The effect of topography on the determination of the geoid using analytical downward continuation

The method of analytical downward continuation has been used for solving Molodensky’s problem. This method can also be used to reduce the surface free air anomaly to the ellipsoid for the determination of the coefficients of the spherical harmonic expansion of the geopotential. In the reduction of airborne or satellite gradiometry data, if the sea level is chosen as reference surface, we will encounter the problem of the analytical downward continuation of the disturbing potential into the earth, too. The goal of this paper is to find out the topographic effect of solving Stoke’sboundary value problem (determination of the geoid) by using the method of analytical downward continuation. It is shown that the disturbing potential obtained by using the analytical downward continuation is different from the true disturbing potential on the sea level mostly by a −2πGρh 2/p. This correction is important and it is very easy to compute and add to the final results. A terrain effect (effect of the topography from the Bouguer plate) is found to be much smaller than the correction of the Bouguer plate and can be neglected in most cases. It is also shown that the geoid determined by using the Helmert’s second condensation (including the indirect effect) and using the analytical downward continuation procedure (including the topographic effect) are identical. They are different procedures and may be used in different environments, e.g., the analytical downward continuation procedure is also more convenient for processing the aerial gravity gradient data. A numerical test was completed in a rough mountain area, 35°<ϕ<38°, 240°<λ<243°. A digital height model in 30″×30″ point value was used. The test indicated that the terrain effect in the test area has theRMS value ±0.2−0.3 cm for geoid. The topographic effect on the deflections of the vertical is around1 arc second.     

Relationship among titanium,rare earth elements,U–Pb ages and deformation microstructures in zircon: Implications for Ti-in-zircon thermometry

A zircon grain in an orthopyroxene–garnet–phlogopite–zircon–rutile-bearing xenolith from Udachnaya, Siberia, preserves a pattern of crystallographic misorientation and subgrain microstructure associated with crystal–plastic deformation. The zircon grain records significant variations in titanium (Ti) from 2.6 to 30 ppm that corresponds to a difference in calculated Ti-in-zircon temperatures of over several hundred degrees Celsius. The highest Ti concentration is measured at subgrain centres (30 ppm), and Ti is variably depleted at low-angle boundaries (down to 2.6 ppm). Variations in cathodoluminescence coincide with the deformation microstructure and indicate localised, differential enrichment of rare earth elements (REE) at low-angle boundaries. Variable enrichment of U and Th and systematic increase of Th/U from 1.61 to 3.52 occurs at low-angle boundaries. Individual SHRIMP-derived U–Pb ages from more deformed zones (mean age of 1799 ± 40, n = 22) are systematically younger than subgrain cores (mean age of 1851 ± 65 Ma, n = 7), and indicate that open system behaviour of Ti–Th–U occurred shortly after zircon growth, prior to the accumulation of significant radiogenic Pb. Modelling of trace-element diffusion distances for geologically reasonable thermal histories indicates that the observed variations are ~ 5 orders of magnitude greater than can be accounted for by volume diffusion. The data are best explained by enhanced diffusion of U, Th and Ti along deformation-related fast-diffusion pathways, such as dislocations and low-angle (< 5°) boundaries. These results indicate chemical exchange between zircon and the surrounding matrix and show that Ti-in-zircon thermometry and U–Pb geochronology from deformed zircon may not yield information relating to the conditions and timing of primary crystallisation.     

Post-peak,fluid-mediated modification of granulite facies zircon and monazite in the Trivandrum Block,southern India

The quarry at Kottavattom in the Trivandrum Block of southern India contains spectacular examples of fluid-assisted alteration of high-grade metamorphic rocks. Garnet-biotite gneiss has undergone a change in mineral assemblage to form submetre scale orthopyroxene-bearing patches, later retrogressed to form an amphibole-bearing lithology. These patches, often referred to as arrested or incipient charnockite, crosscut the original metamorphic foliation and are typically attributed to passage of a low aH₂O fluid through the rock. Whilst this conversion is recognised as a late stage process, little detailed chronological work exists to link it temporally to metamorphism in the region. Zircon and monazite analysed from Kottavattom not only record metamorphism in the Trivandrum Block but also show internal, lobate textures crosscutting the original zoning, consistent with fluid-aided coupled dissolution-reprecipitation during formation of the orthopyroxene-bearing patches. High-grade metamorphism at the quarry occurred between the formation of metamorphic monazite at ~585 Ma and the growth of metamorphic zircon at ~523 Ma. The fluid-assisted alteration of the garnet-biotite gneiss is poorly recorded by altered zircon with only minimal resetting of the U–Pb system, whereas monazite has in some cases undergone complete U–Pb resetting and records an age for fluid infiltration at ~495 Ma. The fluid event therefore places the formation of the altered patches at least 25 Myr after the zircon crystallisation in the garnet-biotite gneiss. The most likely fluid composition causing the modification and U–Pb resetting of zircon and monazite is locally derived hypersaline brine.     

