A crustal seismic velocity model for the UK, Ireland and surrounding seas

A regional model of the 3-D variation in seismic P -wave velocity structure in the crust of NW Europe has been compiled from wide-angle reflection/refraction profiles. Along each 2-D profile a velocity–depth function has been digitised at 5 km intervals. These 1-D velocity functions were mapped into three dimensions using ordinary kriging with weights determined to minimise the difference between digitised and interpolated values. An analysis of variograms of the digitised data suggested a radial isotropic weighting scheme was most appropriate. Horizontal dimensions of the model cells are optimised at 40 × 40 km and the vertical dimension at 1 km. The resulting model provides a higher resolution image of the 3-D variation in seismic velocity structure of the UK, Ireland and surrounding areas than existing models. The construction of the model through kriging allows the uncertainty in the velocity structure to be assessed. This uncertainty indicates the high density of data required to confidently interpolate the crustal velocity structure, and shows that for this region the velocity is poorly constrained for large areas away from the input data.     

The constrained normal form algorithm

This paper describes an algorithm which brings a regularizable polynomial perturbation of a three degree of freedom Kepler problem into a normal form which Poisson commutes with the Kepler Hamiltonian. We illustrate the alogrithm with an example: the quadratic Zeeman effect. For other applications of this algorithm see [1],[4], and [5]. The authors have written a program in MAPLE which implements the constrained normal form.     

Solar soft X-rays and solar activity

Flare-associated soft X-ray bursts (8–12 Å) are examined for 283 events observed by OSO-III. These bursts are shown to be predominantly thermal in nature. Their time-profiles are roughly similar to those of the associated H flares, although the X-ray burst begins about two minutes earlier, on the average. The strength of the soft X-ray burst is directly related to the area and brilliance of the flare, the age and flare-richness of the associated plage, and the general level of solar activity at the time of the burst. The peak enhancements in the soft X-ray and H emission rates during flares are of the same order of magnitude, as are the total flare energies radiated at these wavelengths. We estimate that soft X-radiation accounts for up to 10% of a flare's total electromagnetic emission.NRC/NAS Resident Research Associate.     

Gravity-gradient stabilization of gyrostat satellites with rotor axes in principal planes

Three special classes of equilibrium orientations of gyrostat satellites subject to gravitational torques have been treated in the literature. Here we find the set of all equilibria for a restricted class of gyrostat configurations. Those configurations for which the internal angular momentum vector (or the rotor axis) is aligned with a principal axis have been treated in a separate work, where it is shown that at one, and only one, rotor speed there exists a continuum of equilibrium orientations. When the rotor axis is moved away from a principal axis in such a way that it is contained in a plane formed by two principal axes, it is shown that the continuum disappears, and we have a new set of eight equilibrium orientations which have not previously been described. The stability of these orientations is then investigated using the Hamiltonian as a Liapunov testing function. For properly chosen satellite inertia ratios some of these orientations are stable, and might be used in future gravitygradient stabilized satellites.This research is sponsored by the United States Air Force under Project RAND-Contract No. F44620-67-C-0045-monitored by the Directorate of Operational Requirements and Development Plans, Deputy Chief of Staff, Research and Development, Hq. USAF. Views or conclusions contained in this study should not be interpreted as representing the official opinion or policy of the United States Air Force. The material presented here was originally published in RAND Corporation Memorandum RM-5921-PR. The author wishes to acknowledge his indebtedness to Dr. R. E. Roberson for helpful discussions, and for suggesting a research area, part of which is treated here.     

Optimal configurations for dual-spin satellites subject to gravitational torques

Dual-spin or gyrostat satellites subject to gravitational torques can adopt an infinite number of possible equilibria obtained by adjusting the magnitude and direction of the rotor angular momentum within the satellite. This paper seeks to answer the question, which of these equilibria is best — and best is chosen here to mean most stable in the sense that the energy required to perturb the orientation by any prescribed amount is maximized, i.e. the smallest eigenvalue of the Hessian matrix of the dynamic potential energy is maximized. Using this criterion, it is shown that the conventional configuration for dual-spin satellites with the angular momentum of the rotor, the spacecraft principal axis of maximum moment of inertia, and the perpendicular to the orbital plane coincident is not always the best orientation. The optimal configuration is shown to have the minimum moment of inertia always aligned with the local vertical, but the principal axis of maximum moment of inertia, shifts from the perpendicular to the orbital plane to lying in-plane as the angular momentum of the rotor is increased from zero (corresponding to a rigid gravity gradient satellite) to some sufficiently large value which is determined as a function of parameters. For angular momentum greater than this value, global optimality is established analytically, and otherwise local optimality is proved analytically with global optimality demonstrated numerically.     

A SPATIAL ANALYSIS OF AGRICULTURAL INTENSITY IN A BASOTHO VILLAGE OF SOUTHERN AFRICA

The effect of distance upon agricultural production should be as apparent among primitive subsistence agriculturalists as in market-oriented societies. This analysis of yield variations among the Basotho of southern Africa attempts to determine the frictional effect of distance. The results show that distance does not explain variations in yield even when other physical factors are held constant. Perhaps such variables as household characteristics, not included in the analysis, would provide a better explanation.