Integration error over very long time spans     

Andrea Milani  Anna M. Nobili 《Celestial Mechanics and Dynamical Astronomy》1987,43(1-4):1-34

The main limit to the time span of a numerical integration of the planetary orbits is no longer set by the availability of computer resources, but rather by the accumulation of the integration error. By the latter we mean the difference between the computed orbit and the dynamical behaviour of the real physical system, whatever the causes. The analysis of these causes requires an interdisciplinary effort: there are physical model and parameters errors, algorithm and discretisation errors, rounding off errors and reliability problems in the computer hardware and system software, as well as instabilities in the dynamical system. We list all the sources of integration error we are aware of and discuss their relevance in determining the present limit to the time span of a meaningful integration of the orbit of the planets. At present this limit is of the order of 10⁸ years for the outer planets. We discuss in more detail the truncation error of multistep algorithms (when applied to eccentric orbits), the coefficient error, the method of Encke and the associated coordinate change error, the procedures used to test the numerical integration software and their limitations. Many problems remain open, including the one of a realistic statistical model of the rounding off error; at present, the latter can only be described by a semiempirical model based upon the simpleN ² formula (N=number of steps, =machine accuracy), with an unknown numerical coefficient which is determined only a posteriori.  相似文献   

Neutron techniques     

Glenn M. Frye Jr.  Philip P. Dunphy  Edward L. Chupp  Paul Evenson 《Solar physics》1988,118(1-2):321-346

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Melting of the subcontinental lithospheric mantle by the Emeishan mantle plume; evidence from the basal alkaline basalts in Dongchuan, Yunnan, Southwestern China   总被引：3，自引：0，他引：3  

Xie-Yan Song  Hua-Wen Qi  Paul T. Robinson  Mei-Fu Zhou  Zhi-Min Cao  Lie-Meng Chen 《Lithos》2008,100(1-4):93-111

The Emeishan continental flood basalt (ECFB) sequence in Dongchuan, SW China comprises a basal tephrite unit overlain by an upper tholeiitic basalt unit. The upper basalts have high TiO₂ contents (3.2–5.2 wt.%), relatively high rare-earth element (REE) concentrations (40 to 60 ppm La, 12.5 to 16.5 ppm Sm, and 3 to 4 ppm Yb), moderate Zr/Nb and Nb/La ratios (9.3–10.2 and 0.6–0.9, respectively) and relatively high _{Nd (t)} values, ranging from − 0.94 to 2.3, and are comparable to the high-Ti ECFB elsewhere. The tephrites have relatively high P₂O₅ (1.3–2.0 wt.%), low REE concentrations (e.g., 17 to 23 ppm La, 4 to 5.3 ppm Sm, and 2 to 3 ppm Yb), high Nb/La (2.0–3.9) ratios, low Zr/Nb ratios (2.3–4.2), and extremely low _{Nd (t)} values (mostly ranging from − 10.6 to − 11.1). The distinct compositional differences between the tephrites and the overlying tholeiitic basalts cannot be explained by either fractional crystallization or crustal contamination of a common parental magma. The tholeiitic basalts formed by partial melting of the Emeishan plume head at a depth where garnet was stable, perhaps > 80 km. We propose that the tephrites were derived from magmas formed when the base of the previously metasomatized, volatile-mineral bearing subcontinental lithospheric mantle was heated by the upwelling mantle plume.  相似文献   

Thermal stability of ladderane lipids as determined by hydrous pyrolysis   总被引：1，自引：0，他引：1  

Andrea Jaeschke  Michael D. Lewan  Ellen C. Hopmans  Stefan Schouten  Jaap S. Sinninghe Damst 《Organic Geochemistry》2008,39(12):1735

Anaerobic ammonium oxidation (anammox) has been recognized as a major process resulting in loss of fixed inorganic nitrogen in the marine environment. Ladderane lipids, membrane lipids unique to anammox bacteria, have been used as markers for the detection of anammox in marine settings. However, the fate of ladderane lipids after sediment burial and maturation is unknown. In this study, anammox bacterial cell material was artificially matured by hydrous pyrolysis at constant temperatures ranging from 120 to 365 °C for 72 h to study the stability of ladderane lipids during progressive dia- and catagenesis. HPLC-MS/MS analysis revealed that structural alterations of ladderane lipids already occurred at 120 °C. At temperatures >140 °C, ladderane lipids were absent and only more thermally stable products could be detected, i.e., ladderane derivatives in which some of the cyclobutane rings were opened. These diagenetic products of ladderane lipids were still detectable up to temperatures of 260 °C using GC-MS. Thus, ladderane lipids are unlikely to occur in ancient sediments and sedimentary rocks, but specific diagenetic products of ladderane lipids will likely be present in sediments and sedimentary rocks of relatively low maturity (i.e., C₃₁ hopane 22S/(22S + 22R) ratio <0.2 or ββ/(αβ + βα + ββ) ratio of >0.5).  相似文献   

