Accurate 2D/3D electromagnetic modeling for time-domain airborne EM systems

The existing industry software cannot deliver correct results for 3D time-domain airborne EM responses. In this paper, starting from the Fourier transform and convolution, we compare the stability of different modeling techniques and analyze the reason for instable calculations of the time-domain airborne EM responses. We find that the singularity of the impulse responses of EM systems at very early time that are used in the convolution is responsible for the instability of the modeling (Fig.1). Based on this finding, we put forward an algorithm that uses step response rather than impulse response of the airborne EM system for the convolution and create a stable algorithm that delivers precise results and maintains well the integral/derivative relationship between the magnetic field B and the magnetic induction dB/dt. A three-step transformation procedure for the modeling is proposed: 1) output the frequency-domain EM response data from the existing software; 2) transform into step-response by digital Fourier/Hankel transform; 3) convolve the step response with the transmitting current or its derivatives. The method has proved to be working very well (Fig. 2). The algorithm can be extended to the modeling of other time-domain ground and airborne EM system responses.Fig. 1: Comparison of impulse and step responses for an airborne EM system Fig. 2: Bz and dBz/dt calculated from step (middle panel) and impulse responses (lower panel) for the same 3D model as in Fig.1.