Extracting useful high-frequency information from wide-field electromagnetic data using time-domain signal reconstruction

The wide-field electromagnetic method is widely used in hydrocarbon exploration,mineral deposit detection,and geological disaster prediction.However,apparent resistivity and normalized field amplitude exceeding 2048 Hz often exhibit upward warping in data,making geophysical inversion and interpretation challenging.The cumulative error of the crystal oscillator in signal transmission and acquisition contributes to an upturned apparent resistivity curve.To address this,a high-frequency information extraction method is proposed based on time-domain signal reconstruction,which helps to record a complete current data sequence;moreover,it helps estimate the crystal oscillator error for the transmitted signal.Considering the recorded error,a received signal was corrected using a set of reconstruction algorithms.After processing,the high-frequency component of the wide-field electromagnetic data was not upturned,while accurate high-frequency information was extracted from the signal.Therefore,the proposed method helped effectively extract high-frequency components of all wide-field electromagnetic data.

CONVERGENCE OF ADAPTIVE EDGE ELEMENT METHODS FOR THE 3D EDDY CURRENTS EQUATIONS

We consider an Adaptive Edge Finite Element Method （AEFEM） for the 3D eddy currents equations with variable coefficients using a residual-type a posteriori error estimator. Both the components of the estimator and certain oscillation terms, due to the occurrence of the variable coefficients, have to be controlled properly within the adaptive loop which is taken care of by appropriate bulk criteria. Convergence of the AEFEM in terms of reductions of the energy norm of the discretization error and of the oscillations is shown. Numerical results are given to illustrate the performance of the AEFEM.