3D Forward Modeling And Inverse Of Controlled-source Electromagnetic Method Under Undulating Terrain

Controlled source electromagnetic method(CSEM)is a geophysical exploration technology that has developed rapidly in recent years.Its basic principle is to use an artificial field source to emit electromagnetic signals and receive the artificial source in a place far away from the field source.The electromagnetic field excited in the formation,air,seawater and other media to obtain the electrical distribution of the medium.As an important geophysical exploration method,CSEM uses a lower measurement frequency,which has the advantages of large detection depth(greater than 2000m),high resolution,high observation efficiency,and strong anti-interference ability in the field.It has been widely used in geophysical research such as exploration and environmental engineering.More and more complex geological exploration targets have brought higher and higher requirements,and the development of three-dimensional CSEM is imminent.Since the measured electromagnetic field data not only contains the information of the underground anomalies,but also is affected by the undulating terrain on the surface current density,it is of great significance to carry out the 3D CSEM forward and inversion research with terrain.Inversion is an indispensable step in electromagnetic data processing.From the perspective of numerical calculation,the inversion method is essentially an optimization algorithm,and forward simulation is its core.Through forward modeling,we can understand the abnormal shape of the electromagnetic response of various geological body combinations,and provide a basis for the interpretation of field measured data.In the forward part of this paper,the vector finite element algorithm is used to simulate the electromagnetic response between media with large electrical differences.Tetrahedral elements are used to mesh the 3D undulating terrain and underground anomalies.In the three-dimensional forward modeling of the electromagnetic method,the solution of large sparse linear equations formed after discretization is crucial.In this paper,the three-dimensional forward modeling of CSEM based on the electromagnetic field control equation is realized.The method of secondary field / primary field separation is adopted to avoid the singularity of the field source point,and the direct solution method is used to calculate the Helmholtz equation of the discretized secondary electric field.Through the numerical experiments of multiple theoretical models,the influence of the undulating terrain is analyzed and the validity and accuracy of the CSEM 3D forward algorithm used in this undulating terrain scene are verified.In terms of inversion,the choice of optimization algorithm is very important in electromagnetic inversion because of its influence on the efficiency of the algorithm.In this paper,based on the 3D CSEM forward algorithm under rolling terrain,the Gauss-Newton(GN)algorithm with faster iteration speed is used to invert the theoretical data after adding noise,and the line search is elaborated in detail.Technical details such as strategy,selection of regularization factors,calculation of sensitivity matrix and normal equations.By designing typical geoelectric models to calculate theoretical synthetic data under the common exploration scenarios(land and ocean)of the controlled source electromagnetic method,the correctness and effectiveness of the controlled source electromagnetic method inversion algorithm proposed in this paper are verified and analyzed Relevant factors affecting the inversion effect.