The Finite-difference Forward Modeling Research For Transient Electromagnetic Method Of 3D

Transient electromagnetic method is widely used and has a very good effect. This paper is a study of three dimensional numerical simulation of transient electromagnetic method and finite difference method is used to simulate the quasi-static Maxwell’s equations. The advantages and disadvantages of this method have been discussed in other papers, so we focus on the initial electromagnetic field calculation methods and the effect of the difference order on the precision of numerical simulation. We also analyzed the influence of the mesh step size and surface-air boundary conditions for numerical simulation accuracy, the rest of the parameters with reference to the experience of our predecessors.There are three methods to calculate the impulse response of initial field that excited vertical magnetic dipole source and a rectangular loop source in a homogeneous half space. Method one: Calculate the electromagnetic field of the step response first, then calculate impulse response according to Faraday’s law of electromagnetic induction by the step response. Method two: Calculate impulse response directly by using time domain electromagnetic pulse response formulas. Method three: Receive the frequency domain electromagnetic formulas first, then calculate the impulse response based on GS algorithm. Through examples, we can get such a conclusion: If the other conditions remain unchanged, there is no big difference between the numerical simulation results that calculated by using three different initial field calculation methods of two different source. The relative error of the numerical solution and the analytical solution is basically less than 10%. From the view of calculation time and calculation stability, method three is time consuming and the results may be bad. Methods two has the highest computational efficiency. Although the computational efficiency of method one is slightly lower than the second method, its calculation results is better than method two. From time consuming and accuracy is considered, it is more appropriate to use method one to calculate the initial electromagnetic pulse response for our three dimensional numerical simulation.If the model is uniform subdivision, the spatial difference scheme can be generalized to arbitrary order, then we can study the effect of the difference format to numerical simulation accuracy. As a result, when the spatial difference order is increased to 6 order, increase the differential order again, such as 8 order and 10 order, also won’t increase the numerical accuracy. However, the high order difference scheme needs more strict time stability conditions and the longer calculation time, the spatial difference order can be selected as the 4 order or 6 order, so that the calculation accuracy will be guaranteed and the computing time will not increase too much. There is no need to use higher order spatial difference scheme that more than 6 order.For the simple model like homogeneous half space model, we can verify the results of numerical simulation through the analytical solution. To verify the correctness, the finite difference simulation results of complex three-dimensional model can be compared with the simulation results of VFEM provide by Li Jian-hui. We can say that numerical simulation results of finite difference method is correct, and has high precision.