The solution of Kepler's equation,I

Methods of iteration are discussed in relation to Kepler's equation, and various initial guesses are considered, with possible strategies for choosing them. Several of these are compared; the method of iteration used in the comparisons has local convergence of the fourth order.WANG Laboratories, Inc.     

The Mordor Alkaline Igneous Complex,Central Australia: PGE-enriched disseminated sulfide layers in cumulates from a lamprophyric magma

The Mordor Alkaline Igneous Complex (MAIC) is a composite intrusion comprising a body of syenite and a funnel-shaped layered mafic–ultramafic intrusion of lamprophyric parentage, the Mordor Mafic–Ultramafic Intrusion or MMUI. The MMUI is highly unusual among intrusions of lamprophyric or potassic parentage in containing primary magmatic platinum-group element (PGE)-enriched sulfides. The MMUI sequence consists largely of phlogopite-rich pyroxenitic cumulates, with an inward dipping conformable layer of olivine-bearing cumulates divisible into a number of cyclic units. Stratiform-disseminated sulfide accumulations are of two types: disseminated layers at the base of cyclic units, with relatively high PGE tenors; and patchy PGE-poor disseminations within magnetite-bearing upper parts of cyclic units. Sulfide-enriched layers at cycle bases contain anomalous platinum group element contents with grades up to 1.5 g/t Pt+Pd+Au over 1-m intervals, returning to background values of low parts per billion (ppb) on a meter scale. They correspond to reversals in normal fractionation trends and are interpreted as the result of new magma influxes into a continuously replenished magma chamber. Basal layers have decoupled Cu and PGE peaks reflecting increasing PGE tenors up-section, due to increasing R factors during the replenishment episode, or progressive mixing of between resident PGE-poor magma and more PGE-enriched replenishing magma. The presence of PGE enriched sulfides in cumulates from a lamprophyric magma implies that low-degree partial melts do not necessarily leave sulfides and PGEs in the mantle restite during partial melting. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Giant submarine landslide grooves in the Neoproterozoic/Lower Cambrian Phe Formation, northwest Himalaya: Mechanisms of formation and palaeogeographic implications

Giant groove casts have been found in the upper Proterozoic to Lower Cambrian Phe Formation (Haimanta Group), a siliciclastic sandstone/shale succession in the Tethyan Zone of the Higher Himalaya tectonic unit. The grooves are among the largest linear erosion structures related to submarine mass-movements observed in the geologic record. They are up to 4 m wide, about 0.2 m deep and can be traced for more than 35 m without changing their character. The grooves are straight, subparallel to cross-cutting striations with shallow semi-circular cross-sections and well-defined superimposed minor ridges and grooves. Groove casts exist on the soles of several sandstone beds within a 73 m thick logged section, commonly associated with flute casts. Their characteristics were compared with several other types of ancient and modern submarine linear erosion structures. A sand-rich, non-channelized basin floor depositional environment is inferred from the lithofacies, the combination of sedimentary structures, the lack of coarse-grained pebbly facies, the lateral continuity of beds, and the lack of channel structures. The grooves probably formed by laminar debris flows/concentrated density flows dragging blocks of already lithified sediment across the basin floor. When the bedding is structurally rotated back to horizontal, the groove casts show consistent North–South oriented palaeocurrent trends, with South-directed palaeocurrent directions indicated by flute casts. These palaeocurrent orientations contrast with previous palaeogeographic reconstructions of this area, which propose sediment delivery from the South. We therefore suggest a new “double provenance” model for the spatial relationship of late Proterozoic to Early Cambrian strata of the Himalaya, in which Lesser and Tethyan Himalayan age-equivalent sediment was deposited in a connected basin, where the former received detritus from the South, and the latter from a hitherto unknown source in the North. One possible candidate for this northern source is the South China Block and an associated Neoproterozoic volcanic arc.     

The WRF model performance for the simulation of heavy precipitating events over Ahmedabad during August 2006

The summer monsoon season of the year 2006 was highlighted by an unprecedented number of monsoon lows over the central and the western parts of India, particularly giving widespread rainfall over Gujarat and Rajasthan. Ahmedabad had received 540.2mm of rainfall in the month of August 2006 against the climatological mean of 219.8mm. The two spells of very heavy rainfall of 108.4mm and 97.7mm were recorded on 8 and 12 August 2006 respectively. Due to meteorological complexities involved in replicating the rainfall occurrences over a region, the Weather Research and Forecast (WRF-ARW version) modeling system with two different cumulus schemes in a nested configuration is chosen for simulating these events. The spatial distributions of large-scale circulation and moisture fields have been simulated reasonably well in this model, though there are some spatial biases in the simulated rainfall pattern. The rainfall amount over Ahmedabad has been underestimated by both the cumulus parameterization schemes. The quantitative validation of the simulated rainfall is done by calculating the categorical skill scores like frequency bias, threat scores (TS) and equitable threat scores (ETS). In this case the KF scheme has outperformed the GD scheme for the low precipitation threshold.     

Doline probability map using logistic regression and GIS technology in the central Ebro Basin (Spain)

In the surroundings of Zaragoza, karstification processes are especially intense in covered karst areas where fluvial terraces lie directly on Tertiary evaporites. Since the beginning of Quaternary, these processes have lead to the development of collapse and subsidence dolines with a wide range of sizes, which have significant economic impacts. To reduce economic impact and increase safety, a regional analysis of this phenomenon is needed for spatial management. Therefore, a probability map of dolines was developed using logistic regression and geographic information system (GIS) techniques. This paper covers the selection of input data, manipulation of data using the GIS technology, and the use of logistic regression to generate a doline probability map. The primary variable in the doline development in this area is geomorphology, represented by the location of endorheic areas and different terrace levels. Secondary variables are the presence of irrigation and the water table gradient.     

