The motion of a satellite in an axi-symmetric gravitational field

The equations for the variation of the osculating elements of a satellite moving in an axi-symmetric gravitational field are integrated to yield the complete first-order perturbations for the elements of the orbit. The expressions obtained include the effects produced by the second to eighth spherical harmonics. The orbital elements are presented in the most general form of summations by means of Hansen coefficients. Due to their general forms it is a simple matter to estimate the perturbations of any higher harmonic by simply increasing the index of summation. Finally, this paper gives the respective general expressions for the secular perturbations of the orbital elements. The formulae presented should be useful for the reductions of Earth-satellite observations and geopotential studies based on them.List of Symbols semi-major axis - C _jk ⁿ (, ) cosine functions of and - e eccentricity of the orbit - f acceleration vector of perturbing force - f sin²t - i inclination of the orbit - J _n coefficients in the potential expansion - M mean anomaly - n mean motion - p semi-latus rectum of the orbit - R, S, andW components of the perturbing acceleration - r radius-vector of satellite - r magnitude ofr - S _jk ⁿ (, ) sine functions of and - T time of perigee passage - u argument of latitude - U gravitational potential - true anomaly - V perturbing potential - G(M₊+m) (gravitational constant times the sum of the masses of Earth and satellite) - _n,k coefficients ofR component of disturbing acceleration (funtions off) - _n,k coefficients ofS andW components of disturbing acceleration (functions off) - mean anomaly at timet=0 - X ₀ ^n,m zero-order Hansen coefficients - argument of perigee - right ascension of the ascending node     

Sr-Nd-Pb isotope ratios, geochemical compositions, and 40Ar/39Ar data of lavas from San Felix Island (Southeast Pacific): Implications for magma genesis and sources

We present the first trace element and age data combined with new Sr, Nd, and Pb isotope ratios on lavas from San Felix Island in the Southeast Pacific. A ⁴⁰Ar/³⁹Ar plateau age of 421 ± 18 ka implies young intraplate volcanic activity in this region relative to the ∼22 Ma old volcanism on the neighbouring Easter seamount chain (ESC). The incompatible element compositions of the San Felix magmas are similar to those of EM1-type basalts from Gough, although the isotopic compositions differ. San Felix formed some 20 Ma after the ESC plume affected the plate in this region but no chemical signature of the ESC material is observed in the young volcanic rocks. The composition of the San Felix basalts indicates a mantle source containing old continental lithospheric material from either metasomatized mantle or recycled sediments, which ascends in a weak mantle plume.     

The linkage between fault throw and footwall scarp erosion patterns: an example from the Bremstein Fault Complex,offshore Mid‐Norway

Studies of normal fault systems in modern extensional regimes (e.g. Basin and Range), and in exhumed, ancient rift basins (e.g. Gulf of Suez Rift) have shown a link between the evolution of fault‐related footwall topography and associated erosional drainage systems. In this study, we use 3D seismic reflection data to image the footwall crest of a gravity‐driven fault system developed during late Middle Jurassic to Early Cretaceous rifting on the Halten Terrace, offshore Mid‐Norway. This 22‐km‐long fault system lacks significant footwall uplift, with hangingwall subsidence accommodating throw accumulation on the fault system. Significant erosion has occurred along the length of the footwall crest and is defined by 96 catchments characterized by erosional channels. These erosional channels consist of small, linear systems up to 750 m long located along the front of the fault footwall. Larger, dendritic channel systems extend further back (up to 3 km normal to fault strike) into the footwall. These channels are up to 7 km long, up to 50 m deep and up to 1 km wide. Fault throw varies along strike, with greatest throw in the centre of the fault decreasing towards the fault tips; localized throw minima are interpreted to represent segment linkage points, which were breached as the fault grew. Comparison of the catchment location to the throw distribution shows that the largest catchments are in the centre of the fault and decrease in size to the fault tips. There is no link between the location of the breached segment linkage points and the location and size of the footwall catchments, suggesting that the first‐order control on footwall erosion patterns is the overall fault‐throw distribution.     

