Transient Electromagnetic Signal Filtering Method Based on Intelligent Optimized Time-Space Fractional-Order Diffusion Equation

To filter out noise in transient electromagnetic (TEM) signals, a Time-Space Fractional-order Diffusion Model (TSFDM) based on intelligent optimization is proposed. Firstly, based on the characteristics of the TEM signal, the signal is subjected to dynamic threshold segmentation processing. Then, the discrete difference method and the Grunwald-Letnikov approximation method with displacement are separately employed to approximate the time Caputo fractional derivative and the space Riemann-Liouville fractional derivative for solving the time-space fractional diffusion equation, this establishes an iterative convergent difference equation, and different smoothing operators corresponding to different stages of signal are set to obtain the TSFDM filter. Moreover, the Harris Hawk algorithm combined with Golden Sine and Energy-updating (GEHHO), is used to find the optimal value of the fitness function to obtain the optimal TSFDM filter for each stage signal. Simulation results show that after using the proposed method, the SNR of the TEM signal has increased by 33 dB, effectively restoring the trend of frequency domain curve changes. Compared to traditional methods, this approach demonstrates better performance in the evaluation metrics. Simulation experiments on geological structure inversion show that filtering and inversion of the noisy TEM signals yield results consistent with directly inverting the original signals.