Modeling Results of On- and Off-time B and dB/dt for Time-domain Airborne EM Systems

Airborne time-domain EM modeling generally uses the convolution of the transmitting current with the system responses. However, if no special attention is paid to the singularity of the system responses, serious stability problem may occur in the modeling of on-time and off-time magnetic induction B and time-derivative of magnetic induction dB/dt. In this paper, after a through investigation of different convolution modes, we choose a stable algorithm for modeling the responses of time-domain airborne EM systems, where the step response of the airborne EM system is calculated and convolved with the transmitting current by Gaussian quadratures. While the algorithm can be used for any arbitrary transmitting waveforms, we choose a half-sine and trapezoid wave as an example. The preliminary results for a half-space model show a clearly consistent integral-derivative relationship between the B and dB/dt responses.