Comparison of the bound influence estimator and the maximum likelihood estimator for magnetotelluric response function

摘要

The first magnetotelluric (MT) response function estimator is based on the least-square theory; the robust procedure can improve its performance. The robust M-estimator gives a small weight to reject the outlier based on the residual between the predicted electric field by the LS estimator and the observed electric field. 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. Alan Chave also creates an open-source code (BIRRP), and it is widely used in the MT community. Chave (2004) showed that the BI-estimator would perform better than M-estimator, but not all the cases. The leverage point corresponds to the large variation of the magnetic field. It may be an energetic signal or active noise. This paper will introduce an M-estimator to compare with the BIRRP code and demonstrate a case study that the leverage point corresponds to the energetic signal. At this condition, the M-estimator performs better than the BI-estimator.