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Description
Robust estimation of transfer functions, power spectra and coherences from magnetotelluric time series employing RATRANS (Alan Chave, personal communications, 1987-90) uses a weighted regression routine which is automatic and data adaptive to overcome the problem of data which do not meet the requirements of a statistical distribution. The method of least squares, usually used to estimate transfer functions, assumes all the data fit a Gaussian distribution model. The least squares regression is easily influenced by the data which do not adhere to the model requirements, and the estimates are biased by those outliers. However, when the data do meet the Gaussian requirement, least squares is the most efficient regression method. The residuals obtained from the robust regression method are first scaled by either of two statistical spread parameters to theoretical model standards, and those that still lie outside the model distribution are downweighted through an iterative process. Two regression methods are utilized in RATRANS to determine the first set of residuals: 1) least squares, L2, and 2) least absolute value, L1. While the least absolute value regression method is more sensitive and, therefore, more robust, it sacrifices efficiency. Each of the two regression methods was paired with a scale choice to test the efficiency of regression and quality of results from normal data and distorted data. The results show that under normal conditions of low noise contamination and minimal distortion any of the four combinations yield comparable results. As data quality worsen, the least squares technique paired with median absolute deviation scaling consistently and efficiently yields better results. However, when the data are severely contaminated by noise or distorted by instrument failure or clipping, even the best robust technique cannot produce reliable results.
