Error analysis for remote reference magnetotellurics

Abstract Remote reference magnetotellurics (MT) yields estimates Z R 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, Z R 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 Z R 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 function in terms of the errors in Z R . By the central limit theorem, the distribution of errors will be Gaussian, independent of the statistics of the signals and noises, provided N is sufficiently large. Thus, confidence limits may be predicted readily. None of the assumptions in the error analysis is particularly restrictive, and the analysis should be applicable to most remote reference MT data. When the analysis is applied to real data, the predicted variances in Z R agree well with those determined from the scatter between values of Z R calculated from disjoint subsets of the original data.