On the stability of magnetotelluric transfer function estimates and the reliability of their variances

Using data from a continuously operating two-station magnetotelluric (MT) array in central California we have computed robust remote reference MT transfer functions (TFs) for each day in the 2 yr period 1996-1997. Typical deviations of the daily estimates from the overall long-term average TF ranged from 2-3 per cent for periods of less than 300 s to about 10 per cent at a period of 2000 s. Day-to-day deviations were largely random, and exhibited little temporal correlation or lone-term trend. There is some evidence for small-frequency independent variations in impedance amplitudes, suggestive of subtle slow changes in near-surface distortion. However, there was no clear seasonal component to this signal, as might be expected if hydrologic changes in the near surface were the cause. Comparison of estimated error bars to TF variability showed that for periods between 10 and 100 s (where coherent noise sometimes biased TF estimates) the standard asymptotic theory for the robust estimator yielded error bars that were too small by as much as a factor of two. At longer and shorter periods these standard error bars were consistent with the actual precision of the TF estimates. We also considered the reliability of error bars computed with two variants on the jackknife approach. For the first approximate scheme we computed the weights for the robust TF estimates once with all data, followed by application of the jackknife to the final weighted least-squares estimate. We show that for this 'fixed-weight' jackknife, variances can be given in closed form even for the remote reference case. Fixed-weight jackknife error bars were larger than those computed in the conventional fashion, but still significantly underestimated the true variability in the 10-100 s bias band, and were systematically too large at other periods. We also tried a subset deletion jackknife, applying the full robust procedure with contiguous subsets of data deleted. Provided large subsets (5 per cent, or approximately 1 hr) were deleted, this approach yielded significantly more realistic error bars in the bias band. However, error bars at periods outside the bias band now significantly overestimated the actual day-to-day variability of TF estimates. The jackknifed error bars were thus always more conservative, though not necessarily more reliable.