Petrogenesis of contrasting granitoid plutons in western Bohemia (Czech Republic)

Summary Late-Variscan granitoid plutons in western Bohemia (Bor, Waidhaus-Rozvadov) have distinct petrographic, geochemical and isotopic features that suggest different magmatic evolutions. The Bor pluton comprises a suite of metaluminous tonalites and quartz diorites (Bor I), weakly peraluminous (monzo-)granites and granodiorites (Bor II) and medium-aluminous, late vein-forming leucomonzogranites (Bor III). The Waidhaus-Rozvadov pluton is strongly peraluminous, comprising a cordierite-biotite granitoid (CBG), the Rozvadov granite (ROG), the Bärnau granite (BÄG) and the subordinate, highly evolved Kreuzstein (Kíový kámen) granite (KG). Geochemical parameters and initial⁸⁷Sr/⁸⁶Sr ratios straddle the boundary between I- and S-type granites in the Bor pluton and are characteristic of purely S-type granites in the Waidhaus-Rozvadov pluton.The Bor II granitoids have been dated by the Rb-Sr whole-rock method at 341±17 Ma (I_Sr = 0.70724±0.00060). K-Ar biotite and muscovite ages of all units of the Bor pluton are mainly in the range 321-315 Ma. The K-Ar mineral ages are in good agreement with recently published U-Pb zircon data of these rocks. The different units of the Waidhaus-Rozvadov pluton have yielded less well-constrained Rb-Sr whole-rock ages, ranging from 313 to 300 Ma. However, the intrusion sequence is constrained by K-Ar muscovite ages (312-302 Ma), which define a systematic decrease towards the chemically more evolved granite types. Taken as a whole, it seems likely that the new radiometric ages characterize two temporally distinct periods of late-Variscan granitoid intrusion. The regional significance of these periods is emphasized by contemporaneous ages previously found in the adjacent northeastern Bavarian granitoids.The initial Sr and Nd isotope systematics indicate that the Bor and the WaidhausRozvadov plutons were derived from different source rocks. The Bor granitoids reflect the influence of less evolved crustal material which may have been similar to paragneisses of the Teplá-Barrandian region, including the Zone of ErbendorfVohenstrauß (ZEV). The Waidhaus-Rozvadov granitoids probably resulted from anatexis of rocks resembling surrounding Moldanubian paragneisses or metapelites. In addition, the two plutons exhibit poorly defined, opposite trends of Nd_(T) variation which are ascribed to assimilation processes.

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Petrogenese kontrastierender Granitplutone in Westböhmen (Tschechien)

