Time-domain Green function solution for transient electromagnetic field

Time-domain near-source electromagnetic method has the merit of strong signal, deep detecting depth and high accuracy. However, the method meet problem, because dipole approximation in the near-source will cause greater error based on traditional electromagnetic theory. Studying direct time domain electromagnetic field analytical formula derivation is one way of solving the problem. Based on point charge hypothesis, TEM field analytical solution has been derived by introducing time-domain Green function in this paper. Integral formula has been used to transform electromagnetic field damping wave equation into Green function integral form. Auxiliary path has been constructed for solving singularity problem. 4-tuple generalized integral formula of time-domain electromagnetic field response has been arrived by using Jordan's lemma, the residue theorem and generalized function method. Direct-time-domain exact solution of D'Alembert equations firstly has been derived, whose form is agree with the traditioanl "matching" result, which show that the method of time-domain electromagnetic field based on Green function is right. Then, the direct-time-domain formula of diffusion function also has been given. After the copmaresion the numerical result between point charge Green function exact sulotion and approximate solution, it can be concluded that the derivation formula in this paper has higher precision. Furtherly, the full-space TEM direct-time-domain solution due to loop-source has been derived using integral method. The achievement lay a theoretical fundation for solving the problem of TEM All-Zone detection with directy time domain analytical solution.