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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.

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, Stevenson JM, Hammer PTC, Zumberge MA, Parker RL, Fox CG, Meis PJ.  1990.  A seafloor and sea surface gravity survey of Axial Volcano. Journal of Geophysical Research-Solid Earth and Planets. 95:12751-12763.   10.1029/JB095iB08p12751   AbstractWebsite

Seafloor and sea surface gravity measurements are used to model the internal density structure of Axial Volcano. Seafloor measurements made at 53 sites within and adjacent to the Axial Volcano summit caldera provide constraints on the fine-scale density structure. Shipboard gravity measurements made along 540 km of track line above Axial Volcano and adjacent portions of the Juan de Fuca ridge provide constraints on the density over a broader region and on the isostatic compensation. The seafloor gravity anomalies give an average density of 2.7 g cm−3 for the uppermost portion of Axial Volcano, The sea surface gravity anomalies yield a local compensation parameter of 23%, significantly less than expected for a volcanic edifice built on zero age lithosphere. Three-dimensional ideal body models of the seafloor gravity measurements suggest that low-density material, with a density contrast of at least 0.15 g cm−3, may be located underneath the summit caldera. The data are consistent with low-density material at shallow depths near the southern portion of the caldera, dipping downward to the north. The correlation of shallow low-density material and surface expressions of recent volcanic activity (fresh lavas and high-temperature hydrothermal venting) suggests a zone of highly porous crust. Seminorm minimization modeling of the surface gravity measurements also suggest a low-density region under the central portion of Axial Volcano. The presence of low-density material beneath Axial caldera suggests a partially molten magma chamber at depth.

Hildebrand, JA, Parker RL.  1987.  Paleomagnetism of Cretaceous Pacific Seamounts revisited. Journal of Geophysical Research-Solid Earth and Planets. 92:12695-12712.   10.1029/JB092iB12p12695   AbstractWebsite

The paleomagnetism of Cretaceous Pacific seamounts is reexamined. Herein techniques for nonuniform magnetic modeling are applied to determine paleomagnetic pole positions and their associated confidence limits. Modeling techniques are presented for reconstruction of both uniform and nonuniform components of the seamount magnetization. The uniform component yields an estimate of the paleomagnetic pole position, and the nonuniform component accounts for irregularities in the seamount magnetization. A seminorm minimization approach constructs maximally uniform magnetizations and is used to represent seamount interiors. A statistical modeling approach constructs random nonuniform magnetizations and is used to determine the confidence limits associated with each pole position. Mean paleopoles are calculated for groups of seamounts, including their associated error bounds. The mean paleopole for seven reliably dated Upper Cretaceous seamounts is located close to the position predicted by Pacific-hotspot relative motion. The paleopole for five seamounts with Cretaceous minimum dates is located west of the hotspotpredicted apparent polar wander path and may represent a Lower Cretaceous or Upper Jurassic pole.

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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Hobbs, UA, Parker RL.  1978.  Limitations on the parameters of the solar wind in modelling lunar electromagnetic induction. Geophysical Journal of the Royal Astronomical Society. 52:433-439.: Blackwell Publishing Ltd   10.1111/j.1365-246X.1978.tb04241.x   AbstractWebsite

Summary. A striking feature of the day-side response of the Moon to periodic fluctuations in the solar wind is the rapid rise, and subsequent fall, in the amplitude of the transfer function as the inducing field frequency increases. This behaviour can be characterized by the amplitude values at the two frequencies 24 and 40 mHz. Before the response of a conductivity model representing the Moon can be calculated at a given frequency, the parameters (ν, θ) (where ν is the solar wind speed and θ is the angle between the solar wind velocity and the magnetic field propagation direction) have to be specified. By applying some results due to Parker (1972) to the above two data points, we have determined constraints on the parameter space (ν, θ). In particular, we determine the region of the (ν, θ) space in which conductivity models may be found that satisfy our data pair. Outside this region, there are no conductivity models satisfying the data pair, and hence many (ν, θ) values are inconsistent with the original data and the model assumptions.

Huestis, SP, Parker RL.  1977.  Bounding the thickness of the oceanic magnetized layer. Journal of Geophysical Research. 82:5293-5303.   10.1029/JB082i033p05293   AbstractWebsite

We present a theory for placing a lower bound on the thickness of the oceanic magnetized layer using magnetic anomaly observations and estimates of the intensity of magnetization; the theory makes only a minimum number of assumptions regarding the spatial distribution of the magnetization. The principle of the method is based upon the fact that thin layers imply high magnetizations. We show how to calculate the source distribution that has minimum intensity yet fits the data and is confined to a given thickness layer; because the minimum intensity must be a monotonically decreasing function of layer thickness, it follows that an upper bound on the intensity allows us to obtain a lower limit on the thickness. The practical calculations are performed by using linear programing. The method is applied to two sets of near-bottom magnetic profiles, one on the Galápagos Spreading Center at 86°W and the other set on the Pacific-Antarctic Ridge at 51°S. In the first area we conclude that the magnetic layer must be at least 450 m thick, and in the other a crossing of the Jaramillo event indicates that the magnetic layer is probably more than 1000 m in thickness.

Huestis, SP, Parker RL.  1979.  Upward and downward continuation as inverse problems. Geophysical Journal of the Royal Astronomical Society. 57:171-188.: Blackwell Publishing Ltd   10.1111/j.1365-246X.1979.tb03779.x   AbstractWebsite

Summary. The formalism of Backus & Gilbert is applied to the problems of upward and downward continuation of harmonic functions. We first treat downward continuation of a two-dimensional field to a level surface everywhere below the observation locations; the calculation of resolving widths and solution estimates is a straightforward application of Backus—Gilbert theory. The extension to the downward continuation of a three-dimensional field uses a delta criterion giving resolving areas rather than widths. A feature not encountered in conventional Backus—Gilbert problems is the requirement of an additional constraint to guarantee the existence of the resolution integrals. Finally, we consider upward continuation of a two-dimensional field to a level above all observations. We find that solution estimates must be weighted averages of the field not only on this level, but also on a line passing between the observations and sources. Weighting on the lower line may be traded off against resolution on the upper level.