Zusammenfassung Spätvariscische Granitplutone in Westböhmen (Bor, Waidhaus-Rozvadov) weisen petrographische, geochemische und isotopische Kontraste auf, die unterschiedliche magmatische Entwicklungen nahelegen. Der Bor Pluton umfaßt metalumine Tonalite und Quarzdiorite (Bor I), schwach peralumine (Monzo-)granite und Granodiorite (Bor II) und mäßig alumine, gangbildende Leukomonzogranite (Bor III). Der WaidhausRozvadov Pluton besitzt stark peralumine Zusammensetzung und läßt sich in einen Cordierit-Biotit Granitoid (CBG), den Rozvadov Granit (ROG), den Bärnau Granit (BÄG) und den stofflich hochentwickelten Kreuzstein (Kíový kámen) Granit (KG) untergliedern. Geochemische Parameter und initiale⁸⁷Sr/⁸⁶Sr-Verhältnisse liegen im Falle des Bor Plutons im Übergangsbereich zwischen I- und S-Typ Graniten und im Falle des Waidhaus-Rozvadov Plutons im Bereich reiner S-Typ Granite.Die Bor II Granitoide wurden nach der Rb-Sr Gesamtgesteinsmethode auf 341±17 Ma (I_Sr = 0.70724±0.00060) datiert. K-Ar Biotit- und Muskovitalter der Bor Granitoide liegen zwischen 321 and 315 Ma. Die K-Ar Mineralalter stehen im Einklang mit den kürzlich publizierten U-Pb Zirkondaten dieser Gesteine. Die verschiedenen Teilintrusionen des Waidhaus-Rozvadov Plutons liefern weniger gut definierte Rb-Sr Gesamtgesteinsalter zwischen 313 and 300 Ma. Die Intrusionsabfolge läßt sich dennoch durch K-Ar Muskovitalter festlegen (312-302 Ma), die eine systematische Abnahme von den weniger zu den starker entwickelten Granittypen aufweisen. Als Ganzes betrachtet dokumentieren die neuen radiometrischen Daten zwei zeitlich voneinander getrennte spdtvariscische Intrusionsereignisse. Die regionale Signifikanz dieser Ereignisse wird durch eine analoge Altersverteilung in den benachbarten nordostbayerischen Granitoiden untermauert.Anhand der initialen Sr und Nd Isotopensystematik können für die Bor und Waidhaus-Rozvadov Plutone unterschiedliche Quellen abgeleitet werden. Die Bor Granitoide spiegeln den Einfluß von gering entwickelten krustalen Material wider, das ähnliche stoffliche Eigenschaften besaß, wie Paragneise des Teplá-Barrandiums und der Zone von Erbendorf-Vohenstrauss (ZEV). Die Waidhaus-Rozvadov Granitoide lassen sich als Derivate moldanubischer Paragneise and Metapelite oder vergleichbarer Gesteine auffassen. Die zwei Plutone weisen schwach ausgeprägte gegensätzliche Nd_(T)-Variationen auf, was auf unterschiedliche Assimilationsprozesse zurückgeführt wird.

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With 10 Figures     

Fossil midge associations and the historical status of fish in acidified lakes

Chaoborid and chironomid (Diptera) fossils were examined in sediment cores form nine Ontario Precambrian Shield lakes that were fishless in 1979. An abundance of Chaoborus americamus (intolerant of predation by fish) throughout cores from four lakes indicated that they were fishless historically. Occurrence of Chaoborus punctipennis and C. flavicans and absence of C. americanus in cores, except near the surface in two cases, indicated that four other lakes were inhabited by fish historically. One of these was probably periodically fishless as suggested by fluctuations among these Chaoborus species. The ninth lake was not suitable for Chaoborus; only one specimen of C. trivittatus was found in this core. Chironomid fossil associations were substantially different in historically fishless and inhabited lakes. Fishless lakes had chironomids typical of eutrophic conditions indicating that seasonal oxygen depletion likely was inimical to fish. Chironomid associations of oligotrophic waters occurred in lakes historically inhabited by fish. Both good water quality and accessibility were required for long-term habitation by fish. Partial recovery of alkalinity and rise in pH were accompanied by substantial re-invasion by fish in two lakes which had been inhabited historically by fish. Diptera associations provide valuable information on the historical suitability of lakes for fish and the presence/absence of fish in regions where acidification of surface waters has occurred.     

Effects of convective available potential energy,temperature and humidity on the variability of thunderstorm frequency over Bangladesh

Theoretical and Applied Climatology - The present study examines the effects of convective available potential energy (CAPE), temperature and humidity on the spatiotemporal variation of...     

The wavelet method as an alternative for reducing ionospheric effects from single-frequency GPS receivers

The ionospheric effect is one of the major errors in GPS data processing over long baselines. As a dispersive medium, it is possible to compute its influence on the GPS signal with the ionosphere-free linear combination of L1 and L2 observables, requiring dual-frequency receivers. In the case of single-frequency receivers, ionospheric effects are either neglected or reduced by using a model. In this paper, an alternative for single-frequency users is proposed. It involves multiresolution analysis (MRA) using a wavelet analysis of the double-difference observations to remove the short- and medium-scale ionosphere variations and disturbances, as well as some minor tropospheric effects. Experiments were carried out over three baseline lengths from 50 to 450 km, and the results provided by the proposed method were better than those from dual-frequency receivers. The horizontal root mean square was of about 0.28 m (1σ).     

