An Efficient Numerical Simulation Of Aem In Frequency/time Domain Based On Scattering Field Coupled Potentials In 3-D Undulating Terrain

The rapid development of domestic economy leads to the increasing demand for mineral resources,so the research and development of various geophysical exploration methods and means has become an important research topic.Airborne electromagnetic method(AEM)has the advantages of portability,flexibility,low cost and high efficiency,which can be applied to mineral resources and groundwater exploration and development in various complicated terrain areas(such as forests,mountains,swamps,lakes,deserts,etc.).It is very important to study and develop the three-dimensional forward modeling method for AEM system parameters optimization and processing and interpretation of measurement data.In this paper,an efficient numerical simulation algorithm for AEM response in frequency/time domain under undulating terrain is studied based on three-dimensional finite volume method of scattering field coupled potentials.Coupled potential three-dimensional finite volume method can not only solve the problem of poor discrete accuracy near the layer interface of the finite difference method,but also can choose a simpler grid to simulate the complex model compared with the finite element method,and can effectively solve the problem of low induction number with large contrast resistivity in AEM.Therefore,it is an important method for AEM 3-D forward modeling.In order to improve the efficiency of forward modeling and the calculation accuracy of near and far fields in the whole calculation area,the electromagnetic(EM)field is decomposed into the superposition of layered background EM field and three-dimensional scattering EM field according to the distribution of formation conductivity,and the Green function library of layered background electric field is established by using the Transmission Line Method(TLM).At the same time,the scattering current on any grid node in the 3d local scatterer is determined quickly by two-dimensional Newton interpolation technique.On this basis,a set of Helmholtz equation and electromagnetic field coupled potential scattering current discrete method are established by using three-dimensional coupled potential finite volume method and Yee staggered grid and equivalent conductivity heterogeneity standardization method.According to the characteristics of AEM moving sampling in large area,the discrete right end terms generated from different positions are combined,and the AEM responses of all emission sources in the frequency domain are solved by the direct method solver PARDISO.Finally,the AEM response in frequency domain of different frequencies is converted into the AEM response in time domain by frequency-time conversion technology.In this paper,the relevant principles of scattering field coupled potentials finite volume method and the AEM forward modeling theory are described in detail.The effectiveness of the algorithm is verified by numerical simulation results and the AEM response in frequency/time domain under the target layer fluctuation model is investigated.The specific contents mainly include the following parts:(1)According to the distribution of ground conductivity,the EM field is decomposed into the superposition of layered background EM field and threedimensional scattering EM field,and the Helmholtz equation of the scattering field coupled potential in the frequency-space domain is derived.The discretization process of coupled potential Helmholtz equation and space scattered current on Yee's staggered grid by finite volume method and the method of direct method solver PARDISO to solve the EM field of moving source is given.In order to improve the discretization accuracy of the equation,a standardized method is used to calculate the equivalent conductivity on the heterogeneous grid cells in the discrete process.(2)Based on the analytical solutions of voltage function and current function of background electromagnetic field and current source of "TE wave" obtained by TLM,a set of subdivision nodes are divided in cylindrical coordinate system,through cubic spline interpolation and Gauss-Legendre integration,the numerical solutions of voltage function and current function of "TE wave" current source on each columnar node are calculated,and the Green function library of background electric field is established.Finally,the background EM field of scattering points is calculated by two-dimensional Newton interpolation technique.(3)With the help of frequency-time conversion technology and cubic spline interpolation algorithm,the principle and calculation method of the AEM response in the time domain which transforms the frequency domain AEM response into step wave and arbitrary waveform excitation source are given.(4)Compared with calculation results of 2.5-D numerical mode-matching method(NMM)and literature,the validity of the proposed algorithm is verified,and then the AEM response in frequency/time domain under the undulating terrain of the target layer is calculated.It shows that the finite volume method of scattering field coupled potentials can be applied to the three-dimensional forward modeling of AEM well lay a solid foundation for the future three-dimensional inversion.