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Parker, RL.  2011.  New analytic solutions for the 2-D TE mode MT problem. Geophysical Journal International. 186:980-986.   10.1111/j.1365-246X.2011.05091.x   AbstractWebsite

A closed-form solution is given for a 2-D, transverse electric mode, magnetotelluric (MT) problem. The model system consists of a finite vertical thin conductor with variable integrated conductivity over a perfectly conducting base. A notable property of the solution is that the frequency response possesses a single pole in the complex plane. Systems with finitely many resonances play a central role in the 1-D MT inverse problem based on finite data sets, but until now, no 2-D system of this kind was known. The particular model is shown to be just one of a large class of thin conductors with same the property, and further examples are given. The solutions of the induction problem for members of this family can often be written in compact closed form, making them the simplest known solutions to the 2-D MT problem.

Ander, ME, Zumberge MA, Lautzenhiser T, Parker RL, Aiken CLV, Gorman MR, Nieto MM, Ferguson JF, McMechan GA.  1989.  A new field experiment in the Greenland Ice Cap to test Newton's inverse square law. Annals of the New York Academy of Sciences. 571:672-680.   10.1111/j.1749-6632.1989.tb50553.x   AbstractWebsite

Recent experimental evidence suggests that Newton’s law of gravity may not be precise. There are modern theories of quantum gravity that, in their attempts to unify gravity with other forces of nature, predict non-Newtonian gravitational forces that could have ranges on the order of 102-105 m. If they exist, these forces would be apparent as violations of Newton’s inverse square law. A geophysical experiment was carried out to search for possible finite-range, non-Newtonian gravity over depths of 213-1673 m in the glacial ice of the Greenland ice cap. The principal reason for this choice of experimental site is that a hole drilled through the ice cap already existed and the uniformity of the ice eliminates one of the major sources of uncertainty arising in the first of earlier namely, the heterogeneity of the rocks through which a mine shaft or drill hole passes. Our observations were made in the summer of 1987 at Dye 3, Greenland, in the 2033-m-deep borehole, which reached the basement rock.

Parker, PR, Zumberge MA, Parker RL.  1995.  A new method for fringe-signal processing in absolute gravity meters. Manuscripta Geodaetica. 20:173-181. AbstractWebsite

In all modern absolute gravity meters, an interferometer illuminated with a stabilized laser tracks the motion of a freely falling retroreflector. The value of gravity is measured by timing the passage of interference fringes. Typically, the sinusoidal fringe signal is converted to a series of pulses, a subset of which are input to a time digitizer. In our new system, the fringe signal is digitized with a fast analog-to-digital converter and fit to an increasing-frequency sine wave. In addition to being smaller and less expensive, the system should eliminate some potential systematic errors that may result from imperfect zero-crossing discrimination and pulse pre-scaling.

Parker, RL.  1974.  A new method for modeling marine gravity and magnetic anomalies. Journal of Geophysical Research. 79:2014-2016.   10.1029/JB079i014p02014   AbstractWebsite

A very fast technique involving Fourier transformation can find the gravity or magnetic anomaly of an irregular crustal model as observed on a plane above the material. It is shown how the method can be used to invert the magnetic field data to obtain a magnetization model, but the model so obtained is not unique. The normal restrictions placed on the magnetization models lead to a family of solutions with one degree of freedom.

Henry, M, Orcutt JA, Parker RL.  1980.  A new method for slant stacking refraction data. Geophysical Research Letters. 7:1073-1076.   10.1029/GL007i012p01073   AbstractWebsite

We describe a method for slant stacking seismic records at a number of ranges to synthesize the τ—ρ curve. The seismograms do not have to be evenly spaced in range and the correct three-dimensional point-source geometry is retained throughout. The problem is posed as a linear inverse problem in a form that permits the construction of a special solution in a very efficient manner.

Hildebrand, JA, Chave AD, Spiess FN, Parker RL, Ander ME, Backus GE, Zumberge MA.  1988.  The Newtonian gravitational constant -- on the feasibility of an oceanic measurement. EOS Trans. AGU. 69:779-780. Abstract
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McKenzie, DP, Parker RL.  1967.  The North Pacific: an example of tectonics on a sphere. Nature. 216:1276-1280.   10.1038/2161276a0   AbstractWebsite

Individual aseismic areas move as rigid plates on the surface of a sphere. Application of the Mercator projection to slip vectors shows that the paving stone theory of world tectonics is correct and applies to about a quarter of the Earth's surface.

Parker, RL, Whaler KA.  1981.  Numerical methods for establishing solutions to the inverse problem of electromagnetic induction. Journal of Geophysical Research. 86:9574-9584.   10.1029/JB086iB10p09574   AbstractWebsite

A previous paper (Parker, 1980) sets out a theory for deciding whether solutions exist to the inverse problem of electromagnetic induction and outlines methods for constructing conductivity profiles when their existence has been demonstrated. The present paper provides practical algorithms to perform the necessary calculations stably and efficiently, concentrating exclusively on the case of imprecise observations. The matter of existence is treated by finding the best fitting solution in a least squares sense; then the size of the misfit is tested statistically to determine the probability that the value would be met or exceeded by chance. We obtain the optimal solution by solving a constrained least squares problem linear in the spectral function of the electric field differential equation. The spectral function is converted into a conductivity profile by transforming its partial fraction representation into a continued fraction, using a stable algorithm due to Rutishauser. In addition to optimal models, which always consist of delta functions, two other types of model are examined. One is composed of a finite stack of uniform layers, constructed so that the product of conductivity and thickness squared is the same in each layer. The numerical techniques developed for the optimal model serve with only minor alteration to find solutions in this class. Models of the second kind are smooth. A special form of the response is chosen so that the kernel functions of the Gel'fand-Levitan integral equation are degenerate, thus allowing very stable and numerically efficient solution. Unlike previously published methods for finding conductivity models, these algorithms can provide solutions with misfits arbitrarily close to the smallest one possible. The methods are applied to magnetotelluric observations made by Larsen in Hawaii.