Numerical calculation of the wavefield transformation

By the wavefield transformation, which can transform the diffusive electromagnetic fields to wavefields defined in a time-like variable mathematically, if the corresponding wavefields can be accurately computed from the transient electromagnetic (TEM) sounding data, one would be able to interpret these TEM data using techniques developed for the wavefields such as the seismic migration imaging. In this paper, the Tikhonov regularization method and the L-curve criterion for determing the regularization factor has been adopted to solve an analytical wavefield transformation pair. From our numerical results, we find that, although above method can give us some regularized results correctly, but it also can severely introduce waveform broadening phenomena “numerically" with increasing the observer offset and the conductivity of earth that will severely reduce the imaging resolution in engineering. So, developing a numerical method that can reduce the transformed waveform broadening phenomena is the key issue to apply the wavefield transformation in addition to migration imaging technique interpreting the TEM sounding data.