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.
Lithospheric structure of an Archean craton and adjacent mobile belt revealed from 2-D and 3-D inversion of magnetotelluric data : example from southern Congo craton in northern Namibia Khoza, T. David; Jones, Alan G.; Muller, Mark R.; Evans, Rob L.; Miensopust, Marion P.; Webb, Susan J. (John Wiley & Sons, 2013-08-09)Archean cratons, and the stitching Proterozoic orogenic belts on their flanks, form an integral part of the Southern Africa tectonic landscape. Of these, virtually nothing is known of the position and thickness of the ...
Prediction of silicate melt viscosity from electrical conductivity : a model and its geophysical implications Pommier, Anne; Evans, Rob L.; Key, Kerry; Tyburczy, James A.; Mackwell, Stephen; Elsenbeck, James R. (John Wiley & Sons, 2013-06-12)Our knowledge of magma dynamics would be improved if geophysical data could be used to infer rheological constraints in melt-bearing zones. Geophysical images of the Earth's interior provide frozen snapshots of a dynamical ...
Chave, Alan D. (Oxford University Press on behalf of The Royal Astronomical Society, 2013-10-25)The statistical properties of the Swift skew, the phase-sensitive 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 ...