Three-Dimensional Gravity Modeling In All Space

We review available analytical algorithms for the gravity effect and gravity gradients especially the vertical gravity gradient due to a right rectangular prism, a right polygonal prism, and a polyhedron. The emphasis is placed on an investigation of validity, consistency, and especially singularities of different algorithms, which have been traditionally proposed for calculation of the gravity effect on ground (or outside anomalous bodies), when they are applied to all points in space. The rounding error due to the computer floating point precision is estimated. The gravity effect and vertical gradient of gravity in three dimensions caused by a cubic model are calculated by different types of algorithms. The reliability of algorithms for the calculation of gravity of a right polygonal prism and a polyhedron is further verified by using a regular polygonal prism approximating a vertical cylinder and a regular polyhedron approximating a sphere, respectively. By highlighting Haáz-Jung-Plouff and Okabe-Steiner-Zilahi-Sebess' formulae for a right rectangular prism, Plouff's algorithm for a right polygonal prism, and Gouml;tze and Lahmeyer's algorithm for a polyhedron and removing their singularities, we demonstrate that these formulae and algorithms can be used to model the gravity anomaly and its vertical gradient at all possible computation positions.     

Magmatic and hydrothermal R.E.E. fractionation in the Xihuashan granites (SE China)

The Xihuashan stock (South Jiangxi, China) is composed of cogenetic granitic units (granites Xe, a, c, d and b) and emplaced during the Yanshanian orogeny (153±0.2 Ma). They are two feldspars, Fe-rich biotite±garnet and slightly peraluminous granites. Primary accessory minerals are apatite 1, monazite, zircon, uranothorite±xenotime in granites Xe and a, zircon, uranothorite, uraninite, betafite, xenotime 1; hydrothermal minerals are monazite altered into parisite and apatite 2, Y-rich parisite, yttroparisite, Y-rich fluorite and xenotime 2 in granites c and b. Petrographic observations, major element, REE, Y and Rb–Sr isotropic data point to a magmatic suite (granites Xe and a granites c and d granite b) distinct from hydrothermal Na-or K-alteration of b. From granite Xe to granite b, LREE, Eu, Th and Zr content are strongly depleted, while HREE, Y and U content increase. During K-alteration of b, these variations are of minor importance. Major and accessory mineral evidences, geochemical and fluid inclusion results indicate two successive alteration fluids interacting with b, (1) a late-magmatic F^– and CO₂–rich fluid and (2) a post-magmatic, aqueous and slightly saline fluid. The depletion of LREE and Th content and the increase in HREE, Y and U content correspond, in the magmatic suite to the early fractionation of monazite in the granites where there is no hydrothermal alteration (granites Xe and e) and to the hydrothermal alteration of monazite into parisite and secondary apatite, intense new formation of yttroparisite, Y enrichment and U loss in the uranothorite and late crystallization of uraninite in the granites c and b. Moreover, simulated crystallization of monazite and temperature of monazite saturation show early fractionation of monazite from the magma in the less evolved granites (Xe and e) and prevailing hydrothermal leaching of monazite in the most evolved granites (c-d and b) related to a late-magmetic event. The slight variations of REE, Y, Th and U content in the K-altered granites compared to granite b emphazes the distinct chemical nature of the successive hydrothermal fluids. Rb–Sr and Sm–Nd isotopic results point to a 30 Ma period of time between the late-magmatic and the post-magmatic fluid circulation.     

Centrifugal instability of the jovian magnetosphere and its interaction with the solar wind

The outer regions (r > 2.3 R_j; R_j = radius of Jupiter) of the magnetosphere of Jupiter will systematically accumulate plasma. If sufficient plasma accumulates, the field lines must open to allow the plasma to escape. Available energy sources appear able to supply plasma at a high enough rate to keep the field lines constantly open beyond about 60 R_J. We suggest that the solar wind interaction with Jupiter may be essentially different from that with the Earth, with the Jovian magnetosphere opening up to form a planetary wind.     