Experimental solidification of anhydrous latitic and trachytic melts at different cooling rates: The role of nucleation kinetics   总被引：1，自引：0，他引：1  

Gianluca Iezzi  Silvio Mollo  Guido Ventura  Andrea Cavallo  Claudia Romano 《Chemical Geology》2008,253(3-4):91-101

Two sets of cooling experiments were run at atmospheric conditions for two anhydrous starting latitic and trachytic melts: 1) five cooling rates (25, 12.5, 3, 0.5, and 0.125 °C/min) between 1300° and 800 °C, and 2) a 0.5 °C/min cooling rate from 1300 °C with quench temperatures at 1200°, 1100°, 1000° and 900 °C. Trachytic run-products are invariably glassy. Nucleation is also suppressed in the latitic run-products at the three highest cooling rates. Conversely, in the 0.5 and 0.125 °C/min runs, latites have a crystal content of  90 vol.%. The phases are: plagioclase, clinopyroxene, glass and iron-bearing oxide (in order of abundance). The variable quench temperatures, investigated by coupling experiments with Pt wire and Pt capsule sample containers in set 2, again did not produce crystallization of trachyte, whereas latitic samples are characterized by  10 vol.% of oxides, pyroxenes and plagioclase (in order of appearance), at temperature < 1000 °C. Effects of (preferential) heterogeneous nucleation on sample holders, of superheating degree, and chemical species loss during cooling are absent for both melt compositions. The difference of solidification paths between these two silicate melts can be ascribed only to their small chemical differences. In comparison with calculated equilibrium conditions all the experimental latitic and trachytic run-products revealed strong kinetic effects, interpretable in the light of the nucleation theory. The glass-forming ability (GFA) of trachyte is higher, whereas their critical cooling rate (Rc) is lower (< 0.125 °C/min), in comparison to latitic melts (Rc > 0.5 °C/min). The experimental results carried out in this study can be applied to lava flows and domes; trachytic lavas are able to flow for longer period with respect to latitic ones in a metastable condition. Glass-rich terrestrial lavas, i.e. obsidians, can be the result of sluggish nucleation kinetics due to the relative high polymerisation of evolved silicate melts.  相似文献   

Sulfur isotope measurement of sulfate and sulfide by high-resolution MC-ICP-MS   总被引：4，自引：0，他引：4  

Paul R. Craddock  Olivier J. Rouxel  Lary A. Ball  Wolfgang Bach   《Chemical Geology》2008,253(3-4):102-113

We have developed a technique for the accurate and precise determination of ³⁴S/³²S isotope ratios (δ³⁴S) in sulfur-bearing minerals using solution and laser ablation multiple-collector inductively coupled plasma mass spectrometry (MC-ICP-MS). We have examined and determined rigorous corrections for analytical difficulties such as instrumental mass bias, unresolved isobaric interferences, blanks, and laser ablation- and matrix-induced isotopic fractionation. Use of high resolution sector-field mass spectrometry removes major isobaric interferences from O₂⁺. Standard-sample bracketing is used to correct for the instrumental mass bias of unknown samples. Background on sulfur masses arising from memory effects and residual oxygen-tailing are typically minor (< 0.2‰, within analytical error), and are mathematically removed by on-peak zero subtraction and by bracketing of samples with standards determined at the same signal intensity (within 20%). Matrix effects are significant (up to 0.7‰) for matrix compositions relevant to many natural sulfur-bearing minerals. For solution analysis, sulfur isotope compositions are best determined using purified (matrix-clean) sulfur standards and sample solutions using the chemical purification protocol we present. For in situ analysis, where the complex matrix cannot be removed prior to analysis, appropriately matrix-matching standards and samples removes matrix artifacts and yields sulfur isotope ratios consistent with conventional techniques using matrix-clean analytes. Our method enables solid samples to be calibrated against aqueous standards; a consideration that is important when certified, isotopically-homogeneous and appropriately matrix-matched solid standards do not exist. Further, bulk and in situ analyses can be performed interchangeably in a single analytical session because the instrumental setup is identical for both. We validated the robustness of our analytical method through multiple isotope analyses of a range of reference materials and have compared these with isotope ratios determined using independent techniques. Long-term reproducibility of S isotope compositions is typically 0.20‰ and 0.45‰ (2σ) for solution and laser analysis, respectively. Our method affords the opportunity to make accurate and relatively precise S isotope measurement for a wide range of sulfur-bearing materials, and is particularly appropriate for geologic samples with complex matrix and for which high-resolution in situ analysis is critical.  相似文献   

