On solving Kepler's equation for nearly parabolic orbits

We deal here with the efficient starting points for Kepler's equation in the special case of nearly parabolic orbits. Our approach provides with very simple formulas that allow calculating these points on a scientific vest-pocket calculator. Moreover, srtarting with these points in the Newton's method we can calculate a root of Kepler's equation with an accuracy greater than 0.001 in 0–2 iterations. This accuracy holds for the true anomaly || 135° and |e – 1| 0.01. We explain the reason for this effect also.Dedicated to the memory of Professor G.N. Duboshin (1903–1986).     

A filament eruption and accompanying coronal field changes on November 5, 1992

An H filament eruption on November 5, 1992 was fully observed in H with the Hida Flare Monitoring Telescope, while Yohkoh's Soft X-ray Telescope observed the pre- and post-eruption evolution of the coronal magnetic fields. From the H data, including the red and blue wings, we have reconstructed the rise of the filament, including trajectory, velocity, and acceleration. In combination with the Yohkoh data this reconstruction suggests that the filament had several interactions with other coronal magnetic fields during the eruption. The Yohkoh data also shows pre-eruption changes in the coronal fields and several post-eruption bright coronal structures. The pre-eruption changes are interpreted as a partial opening of the corona, indicating that it is not necessary to have a complete opening of the corona in order for a filament to erupt and we discuss the several possible contributions from emerging flux. The post-event bright coronal structures are compared with theory and with a cleaner filament eruption event on July 31, 1992. These comparisons suggest that, although there are many similarities, it is hard to completely reconcile the observations with the existing theory.     

Some comparisons between mining-induced and laboratory earthquakes

Although laboratory stick-slip friction experiments have long been regarded as analogs to natural crustal earthquakes, the potential use of laboratory results for understanding the earthquake source mechanism has not been fully exploited because of essential difficulties in relating seismographic data to measurements made in the controlled laboratory environment. Mining-induced earthquakes, however, provide a means of calibrating the seismic data in terms of laboratory results because, in contrast to natural earthquakes, the causative forces as well as the hypocentral conditions are known. A comparison of stick-slip friction events in a large granite sample with mining-induced earthquakes in South Africa and Canada indicates both similarities and differences between the two phenomena. The physics of unstable fault slip appears to be largely the same for both types of events. For example, both laboratory and mining-induced earthquakes have very low seismic efficiencies where _a is the apparent stress and is the average stress acting on the fault plane to cause slip; nearly all of the energy released by faulting is consumed in overcoming friction. In more detail, the mining-induced earthquakes differ from the laboratory events in the behavior of as a function of seismic momentM ₀. Whereas for the laboratory events 0.06 independent ofM ₀, depends quite strongly onM ₀ for each set of induced earthquakes, with 0.06 serving, apparently, as an upper bound. It seems most likely that this observed scaling difference is due to variations in slip distribution over the fault plane. In the laboratory, a stick-slip event entails homogeneous slip over a fault of fixed area. For each set of induced earthquakes, the fault area appears to be approximately fixed but the slip is inhomogeneous due presumably to barriers (zones of no slip) distributed over the fault plane; at constant , larger events correspond to larger _a as a consequence of fewer barriers to slip. If the inequality _a / 0.06 has general validity, then measurements of _a =µE _a /M ₀, where is the modulus of rigidity andE _a is the seismically-radiated energy, can be used to infer the absolute level of deviatoric stress at the hypocenter.     

Evidence of magmatic CO2-rich fluids in peraluminous graphite-bearing leucogranites from Deep Freeze Range (northern Victoria Land,Antarctica)

