Finite-difference Time-domain Of Transient Electromagnetic Forward Modeling

Today, Transient Electromagnetic Method(TEM) is not only applied in oil exploration and metallic mineral exploration widely, but also widely used in engineering, such as mined-out areas exploration and bedrock detection. In contrast, the data processing and interpretation of TEM is not that well, one reason of this phenomenon is the complexity of TEM, another reason is that the computer hardware is not that advanced at that times. With the development of the computational software and hardware technology, it is possible to simulate the transient electromagnetic field precisely nowadays. And to do the simulation is important to its subsequent data processing and interpretation, it is also the foundation of inversion in the future.There is mainly three methods to simulate transient electromagnetic field: finite difference method, finite element method, integral equation method. We used finite-difference time-domain(FDTD) method in this paper. To introduce mainly in 2 dimensional model, in this paper, we introduced the finite difference grid which was firstly proposed by Yee in 1966[4], deduced the explicit and unconditionally stable difference form of the equations of electromagnetic field, discussed the approximate way to import the source and the solution of boundary condition problem of earth-air interface and boundary below the surface, also proposed a preferably time-stepping size.On the foundation of above, we used C++ to program the calculate programs, and python+matplotlib to plot and export the figures. The difficulty in programming was to solve the boundary problem of earth-air interface. Firstly we interpolate the electric field of the surface to uniform spacing with the cubic spline interpolation, then did the forward Fast-Fourier-Transform and multiplied the upward-continuation factor, did the inverse FFT at last. We did the interpolation and FFT by using the open source library that is GSL and FFTW3 separately[32,33]. Then we verified the correctness of the algorithm by comparing the FDTD result with analytic result of half-space, simulated there-layers model, vertical and inclined low-resistivity plate model, double vertical low-resistivity plate model and low-resistivity overburden model, which all have electrical line source on the surface. We also computed a few models using three-dimensional FDTD. The result proved that FDTD is a effective method to simulate TEM.