Error bounds for perturbation methods

There are many papers dealing with the problem of error bounds for perturbation methods (development with respect to a small parameter, method of averaging, stroposcopic method etc.). The majority of these bounds, however, is very pessimistic and does not really reflect the qualities of the underlying perturbation method. In this paper a new attempt is made to overcome this problem. By using a new comparison theorem and the higher order approximations we are led not only to upper bounds, but to lower bounds as well.     

Consistent estimation of geodetic parameters from SLR satellite constellation measurements

In this paper, we consistently estimate geodetic parameters such as weekly 3-D station coordinates, Earth orientation parameters (EOP) including daily x/y-pole coordinates and the excess length of day \(\Delta \hbox {LOD}\), and selected weekly Earth’s gravitational field (Stokes) coefficients up to degree and order 6 from Satellite Laser Ranging measurements to up to 11 geodetic satellites. The SLR constellation consists of LAGEOS-1/2, Etalon-1/2, Stella, Starlette, Ajisai, Larets, LARES, BLITS and WESTPAC, and its observations cover a time span of 38 years ranging from February 16, 1979, to April 30, 2017. If multiple satellites with various altitudes and orbit inclinations are combined, correlations between estimated parameters are significantly reduced. This allows us (i) to investigate the ability of satellite constellations to reduce existing correlations and (ii) to estimate reliable parameters with higher precision compared to the standard 4-satellite constellation (LAGEOS-1/2, Etalon-1/2) which is currently used by the International Laser Ranging Service for the determination of the Terrestrial Reference Frame (TRF) and EOP products. In particular, the Stokes coefficients, EOP and TRF datum parameters (three translations, three rotations, one scale factor), which are highly correlated with satellite-specific orbit parameters, are improved. From our investigations, we found for an 11-satellite solution compared to the above-mentioned 4-satellite solution a decrease in the scatter of the TRF datum parameters of up to 37%, the transformation residuals are decreased by up to 22%, the scatter of the EOP is decreased by up to 22%, and their mean values are decreased by up to 84% w.r.t. the reference solutions. The largest improvement is obtained for the Stokes coefficients which significantly benefit from a combination of multiple satellites (inclinations and orbit altitudes). In total, single coefficients are improved by up to 93% and the overall improvement is up to 74%. Moreover, it could be clearly identified that Ajisai significantly disturbs the TRF solution due to an erroneous center-of-mass correction. We further quantify the impact of specific satellites on the determination of different geodetic parameters and finally evaluate the potential of the existing SLR-tracked spherical satellite constellation to support the goals of GGOS.     

http://www.sciencedirect.com/science/article/pii/S1674987112001569

The southeastern Anatolia comprises numbers of tectono-magmatic/stratigraphic units such as the metamorphic massifs,the ophiolites,the volcanic arc units and the granitoid rocks.All of them play important role for the late Cretaceous evolution of the southern Neotethys.The spatial and temporal relations of these units suggest the progressive development of coeval magmatism and thrusting during the late Cretaceous northward subduction/accretion.Our new U-Pb zircon data from the rhyolitic rocks of the wide-spread volcanic arc unit show ages of(83.1±2.2)-(74.6±4.4) Ma. Comparison of the ophiolites,the volcanic arc units and the granitoids suggest following late Cretaceous geological evolution.The ophiolites formed in a suprasubduction zone(SSZ) setting as a result of northward intra-oceanic subduction.A wide-spread island-arc tholeiitic volcanic unit developed on the top of the SSZ-type crust during 83-75 Ma.Related to regional plate convergence, northward under-thrusting of SSZ-type ophiolites and volcanic arc units was initiated beneath the Tauride platform(Malatya-Keban) and followed by the intrusion of l-type calc-alkaline volcanic arc granitoids during 84-82 Ma.New U-Pb ages from the arc-related volcanic-sedimentary unit and granitoids indicate that under-thrusting of ophiolites together with the arc-related units beneath the Malatya-Keban platform took place soon after the initiation of the volcanic arc on the top of the SSZtype crust.Then the arc-related volcanic-sedimentary unit continued its development and lasted at～75 Ma until the deposition of the late Campanian—Maastrichtian shallow marine limestone.The subduction trench eventually collided with the Bitlis-Ptrge massif giving rise to HP-IT metamorphism of the Bitlis massif.Although the development of the volcanic arc units and the granitoids were coeval at the initial stage of the subduction/accretion both tectono-magmatic units were genetically different from each other.     

