Robust M-Estimation of Magnetotelluric Impedance Tensors

Abstract

In situations in which Gaussian error assumptions are not valid, estimation procedures based on the least squares (LS) algorithm can be seriously misleading. It is then essential to use statistical procedures that are robust, in the sense of being relatively resistant or insensitive to the presence of a moderate number of outliers (abnormal data) superimposed on a common Gaussian noise background. This paper demonstrates the implementation of the robust regression M-estimate to magnetotelluric (MT) data. Like the LS estimate, the M-estimate minimizes the difference between prediction and observation, but it differs from the LS estimate in that it defines the measure of misfit in a way that does not allow a few bad points to dominate the estimate. Starting with the description of this estimate, several algorithms for computation are discussed and applied to estimate MT impedance. Using synthetic and real data, it is shown that, in comparison with the remote reference (RR) method (which is based on LS), robust procedures yield impedance estimates that are no worse than RR, and are often better.