Multistation magnetotellurics. Final report, 1 January 1996--30 June 1997 Page: 4 of 85
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are provided in Egbert . Some additional examples and discussion of results are
presented in the next section.
To allow for the possibility of coherent noise we have adopted a multi-stage proce-
dure. In the first stage the MT array data is decomposed into coherent and incoherent
components, outliers in all channels are cleaned up, and an appropriate scaling (i.e., the
incoherent noise amplitude) i5 determined for each channel. This is accomplished for
channel j by: (a) robustly computing principal components (PCs) of (some or all of) the
remaining data channels; and ;b) estimating the incoherent noise scale from the residuals
to a robust regression of chanr el j on all significant PCs. The procedure is iterated, with
cleaned up data (from the previous iteration) used to compute the PCs for subsequent
iterations, and residual variances are converted to approximately unbiased estimates of
incoherent noise variances by solving a small system of linear equations (see Appendix A,
Using the cleaned scaled data, issues of coherent noise and optimal impedance estima-
tion can be addressed. As a first step in this stage we compute diagnostics for coherent
noise. Useful diagnostics include eigenvalues of the scaled spectral density matrix, canon-
ical coherences, canonical covariances, and eigenvector plots. these diagnostics allow us
to determine which stations and which frequency ranges (if any) are contaminated by
coherent noise. If we find that coherent noise is not a serious problem, impedances can
now be estimated. For this purDose we propose several robust variants on the multivariate
errors-in-variables estimator, which we refer to generically as RMEV estimators. These
schemes use information from all data channels to define optimal reference fields, and to
protect against outliers in all components.
When MT data is severely contaminated by coherent noise (as for the example small
arrays south of San Francisco, CA. considered in Egbert ), we have not found
any completely general or automatic "statistical trick" which can guarantee reasonable
results. However, the multivariate approach allows a greatly enhanced understanding of
signal and noise characteristics, which can (in some circumstances) allow us to greatly
reduce biases due to coherent noise. One general approach we have found useful is to
compute diagnostics for coherent noise contamination which are resolved in both time
and frequency. To stabilize (and reduce random errors in) these diagnostics (which have
only a small number of degrees of freedom) we first project the data vectors onto the
coherent signal/noise space. Time/frequency resolved diagnostics can clarify the degree
to which MT parameter estimates are likely to be contaminated by coherent noise, and
allow us to identify which parts of the data are least effected.
Provided coherent noise is Intermittent, an initial data screening based on these di-
agnostics can greatly improve MT parameter estimates. Furthermore, once we have rea-
sonable "starting guess" estimates of MT transfer functions, the geometrical character of
coherent noise fields can be estimated, and robust schemes can be tailored to eliminate
or downweight such noise throughout the data, further reducing bias.
In summary, there are three (possible) goals of multivariate analysis with multmtrn.
The first is to understand the character of the signal and noise. Can the situation be rea-
sonably characterized by the standard quasi-uniform (plane wave) MT source assumption
with incoherent noise added to each channel? Or is there evidence for consistent coherent
noise? The program produces output which make it fairly simple to verify if the former
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Egbert, G. D. Multistation magnetotellurics. Final report, 1 January 1996--30 June 1997, report, 1997-23~; Corvallis, Oregon. (digital.library.unt.edu/ark:/67531/metadc712133/m1/4/: accessed February 23, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.