A chromate-contaminated site in southern Switzerland – Part 2: Reactive transport modeling to optimize remediation options

A 2D horizontal reactive transport model of a chromate-contaminated site near Rivera, Switzerland, was developed using the computer code CrunchFlow to evaluate site remediation strategies. Transport processes were defined according to the results of an existing hydrological model, and the definition of geochemical (reactive) processes is based on the results of a detailed mineralogical and geochemical site characterization leading to a comprehensive conceptual site model. Kinetics of naturally occurring Cr(VI) reduction by Fe(II) and natural solid organic matter is quantified by fitting measured Cr isotope ratios to a modeled 1D section along the best constrained flow line. The simulation of Cr isotope fractionation was also incorporated into the 2D model. Simulation of the measured present day Cr(VI) plume and δ⁵³Cr value distribution was used for the 2D model calibration and corresponds to a situation where only monitored natural attenuation (MNA) is occurring. Other 2D model runs simulate alternate excavation scenarios. The simulations show that with an excavation of the top 2–4 m the groundwater Cr(VI) plume can be minimized, and that a deeper excavation depth only diminishes the plume if all the contaminants can be removed. A combination of an excavation of the top 2–4 m and monitoring of the ongoing natural Cr(VI) reduction is suggested as the most ecological and economical remediation strategy, even though a remaining time period with ongoing subsoil Cr(VI) contamination in the order of 1 ka is predicted.     

A chromate-contaminated site in southern Switzerland – Part 1: Site characterization and the use of Cr isotopes to delineate fate and transport

The risk of groundwater contamination by chromate at a former chromite ore processing industrial site in Rivera (Switzerland) was assessed by determining subsoil Cr(VI) concentrations and tracking naturally occurring Cr(VI) reduction with Cr isotopes. Using a hot alkaline extraction procedure, a total Cr(VI) contamination of several 1000 kg was estimated. Jarosite, KFe₃((SO₄)_x(CrO₄)_1−x)₂(OH)₆, and chromatite (CaCrO₄) were identified as Cr(VI) bearing mineral phases using XRD, both limiting groundwater Cr(VI) concentrations. To track assumed Cr(VI) reduction at field scale δ⁵³Cr values of contaminated subsoil samples in addition to groundwater δ⁵³Cr data are used for the first time. The measurements showed a fractionation of groundwater δ⁵³Cr values towards positive values and subsoil δ⁵³Cr towards negative values confirming reduction of soluble Cr(VI) to insoluble Cr(III). Using a Rayleigh fractionation model, a current Cr(VI) reduction efficiency of approximately 31% along a 120 m long flow path was estimated at an average linear groundwater velocity of 3.3 m/d. Groundwater and subsoil δ⁵³Cr values were compared with a site specific Rayleigh fractionation model proposing that subsoil δ⁵³Cr values can possibly be used to track previous higher Cr(VI) reduction efficiency during the period of industrial activity. The findings strongly favor monitored natural attenuation to be part of the required site remediation measures.     

