Abstract
The initial magnetotelluric (MT) response function estimator is based on the least-square theory; it can be severely disturbed by the cultural noise. The different robust procedures have been developed and improve the performance of response function estimation dramatically. It is hard to say which method is better or not. In a specific situation, a different approach has different performance. Therefore, it is important to know the different property of them. Between the robust procedures, the robust M-estimator gives a small weight to reject the outlier based on the residual between the output (electric filed) of the least-squares estimator and the observed data. M-estimator can reduce the influence of unusual data in the electric field (outliers) but are not sensitive to exceptional input (magnetic field) data, which are termed leverage points. The bounded influence (BI) estimator combines the standard robust M-estimator with leverage weighting based on the hat matrix diagonal element's statistics, a standard statistical measure of leverage point. Chave (2004) also creates an open-source code, Bounded Influence Remote Reference Processing (BIRRP), and it is widely used in the MT community. But the leverage point corresponds to the large variation of the magnetic field. It may be an energetic signal or active noise. The performance of the M-estimator and the BI-estimator was dramatically different in the two situations. On the other hand, the repeat median algorithm can protect against unusual data (outlier and leverage point) maximum. We researched the difference property of bound influence (BI-estimator), maximum likelihood (M-estimator), and repeat median (RM-estimator) signal site MT respond function estimator. Three independent code (BIRRP code, robust M-estimator code, and RM-estimator code) are used to compare them. At last, two typical field data are used, making the difference between the bound influence estimator and robust M-estimator transparent. We found that when the leverage point is the energetic signal, the M-estimator will perform better than the BI-estimator. When the leverage point is the active noise, the BI-estimator will work much better than the M-estimator. Finally, we also investigated the ability of the three estimators at a single site.