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Parker, RL.  2010.  Can a 2-D MT frequency response always be interpreted as a 1-D response? Geophysical Journal International. 181:269-274.   10.1111/j.1365-246X.2010.04512.x   AbstractWebsite

Weidelt and Kaikkonen showed that in the transverse magnetic (TM) mode of magnetotellurics it is not always possible to match exactly the 2-D response at a single site with a 1-D model, although a good approximation usually seems possible. We give a new elementary example of this failure. We show for the first time that the transverse electric (TE) mode responses can also be impossible to match with a 1-D response, and that the deviations can be very large.

Medin, AE, Parker RL, Constable S.  2007.  Making sound inferences from geomagnetic sounding. Physics of the Earth and Planetary Interiors. 160:51-59.   10.1016/j.pepi.2006.09.001   AbstractWebsite

We examine the nonlinear inverse problem of electromagnetic induction to recover electrical conductivity. As this is an ill-posed problem based on inaccurate data, there is a critical need to find the reliable features of the models of electrical conductivity. We present a method for obtaining bounds on Earth's average conductivity that all conductivity profiles must obey. Our method is based completely on optimization theory for an all-at-once approach to inverting frequency-domain electromagnetic data. The forward modeling equations are constraints in an optimization problem solving for the electric fields and the conductivity simultaneously. There is no regularization required to solve the problem. The computational framework easily allows additional inequality constraints to be imposed, allowing us to further narrow the bounds. We draw conclusions from a global geomagnetic depth sounding data set and compare with laboratory results, inferring temperature and water content through published Boltzmann-Arrhenius conductivity models. If the upper mantle is assumed to be volatile free we find it has an average temperature of 1409-1539 degrees C. For the top 1000 km of the lower mantle, we find an average temperature of 1849-2008 degrees C. These are in agreement with generally accepted mantle temperatures. Our conclusions about water content of the transition zone disagree with previous research. With our bounds on conductivity, we calculate a transition zone consisting entirely of Wadsleyite has < 0.27 wt.% water and as we add in a fraction of Ringwoodite, the upper bound on water content decreases proportionally. This water content is less than the 0.4 wt.% water required for melt or pooling at the 410 km seismic discontinuity. Published by Elsevier B.V.

Prieto, GA, Parker RL, Thomson DJ, Vernon FL, Graham RL.  2007.  Reducing the bias of multitaper spectrum estimates. Geophysical Journal International. 171:1269-1281.   10.1111/j.1365-246X.2007.03592.x   AbstractWebsite

The power spectral density of geophysical signals provides information about the processes that generated them. We present a new approach to determine power spectra based on Thomson's multitaper analysis method. Our method reduces the bias due to the curvature of the spectrum close to the frequency of interest. Even while maintaining the same resolution bandwidth, bias is reduced in areas where the power spectrum is significantly quadratic. No additional sidelobe leakage is introduced. In addition, our methodology reliably estimates the derivatives (slope and curvature) of the spectrum. The extra information gleaned from the signal is useful for parameter estimation or to compare different signals.

Parker, RL.  1998.  Inversion of on-axis magnetic anomalies. Geophysical Journal International. 134:617-624.   10.1111/j.1365-246X.1998.tb07143.x   AbstractWebsite

The theory for recovering crustal magnetization from along-strike and, especially, axial magnetic profiles is examined. We develop a conventional Fourier technique that takes into account the special magnetic cross-section at a ridge axis including the thinning of layer 2A. Such an approach might be completely inappropriate because it is assumed that the observation path is perpendicular to all the magnetic variability, whereas in fact the path lies in the direction of least magnetic variation. To study this question and to overcome possible deficiencies, we consider a statistical modification of the theory in which the magnetization is treated as a planar stationary process in a thin layer with known power spectrum. The relationship between two signals is studied: the magnetic anomaly on a straight path at the sea surface, and the magnetization in the crust immediately under the observation track. The coherence between the two signals can be calculated, as well as the transfer function between them. We test the ideas with data from a long axial magnetic profile on the southern East Pacific Rise compiled by Gee & Kent. A model power spectrum is estimated from these data: the spectrum is red and, as expected, highly elongated perpendicular to the strike of the ridge. We find strong coherence (gamma(2) > 0.8) between the magnetic anomaly and the subtrack magnetization for wavelengths longer than 50 km, but coherence falls sharply for smaller scales. The naive, 1-D filter theory incorrectly predicts a close relationship clown to much finer scales (3 km). Calculations for hypothetical surveys off-axis predict that there is always a band of high coherence, but only for an on-axis survey does the good correlation extend to infinite wavelength. We conclude that, in a wide variety of circumstances, the magnetic anomaly and the subtrack magnetization are highly correlated in a particular wavelength interval that depends on the shape of the power spectrum.