Fine-grained peraluminous synkinematic leuco-monzogranites (SKG), of Cambro-Ordovician age, occur as veins and sills (up to 20–30 m thick) in the Deep Freeze Range, within the medium to high-grade metamorphics of the Wilson Terrane. Secondary fibrolite + graphite intergrowths occur in feldspars and subordinately in quartz. Four main solid and fluid inclusion populations are observed: primary mixed CO₂+H₂O inclusions + Al₂SiO₅ ± brines in garnet (type 1); early CO₂-rich inclusions (± brines) in quartz (type 2); early CO₂+CH₄ (up to 4 mol%)±H₂O inclusions + graphite + fibrolite in quartz (type 3); late CH₄+CO₂+N₂ inclusions and H₂O inclusions in quartz (type 4). Densities of type 1 inclusions are consistent with the crystallization conditions of SKG (750°C and 3 kbar). The other types are post-magmatic: densities of type 2 and 3 inclusions suggest isobaric cooling at high temperature (700–550°C). Type 4 inclusions were trapped below 500°C. The SKG crystallized from a magma that was at some stage vapour-saturated; fluids were CO₂-rich, possibly with immiscible brines. CO₂-rich fluids (±brines) characterize the transition from magmatic to post-magmatic stages; progressive isobaric cooling (T<670°C) led to a continuous decrease off _{O 2} can entering in the graphite stability field; at the same time, the feldspars reacted with CO₂-rich fluids to give secondary fibrolite + graphite. Decrease ofT andf _{O 2} can explain the progressive variation in the fluid composition from CO₂-rich to CH₄ and water dominated in a closed system (in situ evolution). The presence of N₂ the late stages indicates interaction with external metamorphic fluids.Contribution within the network Hydrothermal/metamorphic water-rock interactions in crystalline rocks: a multidisciplinary approach on paleofluid analysis. CEC program: Human Capital and Mobility     

Nd,Sr, and Pb isotopic characteristics of Cretaceous intrusive rocks from deep levels of the Sierra Nevada batholith,Tehachapi Mountains,California

The Cretaceous gabbroic to granitic intrusive rocks of the Tehachapi Mountains were emplaced at depths of 25–30 km and thus afford a view of deep processes in the Sierra Nevada batholith. They consist of the 115 Ma Tehachapi suite and the 100 Ma Bear Valley suite; new zircon U-Pb age data reveal the presence of the latter as far west as Grapevine Canyon. The Nd, Sr, Pb, and O isotopic whole-rock data and zircon Pb inheritance patterns for the bulk of the suites suggest an origin by mixing between depleted mantlederived magmas and metasedimentary material with a substantial component of old continental material. However, this mixing is not evident in variations between isotopic ratios and chemical and lithologic parameters. This implies that isotopic hybridization of magmas took place deeper than 30 km, and that fractionation processes are likely responsible for the bulk of the chemical variation in this part of the Sierra Nevada batholith. Consideration of the isotopic data in the context of the Sierra Nevada batholith as a whole suggests that the well-known east-to-west isotopic gradients in the batholith may reflect a change in the average isotopic character of the preintrusive frame-work rather than a change in amount of crustal component. On the other hand, the lack of areal gradients in Sr and Nd isotopic ratios in the main study area may indicate a lack of pronounced gradation at deep levels, at least within the western batholith.     

Gold mineralization in As-rich mesothermal gold ores of the Bogosu-Prestea mining district of the Ashanti Gold Belt,Ghana: remobilization of “invisible” gold

The Bogosu-Prestea mining district of southwestern Ghana is a 33 km section of the Early Proterozoic Ashanti Gold Belt. Greenschist facies carbonaceous and carbonate-bearing turbidites and greywackes, and mafic dikes host numerous economic mesothermal gold deposits. Structurally higher ores in the Bogosu concession have brittle deformation and consist of disseminated-sulphide lodes in tectonically-disrupted sedimentary rocks and carbonate-altered mafic dikes. Most gold occurs as micrometre-size particles in arsenian pyrite, and as invisible gold in arsenian pyrite and arsenopyrite. The structurally deeper ores of the adjoining Prestea concession are associated with brittle-ductile deformation and consist of extensive crack-seal quartz-veins and graphitic shear zones. Only minor amounts of invisible gold were detected; in these deeper lodes, gold occurs dominantly as abundant microscopic and larger particles in sulphide/arsenide minerals and in gangue. The gold distribution patterns revealed by SIMS microprobe analysis and ion maps, EMP and colour staining suggest that most of the primary gold in the Bogosu-Prestea system precipitated in solid-solution with sulphide/arsenide minerals. However, post-depositional concentration and redistribution occurred, in increasing degree with: 1) increase in metamorphic/hydrothermal gradients in the gold system (depth), 2) decrease in the refractory properties of the host mineral, and 3) increase in the amount of post-depositional, host-mineral recrystallization and deformation. Gold evolved from primary solid-solution within sulphide/arsenide minerals, to colloidal and micrometre-size particles concentrated in voids, fractures and internal grain boundaries, and finally to microscopic and larger particles at sulphide/arsenide grain margins and in the gangue assemblage. The general conclusions presented here are applicable to As-rich gold deposits of all ages, worldwide. The presence of gold in late fractures is insufficient evidence for late-stage introduction of gold in mesothermal gold systems.     

