Research On Transient Electromagnetic2.5-D FDTD Forward Modeling

Electromagnetic method is one kind of geophysical methodology wiedly used in the exploration of mineral resources and environmental hydrogeology,which can be divided into two kinds: frequency domain electromagnetic and time domain electromagnetic methods.Transient Electromagnetic Method(TEM) belongs to the time domain method. Since1950s,for six decades’ continuous and rapid development,it had achieved considerable progress in theoretical research and application. But forward and inversion of multidimensional problems is very time-consuming and requires high capability of hardware,field data processing and interpretation is still of low level for the1-D interpretation.2.5-D problems represents an important geophysical situation since many geological target may be approximately of two-dimensions,while practical electromagnetic sources are three dimensions.In such cases,since a fully3-D medium is not need any more,the computing time can be greatly reduced by solving just the2.5-D problem.In addition,2.5-D problem is also more accurate than2-D problem in terms of approaching the practical field-geological condition.A2.5-D FDTD numerical method for TEM is presented in this paper.Firstly, We describe a numerical method for time-stepping Maxwell’s equations in2-D,which in a conductive earth reduces to the diffusion equation.The method is based on the classical Dufort-Frankel finite-difference scheme,which is both explicit an stable for any size of the time step.Transient electromagnetic surveys of several classical2-D models are simulated.Secondly, we have derived all expressions of TEM field in homo generous half-space generated by a rectangle loop source in the air space. Then we adopts sine transforms and Gaver-Stehfest transform digital filtering algorithm to reallize the transition form laplace-fourier domain to time domain. Two methods of derivation are listed,including the method base on Lagrange’s interpolation and the method of direct solution in laplace domain.Which laids a solid foundation for the2.5-D FDTD algorithm.Thirdly,the details of2.5-D FDTD algorithm of TEM are discussed.Including the method of choose of wave number,derivation of finite difference equation, the handling of boundary conditions.Finally,The2.5TEM FDTD algorithm computing program written in basic FORTRAN language is presented.Which is more time consuming but more conforming to reality than2-D program. The correctness and reliability of2.5D FDTD algorithm in this paper are proved by carring out the comparison between the numerical simulations and the1D analytical solution.The response characteristics of some typical2-D models are analyzed.