Numerical modeling assessment of three-gate structures for capturing contaminated groundwater     

Paul F. Hudak 《Environmental Geology》2008,55(6):1311-1317

This modeling study evaluated the capability of alternative funnel-and-gate structures with three gates for capturing contaminated groundwater in a hypothetical unconfined aquifer. Simulated interceptor structures were linear and 45 m wide, consisting of three gates and two funnels (walls). One gate occupied the center and two gates occupied the ends of the interceptor structures. The structures, positioned perpendicular to regional groundwater flow, traversed the entire thickness of the aquifer. A total of four structures were evaluated (numbers designate widths of end, center, and end gates, respectively, in meters): 3-3-3, 2-5-2, 1-7-1, and 4-1-4. Particle tracking and zonal water budgets identified shapes of capture zones and discharge patterns for each interceptor structure. A mass transport model, accounting for advection and hydrodynamic dispersion, tested the capability of each structure for capturing a contaminant plume. Results suggest that: time-dependent capture zones underestimate the amount of time to capture a contaminant plume, wide center gates facilitate plume capture, and wide end gates facilitate lateral containment of contaminants. Of the structures simulated, the 2-5-2 configuration was relatively efficient at processing and containing the simulated contaminant plume.  相似文献   

Late Palaeozoic hydrocarbon migration through the Clair field, West of Shetland, UK Atlantic margin     

Darren F. Mark  Paul F. Green  John Parnell  Simon P. Kelley  Martin R. Lee  Sarah C. Sherlock 《Geochimica et cosmochimica acta》2008,72(10):2510-2533

Geochemical analysis of bitumen- and hydrocarbon-bearing fluid inclusions from the Devonian-Carboniferous Clair field indicates that the reservoirs contain a mixture of oils from different marine and lacustrine sources. Reconstruction of the Clair field oil-charge history using fluid inclusion petrography show that oil-charging occurred at times of K-feldspar, quartz and calcite cementation. Temperature–composition–time data yielded from the integration of fluid inclusion microthermometry with high-resolution Ar–Ar dating, date hydrocarbon-bearing K-feldspar overgrowths at 247 ± 3.3 Ma. These data show that in order for oil to be trapped within primary fluid inclusions in K-feldspar overgrowths, hydrocarbon migration throughout the UK Atlantic margin must have been taking place during the Late Palaeozoic and as such, current industry oil-play models based solely on oil charging from Jurassic-Cretaceous marine sources are clearly incomplete and need revision. Apatite fission track analysis and vitrinite reflectance data were used to reconstruct thermal burial histories and assess potential oil generation from Middle Devonian lacustrine source rocks. Thermal history data from wells along The Rona Ridge adjacent to the Clair field show that the Palaeozoic section was heated to greater than 100 °C at some time between 270 and 230 Ma, confirming that Devonian source rocks were mature and expelling oil during the Late Palaeozoic at the time that authigenic K-feldspar overgrowths were growing in the Clair field.  相似文献   

An experimental study of the grain-scale processes of peridotite melting: implications for major and trace element distribution during equilibrium and disequilibrium melting   总被引：1，自引：0，他引：1  

Mauro Lo Cascio  Yan Liang  Nobumichi Shimizu  Paul C. Hess 《Contributions to Mineralogy and Petrology》2008,156(1):87-102

