Research On Robust Impedance Estimation Method For Short-time Magnetotelluric Signals

Magnetotelluric(MT)sounding method observes the natural electromagnetic field in orthogonal directions on the surface.Through impedance estimation,this method can obtain electrical responses at different depths underground,which has the advantages of large exploration depth,low economic cost,and portable instruments.In recent years,magnetotelluric sounding has been widely used in the fields of deep mineral exploration,structural research,and volcanic activity observation.However,the natural electromagnetic signal observed by magnetotelluric sounding is weak,non-stationary and has the characteristics of large frequency bandwidth.Therefore,impedance estimation is greatly affected by noise and observation time.When the noise interference is strong or the observation duration is short,the impedance results often exhibit significant distortion,making it difficult to reliably reflect the underground electrical distribution.This paper focuses on the research of robust impedance estimation for short time magnetotelluric signals and proposes a magnetotelluric time-domain impedance estimation method based on the alternating direction method of multipliers(ADMM),a magnetotelluric noise reduction method based on the improved complementary ensemble empirical mode decomposition with adaptive noise(ICEEMDAN)and the magnetotelluric impedance estimation method based on the variational mode decomposition.These methods are used to enhance the anti-noise ability of impedance estimation and reduce the dependence of impedance estimation on observation duration,so as to achieve the robust impedance estimation in the low-to-medium frequency band(1–0.01 Hz),the suppression of strong noise interference and the robust impedance estimation in low frequency band(below 0.01Hz),respectively.Traditional magnetotelluric impedance estimation is based on the Fourier transform,which has a strict requirement for the stationarity of the magnetotelluric time series.When there is strong noise interference in the signal or the signal observation time is insufficient,the stationarity assumption of the Fourier transform can not be satisfied,and the impedance estimation results often presented with large errors.In this paper,the alternating direction method of multipliers(ADMM)and the polarization analysis of magnetotelluric signal in time-frequency domain are applied to the time-domain impedance estimation,and an ADMM-based magnetotelluric time-domain impedance estimation method is proposed.This method performs impedance in the time domain,which can avoid the Fourier transform on non-stationary electromagnetic field.The introduction of the ADMM algorithm and polarization analysis can further improve the stability,convergence,and robustness of impedance estimation results to noise interference.Applying the ADMM-MT method to the processing of short-time and noisy synthetic data,the results show that this method can effectively identify strong noise periods in signal based on polarization analysis,and the impedance solution based on time domain can reduce the sensitivity of impedance to noise and the dependence on observation time.In the cases of low signal-to-noise ratio,complex noise types,and short observation time,the ADMM-MT method can still maintain a low level of relative error between the obtained results and the pure signal impedance.The processing results of the measured data in Baiyinnuoer area,Inner Mongolia,China show that the ADMM-MT method can effectively improve the impedance estimation results in the low-to-medium frequency bands,and obtain more convergent and gentle apparent resistivity phase curves than traditional impedance estimation methods.However,this time-domain method has shortcomings such as strong sensitivity to persistent noise and poor ability to obtain low-frequency information.In lower frequency bands,this method requires a large amount of computation,has relatively high computational complexity,and is difficult to obtain robust impedance estimation results.The impedance estimation of magnetotelluric signal requires a high signal-to-noise ratio.When the signal to be processed is disturbed by strong noise,the impedance estimation is difficult to obtain a robust magnetotelluric response.Starting from the spectrum characteristics of noise sequence,this paper analyzes the mechanism of strong noise interference affecting impedance estimation results,points out that noise scale and noise waveform are important parameters that determine the impact of noise sequence on magnetotelluric response,and based on this,a multi-scale denoising method for magnetotelluric signal is proposed.In this method,the improved complementary ensemble empirical mode decomposition with adaptive noise(ICEEMDAN)is used to decompose multi-scale noise into different components,and then the short time Fourier transform(STFT)is performed on each component to obtain the time-frequency spectrum,so as to evaluate the impact of noise on the spectrum.This magnetotelluric denoising method based on the ICEEMDAN and STFT(ICMT for short)can filter out small-scale abrupt noise that has a large impact on the magnetotelluric response,and retain large-scale smooth noise that has a small impact,which not only suppresses the impact of noise interference,but also ensures a small loss of effective signal.Different noises are added to the pure magnetotelluric signal to test the denoising performance of the ICMT method.The experimental results show that the ICMT method can effectively reduce the loss of effective signal during the denoising process through multiscale denoising.When the signal-to-noise ratio of the signal to be analyzed is as low as-20 d B,the coherence between the denoising results and the original pure signal can still be maintained at more than 90%.The ICMT method is applied to the processing of low signal-to-noise ratio measured data in a mining area.The results show that the ICMT method can achieve good suppression effects on both strong and persistent noise,thereby improving the impedance estimation results in the low-to-medium frequency bands,enhancing the convergence of the impedance curves,and reducing the frequency error bars.However,the retained large scale smooth noise will still cause dispersion of some frequency points in the low frequency band.Natural electromagnetic signal observed by the magnetotelluric sounding is non-stationary,which dose not meet the stationary assumption of the Fourier transform for signals.In magnetotelluric exploration,it is often necessary to conduct long-term observations to obtain robust low-frequency impedance.In order to reduce the economic cost of long-term observation and enhance the robustness of low-frequency impedance estimation to a certain extent,this paper introduces the variational mode decomposition(VMD)and Hilbert transform into time-frequency domain impedance estimation,and a VMD instantaneous spectrum-based magnetotelluric impedance estimation method(VMT in short)is proposed.The proposed method uses VMD instantaneous spectrum instead of Fourier spectrum for impedance estimation,which can avoid the Fourier transform on electromagnetic signals and reduce the requirement for observation time for impedance estimation.In addition,this method inherits the theoretical framework of the frequency-domain impedance estimation,and combines it with signal noise separation(SNS)methods and bounded influence estimation strategies,which not only has high computational efficiency,but also ensures the robustness of impedance estimation.Synthetic data experiments compare VMD with EMD,instantaneous spectrum with Fourier spectrum,and the VMT method with traditional impedance estimation methods.The results show that the VMD instantaneous spectrum can reliably reflect the spectral characteristics of non-stationary signals,and has a low dependence on the observation duration.When the observation time is short,the VMT method can achieve a more robust impedance in the low frequency band than traditional methods.still ensure the reliability of the low-frequency impedance results.Finally,the VMT method is applied to the processing of broadband magnetotelluric data from Baiyinnuoer Mine in Inner Mongolia and long-period magnetotelluric data from Northern Qinghai-Tibet Plateau.The results show that the sequence length required by the VMT method to obtain robust impedance is systematically shorter than that of the traditional robust method.When the low-noise period is short or the observation period is insufficient,the VMT method can still obtain relatively robust low-frequency impedance,and the apparent resistivity and phase curves obtained have more low frequency points,better convergence,and smaller error bars than the results obtained by the traditional method.