Transfer functions: smooth robust estimates by least-squares and remote reference methods

A method is described for finding the magnetotelluric transfer function that has the least amount of curvature consistent with most of the data and with a 1-D conductivity interpretation over the widest possible frequency range. This could be called an ‘Occam’ transfer function. It is represented by the transfer function for the best fitting 1-D conductivity model times a distortion function. The latter permits smooth departures of the transfer function from the 1-D case if the data are inconsistent with a 1-D interpretation. The transfer function, for single-station or remote reference magnetotelluric data, is found by a method of successive interations that is found to converge within six to eight iterations. The estimate of the transfer functions is made robust by using frequency and time weights that remove the effects of outliers in the time and frequency domain. If the weighted residuals for remote reference data satisfy certain necessary conditions for uncorrelated noise then the contribution to the noise by the electric and magnetic data can be estimated and used to evaluate the least-squares and remote reference estimates. Examples illustrate the application of this method to artificial and real data. The latter consist of hourly cable voltage data from the Florida Straits, 1/256-s remote reference magnetotelluric survey data from the Phillippines and daily magnetic data from Tucson and Honolulu.