Orbital forcing and role of the latitudinal insolation/temperature gradient

Orbital forcing of the climate system is clearly shown in the Earths record of glacial–interglacial cycles, but the mechanism underlying this forcing is poorly understood. Traditional Milankovitch theory suggests that these cycles are driven by changes in high latitude summer insolation, yet this forcing is dominated by precession, and cannot account for the importance of obliquity in the Ice Age record. Here, we investigate an alternative forcing based on the latitudinal insolation gradient (LIG), which is dominated by both obliquity (in summer) and precession (in winter). The insolation gradient acts on the climate system through differential solar heating, which creates the Earths latitudinal temperature gradient (LTG) that drives the atmospheric and ocean circulation. A new pollen-based reconstruction of the LTG during the Holocene is used to demonstrate that the LTG may be much more sensitive to changes in the LIG than previously thought. From this, it is shown how LIG forcing of the LTG may help explain the propagation of orbital signatures throughout the climate system, including the Monsoon, Arctic Oscillation and ocean circulation. These relationships are validated over the last (Eemian) Interglacial, which occurred under a different orbital configuration to the Holocene. We conclude that LIG forcing of the LTG explains many criticisms of classic Milankovitch theory, while being poorly represented in climate models.     

豫西沙沟脉状Ag-Pb-Zn矿床地质特征和成矿流体研究

豫西沙沟薄脉状Ag-Pb-Zn硫化物矿床位于华北陆块南缘熊耳山地区,主要由多金属硫化物-石英-碳酸盐脉型和石英-碳酸盐-绢云母-多金属硫化物蚀变岩型两种矿化类型组成。主要矿脉的矿物共生序列可以分为成矿前的石英-黄铁矿阶段(Ⅰ)、闪锌矿-石英-方铅矿-少量银矿物阶段(Ⅱ1)、方铅矿-石英-闪锌矿-含铁白云石-银矿物阶段(Ⅱ2)和成矿后的方解石-(石英)阶段(Ⅲ)。对不同阶段的成矿流体研究表明,石英-黄铁矿阶段(Ⅰ)中的含氯化钠子晶三相(LVH)包裹体(Ⅰ1)可能是直接从饱和水的结晶岩浆熔体中出溶形成或是由岩浆流体的减压沸腾形成,显示该区很可能存在岩浆流体端元。多金属硫化物阶段(Ⅱ1Ⅱ2)捕获富液相包裹体(LV型)和个别CO2包裹体(C型),这两个阶段流体包裹体反映了主成矿阶段流体的基本特征,结合包裹体气相和液相成分色谱分析以及包裹体初融温度,认为成矿流体应该为中-低温低盐度含CO2的H2O-NaCl体系。其中,阶段(Ⅱ2)的均一温度(145～288℃,平均为194℃)比阶段(Ⅱ1)的均一温度(185～357℃,平均240℃)低46℃;同时,阶段(Ⅱ2)的盐度(1.91%～10.86%,平均6.38%)较阶段(Ⅱ1)盐度(4.65%～10.11%,平均7.77%)略低。对这一温度和盐度的总体下降趋势的合理解释是大气水的逐渐混入。多金属硫化物阶段(Ⅱ1Ⅱ2)之后的方解石-(石英)阶段普遍为富液相包裹体(LV型),该阶段显著降低的温度(129～208℃,平均165℃)和盐度(1.40%～4.03%,平均2.50%),进一步佐证大气水的不断混入。而且,流体混合可能在引起矿石矿物从热液中沉淀方面起到重要作用。     

Temporal variations in bedload transport rates: The effect of progressive bed armouring

The quantitative bedload transport data that are presently available confirm that the generalized bedload transport rate-stream power relationship is applicable to natural streams. However, the bedload transport rate is not solely dependent upon hydraulic parameters, but also upon the inter-relationship between bed material characteristics and flow properties. Segregation of the surficial bed material, as expressed through the development of an armour coat, limits the availability of transportable material. Under such circumstances observed bedload transport rates are less than the predicted values. The effect which the development of an armoured surface has upon the bedload transport rate is described with reference to bedload and bed material sampling in the Borgne d'Arolla, Valais, Switzerland. The data refer to two periods when the resumption of baseflow conditions following flood events which were of a sufficient magnitude to transport all but the coarsest (0·3–0·5 m) particles on the streambed, provided the opportunity for the bed to adjust to a comparatively stable flow regime. Observed and predicted bedload transport rate-stream power relationships are compared. The theoretical relationship does not adequately describe conditions in some gravel-bed channels, since it fails to take into account the effect which armouring may have upon the supply of transportable material.     

Stability of forsterite + CO2 and its bearing on the role of CO2 in the mantle

An experimental determination of the reaction MgCO₃ + MgSiO₃ = Mg₂SiO₄ + CO₂ between 20 and 40 kbars and in the range 1000–1500°C yields an average pressure effect on the equilibrium of 44 bars/°C. This result shows that the assemblage forsterite and carbon dioxide is not stable under most pressure and temperature conditions expected in the upper mantle. Hypotheses requiring the presence of free CO₂ in the low-velocity zone, CO₂ as a drive mechanism for kimberlite emplacement, or action of a free CO₂ phase in ultramafic rocks may need considerable revision.