On the origin of cometary nuclei in the presolar nebula

If we assume that the cometary nuclei originated by the gravitational instability of a dust layer, which formed in the equatorial plane of the outer parts of the presolar nebula (PSN) during a period of approximate equilibrium between gravity, centrifugal force, and the pressure gradient, a simple relation is derived between the PSN's temperature and the upper limit to the mass of the planetesimals. It contains, besides the density of the cometary nuclei _p , only the fraction (by mass) of the condensable elements in the PSN, which became part of the dust particle disc, which, on the basis of available observational evidence on the solid particles in interplanetary and interstellar space and of theoretical considerations on the relationship between them and on the sedimentation process, is found to be of the order of ~10%; this estimate will require still further justification. Assuming a temperature in the range 15–20 K, an equatorial diameter of the PSN of 0.1 pc and _p few 0.1 g/cm³, upper limits for the planetesimal's mass of 10¹⁸g and for their radius of 10 km are obtained (on the basis of conservation of circulation, of mass and of angular momentum in the differentially rotating disc), in fair agreement with observation. With the dispersion of those parts of the PSN — of an assumed original mass of 2–3M —, which did not become part of the Sun or the planets, by the young Sun's activity, the planetesimals must have lost a large part of their gravitational binding energy and their orbits must have become so large (semimajor axis several 10⁴ A.U. or more, if not negative), that stellar perturbations produced the distribution in configurational and in velocity space now observed.Paper dedicated to Professor Hannes Alfvén on the occasion of his 70th birthday, 30 May, 1978.The earlier work done since about 1950 in the U.S.S.R. is described in Safronov (1972).     

Natural speciation of Mn, Ni, and Zn at the micrometer scale in a clayey paddy soil using X-ray fluorescence, absorption, and diffraction

The natural speciation of Mn (0.19 g/kg), Ni (46 mg/kg), and Zn (42 mg/kg) in the argillic horizon (120 cm depth, pH = 5.6) of an Ultisol from a paddy soil in northern Taiwan was investigated by advanced X-ray synchrotron techniques. Microchemical associations were imaged by synchrotron-based X-ray microfluorescence, host minerals were identified by standard and micrometer-resolved X-ray diffraction, and the local coordination environment of Mn, Ni, and Zn was probed using extended X-ray absorption fine structure (EXAFS) spectroscopy on a powdered sample and a soil thin section, and polarized EXAFS spectroscopy on a highly textured self-supporting clay film from the <2 μm fraction of the soil. Manganese was concentrated in Fe-Mn soft mottles (44.4 g/kg) as turbostratic hexagonal birnessite and lithiophorite having Mn³⁺/Mn⁴⁺ atomic ratios of ∼20% and 50%, respectively. Quantitative analysis of high-order scattering paths of the EXAFS spectrum for natural and synthetic lithiophorite revealed that Mn³⁺ and Mn⁴⁺ are ordered in the layer. A structural model is proposed, in which Mn⁴⁺ and Mn³⁺ are ordered similarly to Al and Li in the layer, with Mn³⁺ cations being surrounded by six Mn⁴⁺, and Mn⁴⁺ cations by three Mn³⁺ and three Mn⁴⁺. Similar cation ordering in the manganese and aluminum layers likely provides a more homogeneous local balance of the excess and deficit of charges in each layer and increases the stability of lithiophorite. Ni (r = 0.70 Å) substitutes for Mn (r(Mn⁴⁺) = 0.54 Å, r(Mn³⁺) = 0.65 Å) in the manganese layer in the natural lithiophorite. In contrast, Zn (r = 0.74 Å) fills vacant sites in the gibbsitic layer of natural lithiophorite, in a similar manner as lithium (r = 0.74 Å) in synthetic lithiophorite. The partitioning of Ni and Zn between the two layers is a result of the general preference of Ni, whose size is intermediate between those of Mn³⁺ and Li⁺, for slightly smaller sites. In contrast with nickel, which is detected only where there is lithiophorite, the Zn-lithiophorite association found in Fe-Mn mottles is not representative of the bulk soil. The combined use of X-ray diffraction, and powder and polarized EXAFS spectroscopy revealed that Zn is predominantly bound to hydroxy-Al interlayers sandwiched between 2:1 vermiculite layers in the fine soil matrix. The incorporation of Zn in the gibbsitic layer of both lithiophorite and vermiculite helps increase the stability of these minerals by providing positive charge to balance the negative charge from the 2:1 phyllosilicate layer and the layer of lithiophorite. This binding environment for zinc is probably the main mechanism by which zinc is sequestered in acidic to near-neutral aluminum-rich clayey soils.     