Petrography,mineralogy, and geochemistry of lunar meteorite Sayh al Uhaymir 300

Abstract— We report here the petrography, mineralogy, and geochemistry of lunar meteorite Sayh al Uhaymir 300 (SaU 300). SaU 300 is dominated by a fine‐grained crystalline matrix surrounding mineral fragments (plagioclase, pyroxene, olivine, and ilmenite) and lithic clasts (mainly feldspathic to noritic). Mare basalt and KREEPy rocks are absent. Glass melt veins and impact melts are present, indicating that the rock has been subjected to a second impact event. FeNi metal and troilite grains were observed in the matrix. Major element concentrations of SaU 300 (Al₂O₃ 21.6 wt% and FeO 8.16 wt%) are very similar to those of two basalt‐bearing feldspathic regolith breccias: Calcalong Creek and Yamato (Y‐) 983885. However, the rare earth element (REE) abundances and pattern of SaU 300 resemble the patterns of feldspathic highlands meteorites (e.g., Queen Alexandra Range (QUE) 93069 and Dar al Gani (DaG) 400), and the average lunar highlands crust. It has a relatively LREE‐enriched (7 to 10 x CI) pattern with a positive Eu anomaly (?11 x CI). Values of Fe/Mn ratios of olivine, pyroxene, and the bulk sample are essentially consistent with a lunar origin. SaU 300 also contains high siderophile abundances with a chondritic Ni/Ir ratio. SaU 300 has experienced moderate terrestrial weathering as its bulk Sr concentration is elevated compared to other lunar meteorites and Apollo and Luna samples. Mineral chemistry and trace element abundances of SaU 300 fall within the ranges of lunar feldspathic meteorites and FAN rocks. SaU 300 is a feldspathic impact‐melt breccia predominantly composed of feldspathic highlands rocks with a small amount of mafic component. With a bulk Mg# of 0.67, it is the most mafic of the feldspathic meteorites and represents a lunar surface composition distinct from any other known lunar meteorites. On the basis of its low Th concentration (0.46 ppm) and its lack of KREEPy and mare basaltic components, the source region of SaU 300 could have been within a highland terrain, a great distance from the Imbrium impact basin, probably on the far side of the Moon.     

On the morphological characteristics of overdeepenings in high‐mountain glacier beds

Overdeepenings, i.e. closed topographic depressions with adverse slopes in the direction of flow, are characteristic for glacier beds and glacially sculpted landscapes. Quantitative information about their morphological characteristics, however, has so far hardly been available. The present study provides such information by combining the analysis of (a) numerous bed overdeepenings below still existing glaciers of the Swiss Alps and the Himalaya‐Karakoram region modelled with a robust shear stress approximation and (b) detailed bathymetries from recently exposed lakes in the Peruvian Andes. The investigated overdeepenings exist where glacier surface slopes are low (< 5°–10°), occur in bedrock or morainic material and are most commonly a fraction of a kilometre squared in surface area, hundreds of metres long, about half the length in width and tens of metres deep. They form under conditions of low to high basal shear stresses, at cirque, confluence, trunk valley and terminus positions. The most striking phenomenon, however, is the high variability of their geometries: Depths, surface areas, lengths and widths of the overdeepenings vary over orders of magnitude and are only weakly – if at all – interrelated. Inclinations of adverse slopes do not differ significantly from those of forward slopes and are in many cases higher than so far assumed theoretical limits for supercooling of ascending water and corresponding closure of sub‐glacial channels. Such steep adverse slopes are a robust observation and in support of recently developed new concepts concerning the question about where supercooling of sub‐glacial water and closure of ice channels can or must occur. However, the question of when and under what climatic, topographic and ice conditions the overdeepenings had formed remains unanswered. This open question constitutes a key problem concerning the interpretation of observed overdeepenings, the understanding of the involved glacio‐hydraulic processes and the possibility of realistic predictive modelling of overdeepening formation. Copyright © 2016 John Wiley & Sons, Ltd.     

