Robust M-Estimation of CSAMT Impedance Functions

Abstract

Accurate estimation of impedance functions is essential for the correct interpretation of Controlled Source Audio Magnetotelluric (CSAMT) measurements. Noise is inevitably encountered when CSAMT observations are conducted and, consequently, impedance estimates are usually based on least-squares (LS) approximation. Least squares ultimately assume simple Gaussian statistics. However, estimation procedure based on LS would not be statistically optimal, as outliers (abnormal data) are frequently superimposed on a normal ambient CSAMT noise field, which is approximately Gaussian. In this situation, the estimation can be seriously misleading. It is then essential to use statistical procedures that are robust in the sense of being resistant or insensitive to the presence of the outliers.
This paper proposes an alternative CSAMT estimation procedure based on M-estimators that is robust and efficient in nature. Like the LS estimate, the M-estimate minimizes the difference between prediction and observation, but 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 CSAMT impedance. Using noisy synthetic data, it is shown that the proposed method can produce usable CSAMT impedance functions even under condition of severe noise contamination.