The statistical distribution of magnetotelluric apparent resistivity and phase

Author Posting. © The Authors, 2007. This article is posted here by permission of John Wiley & Sons for personal use, not for redistribution. The definitive version was published in Geophysical Journal International 171 (2007): 127-132, doi:10.1111/j.1365-246X.2007.03523.x.The marginal distributions for the magnetotelluric (MT) magnitude squared response function (and hence apparent resistivity) and phase are derived from the bivariate complex normal distribution that describes the distribution of response function estimates when the Gauss–Markov theorem is satisfied and the regression random errors are normally distributed. The distribution of the magnitude squared response function is shown to be non-central chi-squared with 2 degrees of freedom, with the non-centrality parameter given by the squared magnitude of the true MT response. The standard estimate for the magnitude squared response function is biased, with the bias proportional to the variance and hence important when the uncertainty is large. The distribution reduces to the exponential when the expected value of the MT response function is zero. The distribution for the phase is also obtained in closed form. It reduces to the uniform distribution when the squared magnitude of the true MT response function is zero or its variance is very large. The phase distribution is symmetric and becomes increasingly concentrated as the variance decreases, although it is shorter-tailed than the Gaussian. The standard estimate for phase is unbiased. Confidence limits are derived from the distributions for magnitude squared response function and phase. Using a data set taken from the 2003 Kaapvaal transect, it is shown that the bias in the apparent resistivity is small and that confidence intervals obtained using the non-parametric delta method are very close to the true values obtained from the distributions. Thus, it appears that the computationally simple delta approximation provides accurate estimates for the confidence intervals, provided that the MT response function is obtained using an estimator that bounds the influence of extreme data.This work was supported by NSF grant EAR0309584

Correction of shallow-water electromagnetic data for noise induced by instrument motion

Author Posting. © The Authors, 2004. This is the author's version of the work. It is posted here by permission of Society of Exploration Geophysicists for personal use, not for redistribution. The definitive version was published in Geophysics 70 (2005): G127–G133, doi:10.1190/1.2080748.An unexpected noise source was found in magnetic and sometimes electric field data recorded on the bottom of lakes in the Archean Slave craton (NW Canada) during warm seasons. The noise is due to instrument motion and in some instances direct induction by wind-driven surface gravity waves when the lakes are not ice covered. The noise can be reduced or eliminated by pre-filtering the data with an adaptive correlation noise cancelling filter using instrument tilt records, prior to estimation of magnetotelluric (MT) response functions. Similar effects are to be expected in other shallow water environments, and the adaptive correlation canceller is a suitable method to pre-process MT data to reduce motional noise in the magnetic field. This underscores the importance of ancillary tilt measurements in shallow water MT surveys. In coastal or lake bottom surveys, special efforts to reduce hydrodynamic effects on the instrument should also be pursued.This project was funded by NSF grant EAR-9725556 and EAR-0087699. P.L. ac- knowledges the Fundacion Andes for a postdoctoral grant