Comparison of stable maximum likelihood estimator with traditional robust estimator in magnetotelluric impedance estimation

Abstract

The newly developed stable maximum likelihood estimator (MLE) has been considered to be superior to the traditional robust estimation for Magnetotelluric (MT) transfer functions, based on the examination of field data. However, due to the unknown MT response function for real data, it is difficult to judge the validity of any comparisons between the performance of the two estimators. This can be realized by comparing the performances on synthetic data, as different ideal error distributions can be modeled (e.g., noise contaminated magnetic fields can be simulated by adding desired noise into the assumed clean version). In this paper, we generate synthetic MT data with desired error distributions (e.g. Gaussian and Cauchy distributions) based on the estimated MT impedance and Fourier transformed measured magnetic data (as the input) from one MT site located in southeast part of Tibet Plateau collected under the SinoProbe project. The comparison is demonstrated in terms of the apparent resistivity and phase, and their estimated standard deviations. The performance of the two methods and their variants are tested based on generated synthetic data with various noise patterns. Synthetic tests indicate that their performance in terms of handling noisy data is generally comparable. The bias in the estimation is more sensitive to noise in the input. Then they are applied to process real data from two MT sites in the same region, indicating their solutions are generally similar.