Differentiating Future Commitments on the Basis of Countries’ Relative Historical Responsibility for Climate Change: Uncertainties in the ‘Brazilian Proposal’ in the Context of a Policy Implementation

During the negotiations on the Kyoto Protocol, Brazil proposed allocating the greenhouse gas emission reductions of Annex I Parties according to the relative effect of a country’s historical emissions on global temperature increase. This paper analyses the impact of scientific uncertainties and of different options in policy implementation (policy choices) on the contribution of countries’ historical emissions to indicators of historical responsibility for climate change. The influence of policy choices was found to be at least as large as the impact of the scientific uncertainties analysed here. Building on this, the paper then proceeds to explore the implications of applying the Brazilian Proposal as a climate regime for differentiation of future commitments on the global scale combined with an income threshold for participation of the non-Annex I regions. Under stringent climate targets, such a regime leads to high emission reductions for Annex I regions by 2050, in particular for Europe and Japan. The income threshold assumptions strongly affect the Annex I reductions, even more than the impact of another burden-sharing key. A variant of the Brazilian Proposal, allocating emission reductions on the basis of cumulative emissions since 1990, would lead to a more balanced distribution of emission reductions.     

New estimations of precipitation and surface sublimation in East Antarctica from snow accumulation measurements

Surface mass balance (SMB) distribution and its temporal and spatial variability is an essential input parameter in mass balance studies. Different methods were used, compared and integrated (stake farms, ice cores, snow radar, surface morphology, remote sensing) at eight sites along a transect from Terra Nova Bay (TNB) to Dome C (DC) (East Antarctica), to provide detailed information on the SMB. Spatial variability measurements show that the measured maximum snow accumulation (SA) in a 15 km area is well correlated to firn temperature. Wind-driven sublimation processes, controlled by the surface slope in the wind direction, have a huge impact (up to 85% of snow precipitation) on SMB and are significant in terms of past, present and future SMB evaluations. The snow redistribution process is local and has a strong impact on the annual variability of accumulation. The spatial variability of SMB at the kilometre scale is one order of magnitude higher than its temporal variability (20–30%) at the centennial time scale. This high spatial variability is due to wind-driven sublimation. Compared with our SMB calculations, previous compilations generally over-estimate SMB, up to 65% in some areas.     

Isostatic response of the large-offset Atlantic Equatorial fracture zones

Spectral analysis techniques have been applied to data sets of gravity and topography selected across fracture zones with large offset in the Equatorial and Central Atlantic Ocean and processed independently for each fracture zone. Three simple compensation models, two in local isostatic equilibrium (Airy I and II) and one in regional equilibrium (Plate model) have been tested. It is found that the free-air anomalies are primarily controlled by the topography and its isostatic response. For short wavelengths, admittance can be explained either by the effect of uncompensated sea floor topography with high density basement or by the effect of uncompensated sea floor topography with normal oceanic basement density but accompanied by a crust of constant thickness. For intermediate wavelengths, admittance for the Romanche fracture zone agrees best with a local isostatic model in which compensation is achieved by a less dense material in the upper mantle. No such evidence exists for the Vema and Chain fracture zones for which topography could just as well be regionally supported by an elastic plate 3 to 10 km thick. For longer wavelengths, the admittances computed for the three fracture zones are compatible with a thermal compensation of the topography.