ADMM-Based Method for Estimating Magnetotelluric Impedance in the Time Domain

Abstract

Traditional magnetotelluric (MT) impedance estimations are based on Fourier theory and carried out in the frequency domain, which has a strict stationarity requirement for the analyzed signal. However, the stationarity assumption cannot be satisfied when the data possess a low signal-to-noise ratio and/or a short observation period. These shortcomings can cause significant errors in the MT impedance estimations, especially in the low-to-medium frequency bands. The alternating direction method of multipliers (ADMM) and polarization analysis of the electromagnetic signal can be attached to the time-domain MT impedance estimation to address these shortcomings. This time-domain technique calculates the impedance in the time domain without Fourier transformation, and the ADMM and polarization analysis are applied to further improve the stability and convergence of the impedance estimation. Here, we present an ADMM-based method for MT impedance estimations (ADMM-MT). Various noise are added to a noise-free MT signal to test the performance of ADMM-MT. The results show that ADMM-MT yields impedance estimates with relative recovery errors below 0.2, even when the signal-to-noise ratio of the data is 0 dB and the observation period is 60 min. We then apply ADMM-MT to field data in Inner Mongolia, China. The results indicate that the apparent resistivity curves obtained by ADMM-MT using a short time series are smooth over the 0.001–1-Hz band, which is consistent with the remote reference processing results obtained using a long time series. In contrast, the curves obtained by traditional robust estimation method are strongly biased.