Generalized Error Analysis for Conventional and Remote Reference Magnetotellurics

An error analysis which applies to both conventional and remote reference magnetotelluric impedance and tipper estimates is developed based on the assumption that noise in the field measurements is governed by a complex normal distribution. Under the assumed model of noise it is shown that the theoretical expressions for the variances and covariances derived recently by Gamble et al (1979b) specifically for remote reference estimates apply to conventional estimates as well. However, calculations are biased if the impedance or tipper functions are biased. The impedance and tipper functions are calculated as ratios of two random functions of noisy field measurements. The expressions for the variances and covariances account for noise in both the numerator and denominator of the estimates. They are useful provided the probability that the magnitude of the random error in the denominator exceeds the magnitude of its expected value is small. Expressions for the bias errors of the impedance and tipper functions are obtained in order to assess the relative contributions of random and bias errors to the man squared error of the estimates. The relative magnitude of both random and bias errors depends on the noise level and on the values of the sample coherencies between various pairs of the field measurements used to compute a particular estimate