First results of operating and monitoring an innovative design of a permeable reactive barrier for the remediation of chromate contaminated groundwater

An innovative setup of a permeable reactive barrier (PRB) was installed in Willisau, Switzerland to remediate chromate contaminated groundwater. Instead of a conventional continuous barrier, this PRB consists of cylinders installed in rows: a single row for lower expected Cr^VI-concentrations and an offset double row for higher expected Cr^VI-concentrations. The cylinders are filled with reactive grey cast-Fe shavings mixed with gravel to prevent extensive precipitation of secondary phases in the pore space. The treatment of the contaminants takes place both within the cylinders and in the dissolved Fe^II plume generated downstream of the barrier. Monitoring of the contamination situation over a period of 3 a provided evidence of the mobilization, transport and behavior of the contaminants in the aquifer. Groundwater and reactive material were sampled upstream, within and downstream of the barrier by a Multi-Port Sampling System (MPSS) that revealed the geochemical processes as a function of time and space. Comprehensive chemical analyses included sensitive parameters such as Cr^VI, Fe^II/Fe^III, redox potential, dissolved O₂ and pH. Several campaigns using multiple optical tracers revealed a rather complex hydrological regime at different scales, thereby complicating the barrier performance.     

Accuracy of Laser Ablation U-Pb Zircon Dating: Results from a Test Using Five Different Reference Zircons

Using a state‐of‐the‐art 193 nm‐LA‐MC‐ICP‐MS system and with careful control of analytical procedures, the long term external reproducibility and accuracy of the ages Phanerozoic zircons measured over a period of months using calibrator bracketing for the ²⁰⁶Pb/²³⁸U and ²⁰⁷Pb/²⁰⁶Pb ages were ca. 1% (2 RSD) if a single reference zircon was used for the matrix‐matched calibration. When different reference zircons were used for the calibration, suspicious systematic shifts in the obtained ages were observed and thus a reduction in the overall accuracy of the dating method became obvious. Such shifts were within a few percent range of the U‐Pb and Pb/Pb ages and seemed to vary independently of zircon age and composition. A “test of accuracy” experiment was conducted reducing instrumental effects as far as possible by analysing five different reference zircons mounted on a single mount eight times during the same session. An identical protocol was used for all analyses, with unchanged instrument parameters and with ion beam intensities kept as identical as possible. For data reduction, every zircon served consecutively as the reference zircon for calibration, with the others in the batch treated as unknowns. The known reference age and the four calculated ages obtained using the four other RMs for calibration were then compared. Even using such a strict analytical protocol, shifts in ²⁰⁶Pb/²³⁸U, ²⁰⁷Pb/²³⁵U and ²⁰⁷Pb/²⁰⁶Pb ratios were still present. They varied non‐systematically and ranged from ?4.35% to 3.08% for the investigated age range (1065 Ma to 226 Ma). Assuming the absence of instrumental effects (i.e., memory, dead‐time correction, non‐linearity of ion counters and interdetector calibration, crystallographic orientation, ablation cell geometry and setup, gas flows), the observed shifts were attributed to matrix and/or ablation related effects. It is proposed that non‐spectral matrix effects in the Ar plasma torch resulted in non‐uniform signal enhancement (or depression?) leading to shifts both in elemental and Pb isotopic ratios. Additionally, the ablated particle size distribution could be an important factor controlling plasma conditions and thus mass bias and fractionation. Until such effects are well understood and controlled, it would seem that any LA‐ICP‐MS zircon U‐Pb and ²⁰⁷Pb/²⁰⁶Pb age determination cannot be meaningfully interpreted at below a ca. 3% to 4% (2 RSD) confidence level.     

Earthquakes in Switzerland and surrounding regions during 2008

This report of the Swiss Seismological Service summarizes the seismic activity in Switzerland and surrounding regions during 2008. During this period, 451 earthquakes and 75 quarry blasts were detected and located in the region under consideration. The three strongest events occurred in the Valais, near Lac des Toules (M_L 3.6), and in Graubünden, near Ilanz (M_L 3.7) and Paspels (M_L 4.0). Although felt by the population, they were not reported to have caused any damage. However, with a total of only 15 events with M_L ≥ 2.5, the seismic activity in the year 2008 was far below the average over the previous 33 years.