Fourier analysis of the light curves of eclipsing variables,II

The aim of the present paper will be to extend the Fourier methods of analysis of the light curves of eclipsing binaries, outlined in our previous communication (Kopal, 1975) in connection with systems whose components would appear as uniformly bright discs, to systems whose components exhibit discs characterized by an arbitrary radially-symmetrical distribution of brightness —i.e., an arbitrary law of darkening towards the limb — be it linear or nonlinear.In Section 2 which follows a few brief introductory remarks, fundamental equations will be set up which govern the light changes arising from the mutual eclipses of limb-darkened stars — be such eclipses total, partial or annular; and Section 3 will contain a closed algebraic solution for the elements of the occulation eclipses terminating in total phase. Such a solution proves to be no more complicated than it turned out to be for uniformly bright discs in our previous paper; and calls for no special functions for the purpose — as will be put in proper perspective in the concluding Section 4.The cases of transit eclipses terminating in an annular phase, of partial eclipses of occulation or transit type, will be similarly dealt with by Fourier methods in the next paper of the present series.     

On the structure of Saturn's rings and the ‘real’ rotational period for the planet

An analysis of the Lowell Observatory photographic plates of Saturn gave the following results: (1) ring A and B show peculiar brightness distributions around the planet, from which we conclude that both are composed of particles in synchronous rotation. (2) The leading side of the particles in ring A is brighter than the trailing side by about 4%, which may indicate an interaction between such particles and the interplanetary medium. (3) Scans of the rings across the major axis show a small (～0.3″) region of enhanced brightness, from which we derive a value ofT _s =10^h13 _. ^m 8±5 _. ^m 4 for the actual planetary rotational period of Saturn. (4) In order to explain the synchronous rotation, the particles in ring A have to be at least 42 m in diameter.     

Alpine reworking of Ordovician protoliths in the Western Carpathians: Geochronological and geochemical data on the Muráñ Gneiss Complex, Slovakia

Magmatic protoliths of Ordovician age have been identified in the metamorphic rocks of the Muráñ Gneiss Complex, Veporic Unit (Central Western Carpathians). Vapor digestion single zircon U–Pb dating yields an intrusion age of 464 ± 35 Ma (upper intercept) for the granite protolith. A lower intercept age of 88 ± 40 Ma records amphibolite-facies metamorphic overprint in the Cretaceous, during the Alpine orogeny. Geochemical and isotopic data suggest crustal origin of the orthogneiss. Nd_initial are between − 2.6 and − 5.0 and T_DM^Nd between 1.3 and 1.5 Ga (two-step approach). ⁸⁷Sr / ⁸⁶Sr_initial ratios vary between 0.7247 and 0.7120, and a steep REE pattern further constrains the crustal affinity of these rocks. Associated amphibolite bodies have Nd_initial values of 6.5, ⁸⁷Sr / ⁸⁶Sr_initial ratio of 0.7017, and a flat REE pattern. They are interpreted as MORB derived metabasites. Whole-rock Pb isotope analyses define a linear array in a ²⁰⁶Pb / ²⁰⁴Pb vs. ²⁰⁷Pb / ²⁰⁴Pb diagram with an age of ca. 134 Ma, consistent with intense Alpine metamorphism and deformation.

These basement rocks of the Central Western Carpathians are interpreted as Ordovician magmatic rocks intruded at an active margin of Gondwana. They represent the eastern prolongation of Cambro–Ordovician units of the European Variscides, which were part of the peri-Gondwana superterrane and accreted to Laurussia during the Variscan orogeny. Variscan metamorphic overprint is not recorded by the isotopic data of the Muráñ Gneiss Complex. Alpine metamorphism is the most dominant overprint.     

