Extracting the Virtual Reflected Wavelet from TEM Data Based on Regularizing Method

A pseudo-seismic interpretation method is an alternative way to process and explain transient electromagnetic (TEM) data, and has become a popular research field in recent years. TEM signals which satisfy the diffusion equation can be converted by means of a mathematical transformation into ones which obey the wave equation. For an ill-posed problem of this kind of transformation, a sub-regularization algorithm is developed in this paper to extract a virtual wavelet of the TEM field. According to the conventional designation of TEM recordings, the entire integration period is divided into seven time intervals. In order to avoid low accuracy in the calculations, high-density wavefield data has been calculated based on the former sub-division. Therefore, the virtual wavelet can be extracted successfully by using an optimized algorithm to obtain high-density integral coefficients for all time windows, and a satisfactory condition number of the coefficient matrix while taking a different channel number in each time period. The Tikhonov regularization inversion scheme is used to determine the optimal parameters based on minimizing a least squares misfit, and the Newton iterative formula is used to obtain optimal regularization parameters. Both synthetic model simulations and a real data interpretation example indicate that the proposed pseudo-seismic wavefield method is a suitable alternative way to interpret TEM data.