Transforming a time-domain electromagnetic signal to a frequency-domain electromagnetic response using Gauss elimination method

Time-domain electromagnetic method (TEM) is an electromagnetic prospecting method that has developed rapidly and widely used in recently years. The inversion of this method uses frequency domain electromagnetic method, so the key is how to transform electromagnetic signals from time domain to frequency domain. Aiming at this problem, this paper proposes an inversion algorithm for transforming a time-domain electromagnetic signal to a frequency-domain electromagnetic response. Assuming that the time domain electromagnetic signal is transformed by cosine or sine and fitted by polynomial under the condition of turn-off current, the linear equations composed of these time signals are solved by Gauss elimination method, and then the frequency domain response can be obtained. When this algorithm is applied to the synthesis of the perpendicular magnetic field of the magnetic dipole, the relative error between the inversion frequency domain response and the theoretical result is less than 1%. Thus, this method can maintain a relatively high accuracy when transform the time domain response to the frequency domain response.