The statistical distribution of magnetotelluric apparent resistivity and phase
Citable URI
https://hdl.handle.net/1912/2976As published
https://doi.org/10.1111/j.1365246X.2007.03523.xDOI
10.1111/j.1365246X.2007.03523.xAbstract
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 noncentral chisquared with 2 degrees of freedom, with the noncentrality 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 shortertailed 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 nonparametric 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.
Description
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): 127132, doi:10.1111/j.1365246X.2007.03523.x.
Collections
Related items
Showing items related by title, author, creator and subject.

Statistics of nonlinear internal waves during the Shallow Water 2006 Experiment
Badiey, Mohsen; Wan, Lin; Lynch, James F. (American Meteorological Society, 20160418)During the Shallow Water Acoustic Experiment 2006 (SW06) conducted on the New Jersey continental shelf in the summer of 2006, detailed measurements of the ocean environment were made along a fixed reference track that was ... 
Exploring practical estimates of the ensemble size necessary for particle filters
Slivinski, Laura; Snyder, Chris (American Meteorological Society, 20151111)Particle filtering methods for data assimilation may suffer from the “curse of dimensionality,” where the required ensemble size grows rapidly as the dimension increases. It would, therefore, be useful to know a priori ... 
On the statistics of magnetotelluric rotational invariants
Chave, Alan D. (Oxford University Press on behalf of The Royal Astronomical Society, 20131025)The statistical properties of the Swift skew, the phasesensitive skew and the WAL invariants I1−I7 and Q are examined through analytic derivation of their probability density functions and/or simulation based on a Gaussian ...