Study of geothermal water intrusion due to groundwater exploitation in the Puebla Valley aquifer system, Mexico

Significant intrusion of geothermal water into fresh groundwater takes place in the Puebla Valley aquifer system, Mexico. The decline in the potentiometric surface due to the overexploitation of the groundwater induces this intrusion. This hydrological system comprises three aquifers located in Plio-Quaternary volcanic sediments and Mesozoic calcareous rocks. The hydraulic balance of the aquifer shows that the annual output exceeds the natural inputs by 12 million m³. Between 1973 and 2002, a drop in the potentiometric surface, with an 80 m cone of depression, was identified in a 5-km-wide area located southwest of the city of Puebla. Chemical analyses performed on water samples since 1990 have shown an increase in total dissolved solids (TDS) of more than 500 mg/L, coinciding with the region showing a cone of depression in the potentiometric surface. A three-dimensional flow and transport model, based on the hydrogeological and geophysical studies, was computed by using the MODFLOW and MT3D software. This model reproduces the evolution of the aquifer system during the last 30 years and predicts for 2010 an additional drawdown in the potentiometric surface of 15 m, and an increase in the geothermal water intrusion.     

Catastrophic debris flows near Machu Picchu village (Aguas Calientes), Peru

Slope movements together with intensive river erosion and the following accumulation are the leading processes in the landscape evolution in the area of Machu Picchu village (former Aguas Calientes), which is located close to the Machu Picchu Sanctuary. Debris flows affect not only the bottoms of valleys or canyons, but also debris fans at the termini of the drainage basins, which are heavily inhabited at some places. The most recent event in the Machu Picchu village occurred in April 2004, but several others were documented in a broader area in the last 50 years. The field inspections at Machu Picchu (May and September 2004; June and September 2005) together with oral testimony revealed the nature and behavior of the debris flow. Machu Picchu village can be assessed as a zone with high landslide risk in relation to its urban development. Despite that, the village recorded a rapid growth (threefold population increase) without urban control within the past two decades. Precipitation, which is the main triggering factor of the debris flows, and natural hazard management of the Machu Picchu village are discussed in this paper.     

Will the river Irtysh survive the year 2030? Impact of long-term unsuitable land use and water management of the upper stretch of the river catchment (North Kazakhstan)

The Irtysh river basin all the way from river spring in China across Kazakhstan as far as the Russian part of Siberia is among the most ecologically endangered and affected regions on our planet. The study provides a summary of the historical reasons for anthropological interventions in this area, which began with the construction of plants of the military—industrial complexes in the forties of the last century during World War II. These plants have a major share in extreme high concentrations of heavy metals in surface as well in groundwaters locally. The Semipalatinsk nuclear polygon plays a specific role as a source of contamination of local waters. The release of top secret data enabled us to gain knowledge about serious problems related to high radioactivity of groundwaters, which should spread uncontrollably through a system of secondary fissures activated by nuclear blasts. Another serious problem in this region is the quantitative aspect of contamination. Model simulations of water balance indicate that large industrial development in the spring area in China and continuously increasing water consumption in Kazakhstan may lead to desiccation of the lower stretch of this large river in Siberia during the summer months of 2030.     

The Spačice eclogite: constraints on the P–T–t history of the Gföhl granulite terrane, Moldanubian Zone, Bohemian Massif

Summary In the Kutná Hora Complex, the Běstvina Formation, which is similar to Gf?hl granulite, contains eclogite that has escaped widespread retrograde recrystallization. The eclogite assemblage, garnet + omphacite + quartz + rutile ± plagioclase, yields an estimate for peak metamorphic conditions of 18–20 kbar and 835–935 °C, which is comparable to that determined from felsic granulite, 14–20 kbar and 900–1000 °C. Garnet in eclogite exhibits both prograde and retrograde compositional zoning, from which constraints on thermal history of the Gf?hl terrane can be derived by diffusion modelling. At 900 °C, a garnet grain of 800–1000 μm radius would homogenize in 7.5–11.7 million years, but the existence of compositional gradients on a length scale of 100–200 μm suggests that the duration of peak metamorphism may have been limited to ∼500,000 years. Diffusion modelling of retrograde zoning in garnet yields a cooling rate of 150–100 °C/m.y. for a radius of 800–1000 μm and initial temperature of 900 °C. The relatively brief duration of high-pressure/high-temperature metamorphism and rapid cooling and exhumation of the Gf?hl terrane may be a consequence of lithospheric delamination during Early Carboniferous collision of Bohemia (Teplá-Barrandia) and Moldanubia (Franke, 2000).     

