the EM fields we receive can be divided by different components from anomalous body subsurface and overground topography respectively. Therefore, research on modeling and inversion of three dimensional controlled source EM method with topography is extremely significant.In the modeling, we get the EM fields at the location of anomalous body and topography by implementing the code of calculating fields on layered media with a long wire source. Those EM fields(primary fields) can be used as right hand side items of the governing equation based on second fields and the finite difference method and stagger grid method are implemented to discretize the governing equation along three different axis. In order to solve the discretized equation, we use the Dirichlet boundary condition in the end of different directions and QMR iterative method to get the secondary electric fields at each grid node in the computing area. The magnetic fields can be computed by the electric fields around them and interpolation formula. Numerical examples show that our modeling method is accurate enough and the divergence correction for current density is applied in our research and it is highly efficient in reducing the costing time.In the inversion, we implement the NLCG(Non-Linear Conjugate) method widely used by other researchers to inverse the observed data. In order to reduce the possibilities of pseudo solution, the one dimensional model roughness constraint and the bound value of parameters constraint are applied. After that, the formula of pseudo modeling is derived and it can avoid the long costing time of computing Jacobi matrix. Inversed examples illustrate that the inversion algorithm in our research can make contributions to the good fitting result and recovery of anomalous body.Three dimensional EM inversions are often time-consumed and occupy much memory. We propose the initial solution optimization method, which can reduce the inversed time efficiently according to the decline curve with objective function’s residual and iterative number. We believe this method will be used widely and contribute to the geophysical field work significantly.