Stable isotope study of antimony deposits in the Muratdagi region,western Turkey

The Muratdagi region is rich in antimony deposits having the following common characteristics: post Miocene age, location on the down-thrown blocks next to normal faults, in the vicinity of active or fossil thermal springs, and in contact with carbonate rocks. The isotopic composition of — 7. SMOW of the mineralizing fluid calculated from the measured ° ¹⁸O of quartz and the fluid inclusion microthermometry, is indicative of meteoric water origin. The ° ¹³C of the inclusion CO₂ of — 19.1 to — 25.4 PDB is indicative of interaction with organic material-graphite. The ° ³⁴S of stibnite — 3.6 to — 0.7 is, in view of the mineral assemblage, indicative of magmatic origin of the sulphur. A tightly confined set of structural, lithological, hydrological and geochemical features define a sequence of geochemical processes; formation of acid and reducing fluid, leaching and transport of antimony complexes and precipitation of stibnite within defined lithological units. The set of processes seems to have taken place within a space of 5000 m lateral and 1000 m vertical extension.     

Optical absorption investigation of Cr3+ ion-bearing minerals in the temperature range 77–797 K

The effect of raising temperature on spin-allowed dd-transitions of octahedral Cr³⁺ was studied for various point symmetries of the Cr³⁺-bearing structural sites, i.e. 3 m and 3 with inversion center in spinel and garnets, respectively, or 32, 3, 2 and 1, lacking the inversion centre, in beryl, corundum, diopside and topaz, respectively. For this purpose, crystals of Cr³⁺-bearing spinel, pyrope, andradite, grossular, uvarovite, emerald, ruby, diopside and topaz were analyzed by microprobe, oriented, and measured in polarized radiation (except for the cubic minerals) in the spectral range 30 000 to 11 100 cm^-1 and at temperatures between 77 and 797 K. The evaluation of the intensities, half widths, and energy positions of bands due to Cr³⁺-transitions derived from ⁴ A _2g ⁴ T _2g (F) and ⁴ T _1g (F) as well as of Dq- and B-values derived, had the following results:In all cases, red shift of the above bands and, hence, independent on the site symmetry of Cr³⁺, decreases in the Dq-values were obtained. The dependcies of Dq on T are nearly linear above room temperature and amount between -1.6% in topaz and -5.1% in pyrope in the temperature range studied. From this, values for the local thermal expansion of the Cr³⁺-centered octahedra, _loc, were derived on the basis of the R _M-0 ^-5 -proportionality of 10Dq. Such values are consistently higher than those obtained from X-ray refinements, a method averaging r_m-o for all the respective octahedral positions.     

Effects of water on strength and failure mode of coarse-grained granites at 300°C

Summary Deformation experiments have been performed in a triaxial compression cell at a temperature of 300°C and confining pressures up to 65 MPa using samples of homogeneous, fresh two-mica-granite (RM) and monzogranite (CM). The cylindrical specimens (d=70 mm, h=140 mm, V=540 cm³) were tested undrained under dry (105°C), as received, and water saturated conditions at deformation rates between and . The mechanical behaviour of the two types of coarse-grained, crystalloblastic granites is critically influenced by mineralogical composition, porosity, and the amount of intergranular water present in the samples. The failure stress of the CM granite is at about 65% of that of the RM granite; in both rocks strength decreases with increasing porosity and water content.The presence of interstitial water causes a failure mode of non-localized, homogeneously distributed microcracking in the central parts of the samples, whereas, in runs with dry granites, strain localization along a single shear fracture was observed. When aqueous fluids are present, the macroscopic style of deformation of granites appears to be ductile even at lowP andT conditions. Strength and angle of internal friction are reduced to very low values. The style of deformation, as well as the reduction of strength of the water-saturated rock samples, is due to mechanical and chemical effects of intergranular water at elevated temperatures.The maximum differential stresses measured for these coarse-grained granites are much lower than the strength commonly reported for other granites, e. g. Westerly and Charcoal granites. Our data suggest that the strength of the granitic crust under differential stress is lower than currently deduced from laboratory experiments.     

