On the statistics of magnetotelluric rotational invariants
Chave, Alan D.
MetadataShow full item record
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 model for the magnetotelluric response tensor. The WAL invariants I1−I2 are shown to be distributed as a folded Gaussian, and are statistically well behaved in the sense that all of their moments are defined. The probability density functions for Swift skew, phase-sensitive skew and the WAL invariants I3−I4, I7 and Q are derived analytically or by simulation, and are shown to have no moments of order 2 or more. Since their support is semi-infinite or infinite, they cannot be represented trigonometrically, and hence are inconsistent with a Mohr circle interpretation. By contrast, the WAL invariants I5−I6 are supported on [ − 1, 1], and are inferred to have a beta distribution based on analysis and simulation. Estimation of rotational invariants from data is described using two approaches: as the ratio of magnetotelluric responses that are themselves averages, and as averages of section-by-section estimates of the invariant. Confidence intervals on the former utilize either Fieller's theorem, which is preferred because it is capable of yielding semi-infinite or infinite confidence intervals, or the less accurate delta method. Because section-by-section averages of most of the rotational invariants are drawn from distributions with infinite variance, the classical central limit theorem does not pertain. Instead, their averaging is accomplished using the median in place of the mean for location and an order statistic model to bound the confidence interval of the median. An example using real data demonstrates that the ratio of averages approach has serious systematic bias issues that render the result physically inconsistent, while the average of ratios result is a smooth, physically interpretable function of period, and is the preferred approach.
Author Posting. © Author, 2013. This article is posted here by permission of Oxford University Press on behalf of The Royal Astronomical Society for personal use, not for redistribution. The definitive version was published in Geophysical Journal International 196 (2014): 111-130, doi:10.1093/gji/ggt366.
Showing items related by title, author, creator and subject.
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 ...
Baba, Kiyoshi; Chave, Alan D. (American Geophysical Union, 2005-12-14)The large contrast in electrical conductivity between seawater and the underlying seafloor accumulates boundary electric charges which can severely distort observed electric and magnetic fields. For marine magnetotelluric ...
Baba, Kiyoshi; Tarits, Pascal; Chave, Alan D.; Evans, Rob L.; Hirth, Greg; Mackie, Randall L. (American Geophysical Union, 2006-11-16)The electrical structure of the upper mantle beneath the East Pacific Rise (EPR) at 15°45′S is imaged by inverting seafloor magnetotelluric data obtained during the Mantle ELectromagnetic and Tomography (MELT) experiment. ...