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Lilley, FEM, Parker RL.  1976.  Magnetic daily variations compared between the east and west coasts of Australia. Geophysical Journal of the Royal Astronomical Society. 44:719-724.: Blackwell Publishing Ltd   10.1111/j.1365-246X.1976.tb00304.x   AbstractWebsite

A study of magnetic daily variations shows their vertical component to be enhanced at the west coast of Australia, just as previous work had showed it to be reduced at the east coast. The anomalous contributions appear most likely to be due to induction by the onshore horizontal component of the daily variation field. The Australian data may also indicate regional differences in the structure of the continent.

O'Brien, MS, Parker RL, Constable CG.  1999.  Magnetic power spectrum of the ocean crust on large scales. Journal of Geophysical Research-Solid Earth. 104:29189-29201.   10.1029/1999jb900302   AbstractWebsite

The geomagnetic power spectrum R-l is the squared magnetic field in each spherical harmonic degree averaged over a spherical surface. Satellite measurements have given reliable estimates of the spectrum for the part that originates in the core, but above I = 15, where the geomagnetic field arises primarily from crustal magnetization, there is considerable disagreement between various estimates derived from observation. Furthermore, several theoretical models for the spectrum disagree with each other and the data. We have examined observations from a different source, 5000-km-long Project Magnet aeromagnetic survey lines; we make new estimates of the spectrum which overlap with the wavelength interval accessible to the satellites. The usual way the spectrum is derived from observation is to construct a large spherical harmonic decomposition first, then square, weight, and add the Gauss coefficients in each degree, but this method cannot be applied to isolated flight lines. Instead, we apply a statistical technique based on an idea of McLeod and Coleman which relates the geomagnetic spectrum to the power and cross spectra of magnetic field components measured on the survey lines. Power spectra from the 17 aeromagnetic surveys, all of which were conducted over the oceans, are averaged together to improve geographic coverage and reduce variance, and the average spectra are then inverted for the geomagnetic spectrum R-l. Like most of the theoretical models, our spectrum exhibits a maximum, but at a wavelength of 100 km, about a factor of 2 smaller than the closest theoretical prediction. Our spectrum agrees quite well with the most recent estimates based on satellite observations in the range 20 less than or equal to l less than or equal to 50, but above l=50, our values increase slowly, while all the satellite data suggest a sharply rising curve. In this wavelength range we believe our measurements are more trustworthy. Further work is planned to confirm the accuracy of our spectrum when continental survey paths are included.

Parker, RL, Klitgord KD.  1972.  Magnetic upward continuation from an uneven track. Geophysics. 37:662-668.   10.1190/1.1440289   AbstractWebsite

A new method for continuing two‐dimensional potential data upward from an uneven track is developed with special emphasis on solving a particular practical problem, that of magnetic data taken near the bottom of the ocean. The method is based on the use of the Schwarz‐Christoffel transformation, which maps the original, irregular track into a horizontal straight line. It has been found to be very fast computationally and to suffer none of the restrictions found in some earlier two‐dimensional algorithms.

Parker, RL.  1983.  The magnetotelluric inverse problem. Geophysical Surveys. 6:5-25.   10.1007/bf01453993   AbstractWebsite

The magnetotelluric inverse problem is reviewed, addressing the following mathematical questions: (a)Existence of solutions: A satisfactory theory is now available to determine whether or not a given finite collection of response data is consistent with any one-dimensional conductivity profile. (b)Uniqueness: With practical data, consisting of a finite set of imprecise observations, infinitely many solutions exist if one does. (c)Construction: Several numerically stable procedures have been given which it can be proved will construct a conductivity profile in accord with incomplete data, whenever a solution exists. (d)Inference: No sound mathematical theory has yet been developed enabling us to draw firm, geophysically useful conclusions about the complete class of satisfactory models.Examples illustrating these ideas are given, based in the main on the COPROD data series.

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.

Loncarevic, BD, Parker RL.  1971.  Mid-Atlantic Ridge near 45°N. XVII. Magnetic anomalies and ocean floor spreading. Canadian Journal of Earth Sciences. 8:883-898.   10.1139/e71-080   AbstractWebsite

In the North Atlantic it is difficult to correlate single magnetic profiles with the spreading ocean floor magnetic models. Within the area of intensive surveys at 45° N, it is possible to average the observations in the direction of the trend of the magnetic anomalies. The profile of averaged anomalies for all data between 45° N and 45.5° N correlates well with a magnetic model spreading (with respect to the ridge axes) westwards at 1.28 cm/y and eastwards at 1.10 cm/y, if the trend of the anomalies is assumed to be 015° East of North.

Greenhouse, JP, Parker RL, White A.  1973.  Modelling geomagnetic variations in or near an ocean using a generalized image technique. Geophysical Journal of the Royal Astronomical Society. 32:325-338.   10.1111/j.1365-246X.1973.tb05834.x   AbstractWebsite

A generalized image technique is described for modelling electromagnetic induction in two-dimensional systems, consisting of a thin (Price-type) ocean overlying a perfect conductor in the mantle. The method constructs a Green's function for currents in the ocean by conformally mapping the perfect conductor boundary into a straight line. Examples are given that show the effects to be expected at an ocean-continent boundary with isotherms rising under the ocean, and at a mid-ocean rise where the high temperatures are believed to be quite shallow.

Jackson, A, Constable CG, Walker MR, Parker RL.  2007.  Models of Earth's main magnetic field incorporating flux and radial vorticity constraints. Geophysical Journal International. 171:133-144.   10.1111/j.1365-246X.2007.03526.x   AbstractWebsite

We describe a new technique for implementing the constraints on magnetic fields arising from two hypotheses about the fluid core of the Earth, namely the frozen-flux hypothesis and the hypothesis that the core is in magnetostrophic force balance with negligible leakage of current into the mantle. These hypotheses lead to time-independence of the integrated flux through certain 'null-flux patches' on the core surface, and to time-independence of their radial vorticity. Although the frozen-flux hypothesis has received attention before, constraining the radial vorticity has not previously been attempted. We describe a parametrization and an algorithm for preserving topology of radial magnetic fields at the core surface while allowing morphological changes. The parametrization is a spherical triangle tesselation of the core surface. Topology with respect to a reference model (based on data from the Oersted satellite) is preserved as models at different epochs are perturbed to optimize the fit to the data; the topology preservation is achieved by the imposition of inequality constraints on the model, and the optimization at each iteration is cast as a bounded value least-squares problem. For epochs 2000, 1980, 1945, 1915 and 1882 we are able to produce models of the core field which are consistent with flux and radial vorticity conservation, thus providing no observational evidence for the failure of the underlying assumptions. These models are a step towards the production of models which are optimal for the retrieval of frozen-flux velocity fields at the core surface.