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Constable, CG, Parker RL, Stark PB.  1993.  Geomagnetic field models incorporating frozen-flux constraints. Geophysical Journal International. 113:419-433.   10.1111/j.1365-246X.1993.tb00897.x   AbstractWebsite

Techniques for modelling the geomagnetic field at the surface of Earth's core often penalize contributions at high spherical harmonic degrees to reduce the effect of mapping crustal fields into the resulting field model at the core-mantle boundary (CMB). Ambiguity in separating the observed field into crustal and core contributions makes it difficult to assign error bounds to core field models, and this makes it hard to test hypotheses that involve pointwise values of the core field. The frozen-flux hypothesis, namely that convective terms dominate diffusive terms in the magnetic-induction equation, requires that the magnetic flux through every patch on the core surrounded by a zero contour of the radial magnetic field remains constant, although the shapes, areas and locations (but not the topology) of these patches may change with time. Field models exactly satisfying the conditions necessary for the hypothesis have not yet been constructed for the early part of this century. We show that such models must exist, so testing the frozen-flux hypothesis becomes the question of whether the models satisfying it are geophysically unsatisfactory on other grounds, for example because they are implausibly rough or complicated. We introduce an algorithm to construct plausible fleld models satisfying the hypothesis, and present such models for epochs 1945.5 and 1980. Our algorithm is based on a new parametrization of the field in terms of its radial component B(r) at the CMB. The model consists of values of B(r) at a finite set of points on the CMB, together with a rule for interpolating the values to other points. The interpolation rule takes the specified points to be the vertices of a spherical triangle tessellation of the CMB, with B(r) varying linearly in the gnomonic projections of the spherical triangles onto planar triangles in the planes tangent to the centroids of the spherical triangles. This parametrization of B(r) provides a direct means of constraining the integral invariants required by the frozen-flux hypothesis. Using this parametrization, we have constructed field models satisfying the frozen-flux hypothesis for epochs 1945.5 and 1980, while fitting observatory and survey data for 1945.5 and Magsat data for 1980. We use the better constrained 1980 CMB field model as a reference for 1945.5: we minimize the departure of the 1945.5 CMB field model from a regularized 1980 CMB field model, while constraining the 1945.5 model to have the same null-flux curves and flux through those curves as the 1980 model. The locations, areas and shapes of the curves are allowed to change. The resulting 1945.5 CMB field model is nearly as smooth as that for 1980, fits the data adequately, and satisfies the conditions necessary for the frozen-flux hypothesis.

Gee, JS, Cande SC, Hildebrand JA, Donnelly K, Parker RL.  2000.  Geomagnetic intensity variations over the past 780 kyr obtained from near-seafloor magnetic anomalies. Nature. 408:827-832.   10.1038/35048513   AbstractWebsite

Knowledge of past variations in the intensity of the Earth's magnetic field provides an important constraint on models of the geodynamo. A record of absolute palaeointensity for the past 50 kyr has been compiled from archaeomagnetic and volcanic materials, and relative palaeointensities over the past 800 kyr have been obtained from sedimentary sequences. But a long-term record of geomagnetic intensity should also be carried by the thermoremanence of the oceanic crust. Here we show that near-seafloor magnetic anomalies recorded over the southern East Pacific Rise are well correlated with independent estimates of geomagnetic intensity during the past 780 kyr. Moreover, the pattern of absolute palaeointensity of seafloor glass samples from the same area agrees with the well-documented dipole intensity pattern for the past 50 kyr. A comparison of palaeointensities derived from seafloor glass samples with global intensity variations thus allows us to estimate the ages of surficial lava flows in this region. The record of geomagnetic intensity preserved in the oceanic crust should provide a higher-time-resolution record of crustal accretion processes at mid-ocean ridges than has previously been obtainable.

Parker, RL.  1994.  Geophysical inverse theory. , Princeton, N.J.: Princeton University Press Abstract
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Parker, RL, Shure L.  1985.  Gravitational and magnetic fields of some simple solids of revolution. Geophysical Journal of the Royal Astronomical Society. 80:631-647.: Blackwell Publishing Ltd   10.1111/j.1365-246X.1985.tb05115.x   AbstractWebsite

Summary. Exact spherical harmonic expansions are given for calculating the gravitational and magnetic fields associated with certain uniform solids of revolution. The figures are those made by rotating a conic section about one of its principal axes. The coefficients in the expansions can be computed accurately and efficiently and this approach leads to a very satisfactory method for calculating the fields of geological bodies with approximate circular symmetry about a vertical axis. A complete theory of convergence is given for the expansions. Somewhat unexpectedly, the sphere of convergence is determined by the location of a number of equivalent point or line sources that lie within the body or on its edges.

Hammer, PTC, Hildebrand JA, Parker RL.  1991.  Gravity inversion using seminorm minimization: Density modeling of Jasper Seamount. Geophysics. 56:68-79.   10.1190/1.1442959   AbstractWebsite

A gravity inversion algorithm for modeling discrete bodies with nonuniform density distributions is presented. The algorithm selects the maximally uniform model from the family of models which fit the data, ensuring a conservative and unprejudiced estimate of the density variation within the body. The only inputs required by the inversion are the gravity anomaly field and the body shape. Tests using gravity anomalies generated from synthetic bodies confirm that seminorm minimizing inversions successfully represent mass distribution trends but do not reconstruct sharp discontinuities. We apply the algorithm to model the density structure of seamounts. Inversion of the seasurface gravity field observed over Jasper Seamount suggests the edifice has a low average density of 2.38 g/cm3 and contains a dense body within its western flank. These results are consistent with seismic, magnetic, and petrologic studies of Jasper Seamount.

Zumberge, MA, Ander ME, Lautzenhiser TV, Parker RL, Aiken CLV, Gorman MR, Nieto MM, Cooper APR, Ferguson JF, Fisher E, Greer J, Hammer P, Hansen BL, McMechan GA, Sasagawa GS, Sidles C, Stevenson JM, Wirtz J.  1990.  The Greenland gravitational constant experiment. Journal of Geophysical Research-Solid Earth and Planets. 95:15483-15501.   10.1029/JB095iB10p15483   AbstractWebsite

An Airy-type geophysical experiment was conducted in a 2-km-deep hole in the Greenland ice cap at depths between 213 m and 1673 m to test for possible violations of Newton's inverse square law. The experiment was done at Dye 3, the location of a Distant Early Warning Line radar dome and the site of the deepest of the Greenland Ice-Sheet Program (GISP) drill holes. Gravity measurements were made at eight depths in 183-m intervals with a LaCoste&Romberg borehole gravity meter. Prior to the experiment the borehole gravity meter was calibrated with an absolute gravity meter, and the wireline depth-rinding system used in the borehole logging was calibrated in a vertical mine-shaft against a laser geodimeter. The density of the ice in the region was calculated from measurements taken from ice cores obtained from earlier drilling observations. Ice penetrating radar was employed in order to correct the gravity data for the topography of the ice-rock interface. Surface gravity observations were made to assess the extent to which density variations in the sub-ice rock could affect the vertical gravity gradient. The locations of the gravity observation points were determined with a combination of GPS recording, first-order leveling, and EDM surveying. An anomalous variation in gravity totaling 3.87 mGal (3.87×10−5 m/s2) in a depth interval of 1460 m was observed. This may be attributed either to a breakdown of Newtonian gravity or to unexpected density variations in the rock below the ice.