Error analysis for remote reference magnetotellurics

Remote reference magnetotellurics (MT) yields estimates ZR of the true impedance tensor Z in terms of average crosspowers between a reference field measured at a distant site and the electric and magnetic fields at the sounding location. In contrast to conventional estimates of Z, ZR is unbiased by the noise power in any field, provided the reference is uncorrelated with the noise in the electric and magnetic channels. When bias errors are eliminated, the accuracy of an estimate of Z is determined by random errors. The variance in each element of ZR can be expressed in terms of known average powers, if it is assumed the noises are independent of the signals, and that the noises are stationary. The variances decrease as the number of measurements N contained in the average powers increases. Hence, they can be made arbitrarily small. For small errors, the variance in any function of Z (for example, apparent resistivity, the phase of Z and the skewness), can be obtained from a Taylor expansion of the functio...