Transforming a time-domain electromagnetic signal to a frequency-domain electromagnetic response using regularization inversion

ABSTRACTWide applications of time-domain electromagnetic (TEM) data require 3D inversion. A possible strategy is to use the developed 3D inversion algorithms in frequency-domain (FD) electromagnetic (EM) methods. Thus, the key of the strategy is how to transform the time-domain (t-d) EM signal into the FD. An inversion algorithm has been developed to transform the t-d signal into a corresponding FD response. In this method, a step-off current is presumed. Under this assumption, the Fourier transform relating the EM FD response to the t-d signal becomes a sine or cosine transformation. Using the polynomial approximation method, the transformation turns into a linear equation. From a set of t-d signals, FD responses could be obtained by solving these linear equations in the least-squares sense. To reduce the nonuniqueness of the solution, and enhance the solution stability, an additional smoothness constraint on the FD response is imposed, thus converting the minimization problem into a regularization inver...