Multiple Isotopic Components in Quaternary Volcanic Rocks of the Cascade Arc near Crater Lake, Oregon

Quaternary lavas and pyroclastic rocks of Mount Mazama, CraterLake caldera, and the surrounding area have variable Sr, Nd,and Pb isotopic compositions. High-alumina olivine tholeiites(HAOT) have ⁸⁷Sr/⁸⁶Sr ratios of 0.70346–0.70364; basalticandesite, 0–70349–0.70372; shoshonitic basalticandesite, 0.70374–0.70388; and andesite, 0.70324–0.70383.Dacites of Mount Mazama have ⁸⁷Sr/⁸⁶Sr ratios of 0.70348–0.70373.Most rhyodacites converge on 0.7037. However, rhyodacite ofthe caldera-forming, climactic eruption has ⁸⁷Sr/⁸⁶Sr=0.70354because of an admixed low-⁸⁷Sr/⁸⁶Sr component. Andesitic tomafic-cumulate scoriae of the climactic eruption, and enclavesin preclimactic rhyodacites, cluster in two groups but shownearly the entire ⁸⁷Sr/⁸⁶Sr range of the data set, confirmingpreviously suggested introduction of diverse parental magmasinto the growing climactic chamber. Pb and Nd isotope ratiosdisplay less variation (²⁰⁶Pb/²⁰⁴Pb= 18.838–18.967, ²⁰⁷Pb/²⁰⁴Pb=15.556–15.616,²⁰⁸Pb/²⁰⁴Pb=38.405–38.619; _Nd= +3.9 to +6.1) and generallycovary with ⁸⁷Sr/⁸⁶ Sr ratios. Radiogenic isotope data fromCrater Lake plot with published data for other Cascade volcanoeson isotope ratio correlation diagrams. The isotopic data for the Crater Lake area require sources ofprimitive magmas to consist of depleted mantle and a subductioncomponent, introduced in variable quantity to the depleted mantlewedge. Variable degrees of melting of this heterogeneous mantle,possibly at different depths, produced the diversity of isotopiccompositions and large-ion lithophile element (LILE) abundancesin primitive magmas. Trace element ratios do not indicate presenceof an ocean island basalt (OIB) source component that has beenreported in lavas of some other Cascade volcanoes. Crustal contamination may have affected isotope ratios and LILEconcentrations in evolved HAOT, where initial LILE concentrationswere low. Contamination is more difficult to detect in the calcalkalinelavas because of their higher LILE concentrations and the smallisotopic contrast with likely contaminants, such as mid- tolower-crustal rocks thought to be equivalents of igneous rocksof the Klamath Mountains and associated lower crust. Crustalassimilation appears to be required for calcalkaline rocks onlyby ¹⁸O values, which vary from lows of +5.6 to + 6.0% in HAOTand primitive basaltic andesites to a high of +7.0% in dacite,a range that is too high to be explained by plagioclase-dominatedclosed-system fractional crystallization. Elevated ¹⁸O valuesof differentiated lavas may be attributed to interaction withrelatively ¹⁸O-rich, ⁸⁷Sr-poor crustal rocks. Variably fused granitoid blocks ejected in the climactic eruption,and rarely in late Pleistocene eruptive units, have ¹⁸Opl of–3.4 to +6.5% and ¹⁸O_qz of –2.2 to +8.0% but haveSr, Nd, and Pb isotope ratios similar to volcanic rocks (e.g.⁸⁷Sr/⁸⁶Sr0.7037). Rb and Sr data for glass separates from granodioritessuggest that the source pluton is Miocene. Glass from granodioritehas ⁸⁷Sr/⁸⁶Sr ratios as high as 0.70617. Oxygen isotope fractionationbetween quartz, plagioclase, and glass indicates requilibrationof O isotopes at magmatic temperatures, after ¹⁸O/¹⁶O had beenlowered by exchange with meteoric hydrothermal fluids. Unmeltedgranodiorite xenoliths from pre-climactic eruptive units have¹⁸O values that are consistent with onset of hydrothermal exchangeearly during growth of the climactic magma chamber. Assimilationof such upper-crustal granodiorite apparently lowered ¹⁸O valuesof rhyodacites without significantly affecting their magmaticcompositions in other ways.