Space–time distribution of ancient and active alluvial karst subsidence: examples from the central Ebro Basin,Spain

Space and time variations of alluvial karst subsidence in the central Ebro Basin are analysed in trenches (paleodolines), aerial photographs (historical dolines) and field surveys (present-day active dolines). The measured subsidence rates, as well as a comparison between densities of paleodolines computed in randomly selected scan-lines and density of active dolines computed in maps, suggest that present-day subsidence in favourable areas is more intense than that of Pleistocene times. According to diachronic maps drawn from (a) different aerial photographs taken after 1946 and (b) field surveys on deformations in urbanized areas, subsidence behaved as a nearly steady process while the whole area was used for agriculture. In contrast, rapid changes (through periods of several tens of years) have occurred in urbanized areas, in which dolines expand their boundaries through small marginal collapses, shifting sharply their sinking centres to neighbouring sites. These rapid changes do not have an equivalent in observed paleodolines.     

Suitability analysis for sand and gravel extraction site location in the context of a sustainable development in the surroundings of Zaragoza (Spain)

Zaragoza city is located in the central Ebro Basin, in the Iberian Peninsula. The fluvial terraces formed by the Ebro River present a valuable resource of sand and gravel deposits. However, taking advantage of these available resources implies conflicts with other land use interests like urban and industrial development as well as agricultural use, which has also traditionally occupied the alluvial terraces. These deposits represent a substantial groundwater resource that should be preserved for future generations. The development of spatial decision support systems (SDSS) has greatly assisted efforts for solving land-use conflicts. These systems combine the benefits of geographic information systems (GIS) and decision support methodologies and are therefore suitable to manage sustainable development of urban areas. In this contribution, an extraction suitability map taking into consideration a variety of environmental criteria is created with the help of a SDSS. The method used is the analytical hierarchy process which is integrated in ArcGIS. Areas most suitable to sand and gravel extraction are located in the high terraces, and in those terraces covered by pediments where the thickness of resource is relatively high. These areas are far from valuable natural areas, outside areas most vulnerable to groundwater contamination, and beneath soils with poor irrigation characteristics.     

A new method of estimating the ratio between in situ rock stresses and tectonics based on empirical and probabilistic analyses

This paper describes a new procedure for assessing the ratio between in situ stresses in rock masses by means of K (K = σ_H / σ_v, being σ_H and σ_v principal stress) and tectonics for purposes of engineering geology and rock mechanics. The method combines the use of the logic decision tree and the empirical relationship between the Tectonic Stress Index, TSI, and a series of K in situ values obtained from an extensive database. The decision tree considers geological and geophysical factors affecting stress magnitudes both on the regional and local scale. The TSI index is defined by geological and geomechanical parameters. The method proposed provides an assessment of the magnitude of horizontal stresses of tectonic origin. Results for several regions of Europe are presented and the possible applications of the procedure are discussed.     

Application of precise 142Nd/144Nd analysis of small samples to inclusions in diamonds (Finsch,South Africa) and Hadean Zircons (Jack Hills,Western Australia)

¹⁴⁶Sm–¹⁴²Nd and ¹⁴⁷Sm–¹⁴³Nd systematics were investigated in garnet inclusions in diamonds from Finsch (S. Africa) and Hadean zircons from Jack Hills (W. Australia) to assess the potential of these systems as recorders of early Earth evolution. The study of Finsch inclusions was conducted on a composite sample of 50 peridotitic pyropes with a Nd model age of 3.3 Ga. Analysis of the Jack Hills zircons was performed on 790 grains with ion microprobe ²⁰⁷Pb/²⁰⁶Pb spot ages from 3.95 to 4.19 Ga. Finsch pyropes yield 100 × ?¹⁴²Nd = ? 6 ± 12 ppm, ?¹⁴³Nd = ? 32.5, and ¹⁴⁷Sm/¹⁴⁴Nd = 0.1150. These results do not confirm previous claims for a 30 ppm ¹⁴²Nd excess in South African cratonic mantle. The lack of a ¹⁴²Nd anomaly in these inclusions suggests that isotopic heterogeneities created by early mantle differentiation were remixed at a very fine scale prior to isolation of the South African lithosphere. Alternatively, this result may indicate that only a fraction of the mantle experienced depletion during the first 400 Myr of its history. Analysis of the Jack Hills zircon composite yielded 100 × ?¹⁴²Nd = 8 ± 10 ppm, ?¹⁴³Nd = 45 ± 1, and ¹⁴⁷Sm/¹⁴⁴Nd = 0.5891. Back-calculation of this present-day ?¹⁴³Nd yields an unrealistic estimate for the initial ?¹⁴³Nd of ? 160 ?-units, clearly indicating post-crystallization disturbance of the ¹⁴⁷Sm–¹⁴³Nd system. Examination of ^146,147Sm–^142,143Nd data reveals that the Nd budget of the Jack Hills sample is dominated by non-radiogenic Nd, possibly contained in recrystallized zircon rims or secondary subsurface minerals. This secondary material is characterized by highly discordant U–Pb ages. Although the mass fraction of altered zircon is unlikely to exceed 5–10% of total sample, its high LREE content precludes a reliable evaluation of ¹⁴⁶Sm–¹⁴²Nd systematics in Jack Hills zircons.