Expansion theory for the elliptic motion of arbitrary eccentricity and semi-major axis

In this paper of the series, literal analytical expressions for the coefficients of the Fourier series representation ofG will be established for anyx _i; withn, N positive integers and |_i|<1 fori=1, 2, ... n. Moreover, the recurrence formulae satisfied by these coefficients will also be established. Illustrative analytical examples and a full recursive computational algorithm, with its numerical results, are included. The applications of the recurrence formulae are also illustrated by their stencils. As by-products of the analyses are two important periodic integrals developed analytically and computationally.     

Geochemistry of lamprophyres associated with uranium mineralization, Southeastern Desert, Egypt

Two brecciated shear zones (NNW-SSE) are found crosscutting cataclastic rocks. The cataclastic rocks (3.0 km2) occupy the core of the granitic pluton and enclose a roof pendant of mafic-ultramafic rocks. The NNW-SSE-extending lamprophyre dykes vary in thickness from 0.5 m to 1 m and up to 800 m long, cutting the cataclastic rocks and are composed mainly of plagioclases, amphiboles, relics of pyroxenes and K-feldspar phenocrysts embedded in fine-grained groundmass. They are characterized as being peraluminous, calc-alkaline in composition (chemical trap) and enriched in calcite, sulfide and P2O5. The lamprophyres were affected by hydrothermal alteration (chlorite-carbonate alteration) while the cataclastic rocks were affected by diagenetic alteration (K-feldspar-albite alteration). Uranium mineralization is the product of hydrothermal events and has been investigated by X-ray diffraction (XRD) and environmental scanning electron microscopy (ESEM), involving primary uranium minerals (U3O8) and secondary uranium minerals (uranophane and beta-uranophane, kasolite, torbernite, autonite and meta-autonite) in addition to U- bearing minerals (astrocyanite, betafite and fergusonite). The presence of different mineral parageneses associated with clay minerals indicates that the lamprophyres were subjected to acidic and alkaline mineralizing solutions. Moreover, the U-Zr/U, U-Ce/U values show negative correlations, confirming U-enrichment in both cataclastic rocks and shear zones while the Th-eU/eTh, Th-Zr/Th and Th-Ce/Th values show negative correlations, indicating that the U-bearing solutions are rich in Th in the cataclastic rocks only.     

Seismic velocity and Poisson’s ratio tomography of the crust beneath southwest Anatolia: an insight into the occurrence of large earthquakes

The western part of Anatolia is one of the most seismically and tectonically active continental regions in the world, and much of it has been undergoing NS-directed extensional deformation since the Early Miocene. In this study, we determine 3-D tomographic images of the crust under the southwestern part of the North Anatolian Fault Zone by inverting a large number of arrival time data of P and S waves. From the obtained P- and S-wave velocity models, we estimated the Poisson’s ratio structures for a more reliable interpretation of the obtained anomalies. Our tomographic results confirmed the major tectonic features detected by previous studies and revealed new structural heterogeneities related to the active seismotectonics of the studied area. High P-wave velocity anomalies are recognized near the surface, while at deeper crustal layers, low P-wave velocities are widely distributed. The crustal S-wave velocity and Poisson’s ratio exhibit more structural heterogeneities compared to the P-wave velocity structure. Microearthquake activity is intense along highly heterogeneous zones in the southwestern part, which is characterized by low to high P-wave velocity, low S-wave velocity, and high Poisson’s ratio anomalies. Large earthquakes are also concentrated in zones dominated by low velocities and low to high Poisson’s ratios. Results of the checkerboard and synthetic tests indicate that the imaged anomalies are reliable features down to a depth of 25 km. Moreover, they are consistent with many geological and geophysical results obtained by other researchers along the southwestern part of the North Anatolian Fault Zone. An erratum to this article can be found at     

Formation of juvenile continental crust in the Arabian–Nubian shield: evidence from granitic rocks of the Nakasib suture, NE Sudan

Major and trace element data, U–Pb zircon ages, and initial isotopic compositions of Sr, Nd, and Pb are reported for ten granitic and one rhyolitic rock sample from the neo-Proterozoic Nakasib suture in NE Sudan. Chemical data indicate that the samples are medium- to high-K, "I-type" granitic rocks that mostly plot as "volcanic arc granites" on discriminant diagrams. Geochronologic data indicate that rifting occurred 790±2?Ma and constrain the time of deformation associated with suturing of the Gebeit and Haya terranes to have ended by approximately 740?Ma. Isotopic data show a limited range, with initial ⁸⁷Sr/⁸⁶Sr=0.7021 to 0.7032 (mean=0.7025), εNd(t) =+5.5 to +7.0 (mean=+6.4), and ²⁰⁶Pb/²⁰⁴Pb = 17.50–17.62. Neodymium model ages (T_DM; 0.69–0.85?Ga; mean = 0.76?Ga) are indistinguishable from crystallization ages (0.79–0.71?Ga; mean=0.76?Ga), and the isotopic data considered together indicate derivation from homogeneously depleted mantle. The geochronologic data indicate that the terrane accretion to form the Arabian–Nubian shield began just prior to 750?Ma. The isotopic data reinforces models for the generation of large volumes of juvenile continental crust during neo-Proterozoic time, probably at intra-oceanic convergent margins. The data also indicate that crust formation was associated with two cycles of incompatible element enrichment in granitic rocks, with an earlier cycle beginning approximately 870?Ma and culminating approximately 740?Ma, and the second cycle beginning after pervasive high-degree melts – possibly hot-spot related – were emplaced approximately 690–720?Ma.     

