2013-11-14 – Seminar: Dr Alan Chave
When: 4pm on Thursday November 14th, 2013
Where: DIAS 10 Burlington Road
Speaker: Dr. Alan D. Chave (Woods Hole Oceanographic Institution, Woods Hole, MA, USA)
Title: Magnetotelluric Data, Stable Distributions and Impropriety: An Existential Combination
The author has long noted that the residuals from a robust or bounded influence estimate of the magnetotelluric (MT) response function are systematically long-tailed rather than being consistent with the fundamental robust model of a Gaussian core contaminated by a fraction of outlying data that are removed through processing. Recent investigation has shown that the actual distribution of magnetotelluric residuals is alpha stable. Alpha stable distributions are a family characterized by four parameters, one of which determines the tail thickness. Its upper end member is Gaussian, but for all other stable distributions, the variance is infinite and the distribution tails fall off algebraically rather than exponentially. It will be shown that a stable model for MT data is pervasive, and hence a maximum likelihood estimator (MLE) based on the stable model can be implemented through nonlinear minimization of an objective function. In parallel, it has been observed that MT responses are pervasively improper complex numbers, meaning that they are correlated with their complex conjugate. This has implications for the asymptotic complex Gaussian distribution of the MLE, and if accounted for, results in more realistic error estimates for the MT response function. These issues will be illustrated with data.
Finally, the implications of persistent infinite variance distributions for MT data will be discussed, including the need to abandon a nonstationary model for geomagnetic fluctuations and their origin in fractional derivative processes in the magnetosphere and ionosphere.