The grain-scale processes of peridotite melting were examined at 1,340°C and 1.5 GPa using reaction couples formed by juxtaposing pre-synthesized clinopyroxenite against pre-synthesized orthopyroxenite or harzburgite in graphite and platinum-lined molybdenum capsules. Reaction between the clinopyroxene and orthopyroxene-rich aggregates produces a melt-enriched, orthopyroxene-free, olivine + clinopyroxene reactive boundary layer. Major and trace element abundance in clinopyroxene vary systematically across the reactive boundary layer with compositional trends similar to the published clinopyroxene core-to-rim compositional variations in the bulk lherzolite partial melting studies conducted at similar P–T conditions. The growth of the reactive boundary layer takes place at the expense of the orthopyroxenite or harzburgite and is consistent with grain-scale processes that involve dissolution, precipitation, reprecipitation, and diffusive exchange between the interstitial melt and surrounding crystals. An important consequence of dissolution–reprecipitation during crystal-melt interaction is the dramatic decrease in diffusive reequilibration time between coexisting minerals and melt. This effect is especially important for high charged, slow diffusing cations during peridotite melting and melt-rock reaction. Apparent clinopyroxene-melt partition coefficients for REE, Sr, Y, Ti, and Zr, measured from reprecipitated clinopyroxene and coexisting melt in the reactive boundary layer, approach their equilibrium values reported in the literature. Disequilibrium melting models based on volume diffusion in solid limited mechanism are likely to significantly underestimate the rates at which major and trace elements in residual minerals reequilibrate with their surrounding melt. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.  相似文献   

A depleted, not ideally chondritic bulk Earth: The explosive-volcanic basalt loss hypothesis     

Paul H. Warren 《Geochimica et cosmochimica acta》2008,72(8):2217-2235

It has long been customary to assume that in the bulk composition of the Earth, all refractory-lithophile elements (including major oxides Al₂O₃ and CaO, all of the REE, and the heat-producing elements Th and U) occur in chondritic, bulk solar system, proportion to one another. Recently, however, Nd-isotopic studies (most notably Boyet M. and Carlson R. W. (2006) A new geochemical model for the Earth’s mantle inferred from ¹⁴⁶Sm-¹⁴²Nd systematics. Earth Planet. Sci. Lett.250, 254-268) have suggested that at least the outer portion of the planet features a Nd/Sm ratio depleted to ∼0.93 times the chondritic ratio. The primary reaction to this type of evidence has been to invoke a “hidden” reservoir of enriched matter, sequestered into the deepest mantle as a consequence of primordial differentiation. I propose a hypothesis that potentially explains the evidence for Nd/Sm depletion in a very different way. Among the handful of major types of differentiated asteroidal meteorites, two (ureilites and aubrites) are ultramafic restites so consistently devoid of plagioclase that meteoriticists were once mystified as to how all the complementary plagioclase-rich matter (basalt) was lost. The explanation appears to be basalt loss by graphite-fueled explosive volcanism on roughly 100-km sized planetesimals; with the dispersiveness of the process dramatically enhanced, relative to terrestrial experience, because the pyroclastic gases expand into vacuous space (Wilson L. and Keil K. (1991) Consequences of explosive eruptions on small Solar System bodies: the case of the missing basalts on the aubrite parent body. Earth Planet. Sci. Lett.104, 505-512). By analogy with lunar pyroclastic products, the typical size of pyroclastic melt/glass droplets under these circumstances will be roughly 0.1 mm. Once separated from an asteroidal or planetesimal gravitational field, droplets of this size will generally spiral toward the Sun, rather than reaccrete, because drag forces such the Poynting-Robertson effect quickly modify their orbits (the semimajor axis, in a typical scenario, is reduced by several hundred km during the first trip around the Sun). Assuming a similar process occurred on many of the Earth’s precursor planetesimals while they were still roughly 100 km in diameter, the net effect would be a depleted composition for the final Earth. I have modeled the process of trace-element depletion in the planetesimal mantles, assuming the partial melting was nonmodal and either batch or dynamic in terms of the melt-removal style. Assuming the process is moderately efficient, typical final-Earth Nd/Sm ratios are 0.93-0.96 times chondritic. Depletion is enhanced by a relatively low assumed residual porosity in batch-melting scenarios, but dampened by a relatively high value for “continuous” residue porosity in dynamic melting scenarios. Pigeonite in the source matter has a dampening effect on depletion. There are important side effects to the Nd/Sm depletion. The heat-producing elements, Th, U and K, might be severely depleted. The Eu/Eu^∗ ratio of the planet is unlikely to remain precisely chondritic. One of the most inevitable side effects, depletion of the Al/Ca ratio, is consistent with an otherwise puzzling aspect of the composition of the upper mantle. A perfectly undepleted composition for the bulk Earth is dubious.  相似文献