Two-phase Numerical Model of Powder Avalanche Theory and Application

In this paper the powder snow avalanche is considered as a two-phase flow (air and snow particles). The equations governing this flow are the fluid mechanics conservation laws. The mass and the momentum conservation are considered for each phase. The interaction between the two phases takes into account the drag force between the particle and the air. Owing to high turbulence in the powder flow, a closure model was used based on a modified k - model in order to take into account the reduction of turbulence energy by the particles. The dense avalanche is modeled using the shallow water equations. The formation and the development of the powder avalanche is modeled using a mass and momentum exchanges between the powder flow and the dense flow. The flow area is digitized horizontally and vertically using a finite elements mesh. The numerical scheme is obtained by integrating the equations on each cell. The model thus built was calibrated using laboratory measurements of density current carried out in a flume. The model was successfully applied to reproduce many avalanches observed in France. At the end of this paper, an application of this model to an engineering case study is presented. It concerns the Uzengili path where an avalanche occurred in 1993. In this paper we use the integrated dense/powder avalanche model to define the effect of a powder avalanche flow in this path. Different simulations allow display of maps of the exposed zones for different available snow depths in the starting zone. The results were mapped in terms of dynamic pressure field and recommendations are proposed to the local authorities.     

Diagenetic origin of Basal Anhydrite in the Cretaceous Maha Sarakham salt: Khorat Plateau, NE Thailand

Development of a diagenetic anhydrite bed at the base of the Cretaceous Maha Sarakham Saline Formation (the `Basal Anhydrite' member) of the Khorat Plateau in north-eastern Thailand took place due to leaching and/or pressure dissolution of salt at the contact between an underlying active sandstone aquifer system and an overlying massive halite-dominated evaporite sequence. Basal evaporites composed of halite with intercalated anhydrite of the latter sequence are undergoing dissolution as a result of subsurface flushing, with anhydrite produced as the insoluble residue. The result is a 1·1 m thick interval of nodular anhydrite displaying unique, basin-wide continuity. Observed textures, petrographic features and chemical data from the anhydrite and associated authigenic minerals support the origin of the Basal Anhydrite Member as an accumulation residue from the dissolution of the Maha Sarakham salts. Petrographically, the anhydrite in this unit is made up of crystals that are blocky and recrystallized, sheared, generally elongated and broken, and is bounded at the bottom by organic-rich stylolite surfaces. Authigenic and euhedral dolomite and calcite crystals are associated with the anhydrite. Traces of pyrite, galena and chalcopyrite are present along the stylolite surfaces suggesting supply of fresh water from the underlying sandstone at highly reducing conditions of burial. The δ<sup>34</sup>S of sulphate in the Basal Anhydrite averages 15 ‰ (CDT) and falls within the isotopic composition of the anhydrite in the Cretaceous Maha Sarakham Formation proper and the Cretaceous values of marine evaporites. Measured δ<sup>18</sup>O in dolomite range from ?4·37 to ?14·26‰ (PDB) suggesting a re-equilibration of dolomite with basinal water depleted in <sup>18</sup>O and possible recrystallization of dolomite under relatively elevated temperatures. The δ<sup>13</sup>C, however, varies from +1·57 to ?2·53‰ (PDB) suggesting a contribution of carbon from oxidation of organic matter. This basal anhydrite bed, similar to basinwide beds found at the bottom of many giant evaporite sequences, has always been considered to be depositional. Here, at the base of the Maha Sarakham Formation, we demonstrate that the anhydrite is diagenetic in origin and was formed by accumulation of original anhydrite by dissolution of interbedded halite from waters circulating though the underlying aquifer: it represents an `upside-down' caprock.     

Incorporation of planetary boundary-layer processes into numerical forecasting models

A study has been made of the evolution of the planetary boundary layer height (PBLH), the heat flux, and momentum flux using Clarke's Wangara data for a period of two days and two nights, 33/34–34/35. The observed Wangara data are considered as being an output of the first two internal levels of a general circulation model, at 1000 and 2000 m height. A time-dependent equation has been used to forecast, explicitly, the PBLH for both convectively unstable and stable periods. A comparison is made between observed and computed values whenever possible. In the unstable case, the Deardorff model (1974) has been used for the prediction of the unstable PBLH. Part of the stable case study involved a formulation of a time-dependent model for the prediction of the stable PBLH. The solution obtained from the model compared favourably with the results of a model suggested by Khakimov. Contribution number 382.     

Mercury pollution of Mediterranean sediments around Alexandria,Egypt

Elemental mercury is associated with industrial wastes discharged through the main effluent pipe of the Chlorine-Alkali plant at El-Max area west of Alexandria. The minimal mercury value of 0.1 ppm dry weight is assumed to be the background level for uncontaminated sediments in the area. Mercury level ranged from 8.02 to 15.5 ppm in the beach sands from the polluted area beyond the plant, and from 0.14 to 1.4 ppm in the bottom sediments off Alexandria.The Chlorine-Alkali plant is obviously the major source of mercury pollution. The contribution of land drainage, agricultural and domestic wastes is insignificant.