The statistical distribution of magnetotelluric apparent resistivity and phase
Chave, Alan D.
Lezaeta, Pamela F.
MetadataShow full item record
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.
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.
Showing items related by title, author, creator and subject.
Badiey, Mohsen; Wan, Lin; Lynch, James F. (American Meteorological Society, 2016-04-18)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 ...
Slivinski, Laura; Snyder, Chris (American Meteorological Society, 2015-11-11)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 ...
Segmentation of plate coupling, fate of subduction fluids, and modes of arc magmatism in Cascadia, inferred from magnetotelluric resistivity Wannamaker, Philip E.; Evans, Rob L.; Bedrosian, Paul A.; Unsworth, Martyn J.; Maris, Virginie; McGary, R Shane (John Wiley & Sons, 2014-11-11)Five magnetotelluric (MT) profiles have been acquired across the Cascadia subduction system and transformed using 2-D and 3-D nonlinear inversion to yield electrical resistivity cross sections to depths of ∼200 km. Distinct ...