Reducing Reliance on Observation Duration of Magnetotelluric Impedance Estimation With an Improved Instantaneous Spectrum-Based Method

The natural electromagnetic field observed in magnetotelluric (MT) sounding is nonstationary, making it challenging to obtain reliable frequency spectrum information using the Fourier transform. In practical measurements, long-duration observations of the electromagnetic field signal are often required to obtain accurate low-frequency impedance, resulting in significant technical difficulties and high economic costs. We provide a method for estimating MT impedance using the instantaneous spectrum obtained with variational mode decomposition (VMD). By replacing the Fourier spectrum with the instantaneous spectrum, this approach mitigates the requirement for extended signal observation time when estimating low-frequency impedance. Compared to previous studies on impedance estimation, we analyze the influence of signal period number on spectrum reliability, emphasizing the effectiveness and reliability of instantaneous spectrum in dealing with nonstationary signals. The feasibility of obtaining low-frequency MT impedance from short-duration observations is also discussed. The proposed method employs VMD to extract the instantaneous spectrum and utilizes hat matrix (a projection matrix) and signal noise separation (SNS) techniques to suppress noise interference in the spectrum, thereby enhancing the reliability of the instantaneous spectrum and the resulting impedance estimates. The method is applied to synthetic data with added noise and real data collected in the Qilian region of China, and the results are compared with those obtained by using different methods. The experiments demonstrate that the VMD instantaneous spectrum reliably reflects the spectral characteristics of the signal, exhibiting minimal changes as the signal duration decreases. Therefore, this method can obtain robust low-frequency impedance even with a short MT time series.