Results from a Multi-disciplinary Sedimentary Pilot Study of Tectonic Lake Iznik (NW Turkey) – Geochemistry and Paleolimnology of the Recent Past

A limnogeological reconnaissance study was carried out on Lake Iznik, located in the southeast of the Marmara region of Turkey, involving a seismic survey and collection of short sediment cores. This lake is located on the middle branch of the North Anatolian Fault Zone (NAFZ), a transform plate boundary between the Eurasian and Anatolian Plates. It is, therefore, tectonically active and offers an opportunity to investigate the interplay of sedimentary and seismo-tectonic processes, as well as climate change and human impact in the region. Short cores of the three sub-basins, maximum length of 35.5 cm, recovered non-laminated, blackish clays and silts with varying amounts of biogenic and minerogenic (allochthonous, autochthonous) material, which documented almost the last 80 years of deposition and environmental history. High sedimentation rates in the deeper core sections are accompanied by changes in land use (conversion of woodland to farmland) in the northern areas of Lake Iznik, which caused the deposition of more weathered material (high K/Na ratios) and higher contents of Mn in the lake. A tendency towards eutrophic conditions within the last 20 years is indicated by high nutrient content (N, TOC, P), decreasing C/N-ratios, and characteristic diatom and cladoceran associations. Also increased pollution is revealed by higher Pb, Cu, and Zn contents and increased supply of human and animal faeces (high coprostanol content) during the last two decades. But simultaneous lower sedimentation rates towards the core tops complicate the reconstruction of recent and past eutrophication and pollution states of Lake Iznik. This requires an extension of the pilot study and deeper sediment cores, to recover non-anthropogenic influenced sediment levels.     

Avalanche Risk During Backcountry Skiing – An Analysis of Risk Factors

Skier-triggered avalanches are the main cause of avalanche accidents in backcountry skiing. The risk of accidents during backcountry skiing was analysed statistically and related to factors such as elevation level, aspect, stability rating and the time of the year. The analysis is based on a database about terrain usage and avalanche accidents from a large heli-skiing operator in Canada, which makes it possible to study the conditional probability of accidents given the recorded pattern of terrain usage. This study shows that the historical risk of accidentally triggering an avalanche greater than size 1 depends highly on the stability rating, with the highest risk occurring during “poor” stability. The risk is greater at high elevations, and it is lower during the late season than earlier on. Skier risk does not depend as much on aspect as may be indicated from avalanche data alone. However, it is relatively high in the N–NE–E sector. These factors are not independent of each other and therefore analyses of combined factors were also performed. Questionnaires and interviews were used to gain knowledge about the terrain selection of professional mountain guides. These results indicate that when selecting terrain, guides first look at the overall shape and size of the terrain, but avalanche history of terrain and inclination are also important factors. Finally, remarks in avalanche reports were analysed, and common human factors identified.     

Effect of sampling and linkage on fault length and length–displacement relationship

The power-law exponent (n) in the equation: D=cL ⁿ , with D = maximum displacement and L = fault length, would be affected by deviations of fault trace length. (1) Assuming n=1, numerical simulations on the effect of sampling and linkage on fault length and length–displacement relationship are done in this paper. The results show that: (a) uniform relative deviations, which means all faults within a dataset have the same relative deviation, do not affect the value of n; (b) deviations of the fault length due to unresolved fault tip decrease the values of n and the deviations of n increase with the increasing length deviations; (c) fault linkage and observed dimensions either increase or decrease the value of n depending on the distribution of deviations within a dataset; (d) mixed deviations of the fault lengths are either negative or positive and cause the values of n to either decrease or increase; (e) a dataset combined from two or more datasets with different values of c and orders of magnitude also cause the values of n to deviate. (2) Data including 19 datasets and spanning more than eight orders of fault length magnitudes (10⁻²–10⁵ m) collected from the published literature indicate that the values of n range from 0.55 to 1.5, the average value being 1.0813, and the peak value of n _d (double regression) is 1.0–1.1. Based on above results from the simulations and published data, we propose that the relationship between the maximum displacement and fault length in a single tectonic environment with uniform mechanical properties is linear, and the value of n deviated from 1 is mainly caused by the sampling and linkage effects.