Comparison of atmospheric aerosol backscattering and air mass back trajectories

Summary Atmospheric backscattering from aerosol particulates has been measured over the Atlantic at 10.6 μm wavelength with an airborne, coherent heterodyne, lidar, and corresponding air mass back trajectories have been calculated. These back trajectories (usually extended up to 10 days prior to the backscatter measurement) have shown very diverse origins for the air parcels at different altitudes. In many cases it has been possible to attribute the observed levels of scattering to these origins over oceanic, arctic, continental, industrial etc. regions. This is illustrated by 6 flight records: out of Ascension Island in the South Atlantic; over the Azores in the mid North Atlantic; over the UK and the North Sea; and in the Arctic along 71° North. In each of these regions the profiles of backscatter versus altitude show highly variable features; remarkably different origins for air masses at different altitudes are evident from the corresponding back trajectory analyses. It is thus possible for the first time to present probable explanations for the different levels of scattering observed at different altitudes. Received July 14, 2000 Revised May 14, 2001     

Grain size and mineralogy of Al Batinah beach sediments,Sultanate of Oman

The nature of Al Batinah coast beach sediments in the Sultanate of Oman was investigated by the analysis of grain size and mineralogy. The beach sediments, mostly light-medium gray green, were predominantly fine sands, with the average grain size of all samples about 200 μm. Some of the particles were gravel (2–16 mm), and some were even larger pebble-size particles (16–256 mm). Some mud (sediment <63 μm) was present, mostly in the sub-tidal sediments. The majority of the samples were skewed to the coarse size with coarse tail partly due to the presence of shell fragments. Approximately 50 % of the beach sediments were quartz with different varieties based on shape and size. The second major component of beach sediment was calcium carbonate which varied from 10 to 65 %. The other components in decreasing order consisted of microbreccia, feldspar, pyroxene, igneous rock fragments, biotite flakes, and heavy minerals. The levels of carbonate were lower in NW Al Batinah coast from Harmul to Al Khaburah but were higher in the SE from Al Khaburah to Al Ghubrah. This could be attributed to either lower carbonate production or more sediment input by wadis along the north-western part of Al Batinah coast. The unique and complex nature of these sediments is largely due to the geology of the terrestrial source area in the Hajar Mountains which contains the famous Samail ophiolite complex and the weak sorting along the shoreline in these tide-modified beaches.     

Cr-spinel/olivine and Cr-spinel/liquid nickel partition coefficients from natural samples

The Nernst partition coefficient of nickel (D^Ni) between Cr-spinel and silicate melt in natural systems has been investigated using mid-ocean ridge basalts (MORB) and other volcanic rocks. The Cr-spinel/olivine D^Ni values in volcanic rocks are between 1.2 and 0.3, indicating that the Cr-spinel/liquid D^Ni values vary from slightly higher to significantly lower than the olivine/liquid D^Ni values in natural systems. The Cr-spinel/liquid D^Ni values from the MORB samples vary between 6 and 11, slightly higher than those from the S-bearing experiments of Satari et al. [Satari P., Brenan J. M., Horn I. and McDonough W. F. (2002) Experimental constraints on the sulfide- and chromite-silicate melt partitioning behavior of rhenium and platinum-group elements. Economic Geology97, 385-398]. The results of the MORB samples and the experiments of Satari et al. (2002) indicate a negative correlation between the Cr-spinel/liquid D^Ni and the X_Cr values in Cr-spinels (Cr cation number on the basis of 3 total cations in the spinel structure). Variations of Cr-spinel/liquid D^Ni values with Cr-spinel compositions can be estimated from an empirical equation based on the results of the MORB samples and the experiments by Satari et al. (2002). The choice of Cr-spinel/liquid D^Ni = 10 for numerical modeling by Righter et al. [Righter K., Leeman W. P. and Hervig R. L. (2006) Partitioning of Ni, Co, and V between spinel-structured oxides and silicate melts: importance of spinel composition. Chemical Geology227, 1-25] is reasonable for basaltic systems. For picritic and komatiitic systems a lower value of ∼5 is more appropriate.