Bounded influence magnetotelluric response function estimation

Robust magnetotelluric response function estimators are now in standard use in electromagnetic induction research. Properly devised and applied, these have the ability to reduce the influence of unusual data (outliers) in the response (electric field) variables, but are often not sensitive to exceptional predictor (magnetic field) data, which are termed leverage points. A bounded influence estimator is described which simultaneously limits the influence of both outliers and leverage points, and has proven to consistently yield more reliable magnetotelluric response function estimates than conventional robust approaches. The bounded influence estimator combines a standard robust M-estimator with leverage weighting based on the statistics of the hat matrix diagonal, which is a standard statistical measure of unusual predictors. Further extensions to magnetotelluric data analysis are proposed, including a generalization of the remote reference method which utilizes multiple sites instead of a single one and a two-stage bounded influence estimator which effectively removes correlated noise in the local electric and magnetic field variables using one or more uncontaminated remote references. These developments are illustrated using a variety of magnetotelluric data.