1:1 Ground-track resonance in a uniformly rotating 4th degree and order gravitational field

Using a gravitational field truncated at the 4th degree and order, the 1:1 ground-track resonance is studied. To address the main properties of this resonance, a 1-degree of freedom (1-DOF) system is firstly studied. Equilibrium points (EPs), stability and resonance width are obtained. Different from previous studies, the inclusion of non-spherical terms higher than degree and order 2 introduces new phenomena. For a further study about this resonance, a 2-DOF model which includes a main resonance term (the 1-DOF system) and a perturbing resonance term is studied. With the aid of Poincaré sections, the generation of chaos in the phase space is studied in detail by addressing the overlap process of these two resonances with arbitrary combinations of eccentricity (e) and inclination (i). Retrograde orbits, near circular orbits and near polar orbits are found to have better stability against the perturbation of the second resonance. The situations of complete chaos are estimated in the \(e-i\) plane. By applying the maximum Lyapunov Characteristic Exponent (LCE), chaos is characterized quantitatively and similar conclusions can be achieved. This study is applied to three asteroids 1996 HW1, Vesta and Betulia, but the conclusions are not restricted to them.     

A test case for anomalous fading correction in IRSL dating

Infrared-stimulated luminescence (IRSL) dating of feldspars has the potential to date deposits beyond the age range of quartz optical (OSL) dating. Successful application of feldspar IRSL dating is, however, often precluded due to anomalous-fading, the tunnelling of electrons from one defect site to another. In this paper we test procedures proposed for anomalous-fading correction by comparing feldspar IRSL and quartz OSL dating results on a suite of samples from continental deposits from the southeastern Netherlands. We find that even after anomalous-fading correction IRSL ages underestimate the burial age of the deposits and argue that this may be a consequence of a dependency of anomalous fading rate on the dose rate and on the absorbed dose.     

Tectonic discrimination of basalts with classification trees

Traditionally, geochemical classification of basaltic rocks of unknown tectonic affinity has been performed by discrimination diagrams. Although easy to use, this method is fairly inaccurate because it only uses bi- or trivariate data. Furthermore, many popular discrimination diagrams are statistically not very rigorous because the decision boundaries are drawn by eye, and they ignore closure, thus violating the rules of compositional data analysis. Classification trees approximate the data space by a stepwise constant function, and are a more rigorous and potentially more effective way to determine tectonic affinity. Trees allow the simultaneous use of an unlimited number of geochemical features, while still permitting visualization by an easy-to-use, two-dimensional graph. Two classification trees are presented for the discrimination of basalts of mid-ocean ridge, ocean island, and island arc affinities. The first tree uses 51 major, minor, and trace elements and isotopic ratios and should be used for the classification of fresh basalt samples. A second tree only uses high field strength element analyses and isotopic ratios, and can also be used for basalts that have undergone alteration. The probability of successful classification is 89% for the first and 84% for the second tree, as determined by 10-fold cross-validation. Even though the trees presented in this paper use many geochemical features, it is not a problem if some of these are missing in the unknown sample. Classification trees solve this problem with surrogate variables, which give more or less the same decision as the primary variables. The advantages of the classification tree approach over discrimination diagrams are illustrated by a comparative test on a sample dataset of known tectonic affinities. Although arguably better than discrimination diagrams, classification trees are not perfect, and the limitations of the method are illustrated on a published dataset of basalts from the Pindos Basin (Greece).     

A detailed post‐IR IRSL dating study of the Niuyangzigou loess site in northeastern China

In this study, we report standard quartz SAR OSL and post‐IR infrared (IR) stimulated luminescence (post‐IR IRSL; pIRIR₂₉₀) measurements made on sand‐sized quartz and K‐feldspar extracts from the loess‐palaeosol sequence at Niuyangzigou in northeastern China. The quartz OSL characteristics are satisfactory. Extensive pIRIR_50,290 dose recovery tests were performed by adding doses on top of the natural dose. We found that dose recovery ratios improve significantly when the test dose ranges between ~15 and ~80% of the total dose, and good dose recovery (within ±5% of unity) can be obtained up to ～800 Gy. Otherwise, the dose recovery ratio deviates from unity. The D_e values also depend on the test dose size and so we conclude that the effect of test dose size should be routinely considered in pIRIR dating. First IR stimulation plateau pIRIR₂₉₀ results are compared with multiple elevated temperature ‐pIRIR (MET‐pIRIR) data. It appears that the low temperature MET‐pIRIR data are strongly affected by poor dose recovery, but this is not the case for the pIRIR₂₉₀ results. Natural signal measurements at the highest (first IR) stimulation temperature on a sample expected to be in field saturation suggest that ~10% signal loss occurs in pIRIR signals. Long‐term laboratory bleaching experiments (>80 days) show that a constant (or very difficult to bleach) residual pIRIR₂₉₀ signal is reached after ~300 h, corresponding to a dose of 6.2±0.7 Gy. Quartz OSL and feldspar pIRIR_50,290 ages are in good agreement at least back to c. 70 ka. Beyond this the quartz ages begin to underestimate but the feldspar ages are in agreement with the expected Last Interglacial age palaeosol.     

GPS-derived orbits for the GOCE satellite

The first ESA (European Space Agency) Earth explorer core mission GOCE (Gravity field and steady-state Ocean Circulation Explorer) was launched on 17 March 2009 into a sun-synchronous dusk–dawn orbit with an exceptionally low initial altitude of about 280 km. The onboard 12-channel dual-frequency GPS (Global Positioning System) receiver delivers 1 Hz data, which provides the basis for precise orbit determination (POD) for such a very low orbiting satellite. As part of the European GOCE Gravity Consortium the Astronomical Institute of the University of Bern and the Department of Earth Observation and Space Systems are responsible for the orbit determination of the GOCE satellite within the GOCE High-level Processing Facility. Both quick-look (rapid) and very precise orbit solutions are produced with typical latencies of 1 day and 2 weeks, respectively. This article summarizes the special characteristics of the GOCE GPS data, presents POD results for about 2 months of data, and shows that both latency and accuracy requirements are met. Satellite Laser Ranging validation shows that an accuracy of 4 and 7 cm is achieved for the reduced-dynamic and kinematic Rapid Science Orbit solutions, respectively. The validation of the reduced-dynamic and kinematic Precise Science Orbit solutions is at a level of about 2 cm.     

Influence of topography on tide propagation and amplification in semi-enclosed basins

An idealized model for tide propagation and amplification in semi-enclosed rectangular basins is presented, accounting for depth differences by a combination of longitudinal and lateral topographic steps. The basin geometry is formed by several adjacent compartments of identical width, each having either a uniform depth or two depths separated by a transverse topographic step. The problem is forced by an incoming Kelvin wave at the open end, while allowing waves to radiate outward. The solution in each compartment is written as the superposition of (semi)-analytical wave solutions in an infinite channel, individually satisfying the depth-averaged linear shallow water equations on the f plane, including bottom friction. A collocation technique is employed to satisfy continuity of elevation and flux across the longitudinal topographic steps between the compartments. The model results show that the tidal wave in shallow parts displays slower propagation, enhanced dissipation and amplified amplitudes. This reveals a resonance mechanism, occurring when the length of the shallow end is roughly an odd multiple of the quarter Kelvin wavelength. Alternatively, for sufficiently wide basins, also Poincaré waves may become resonant. A transverse step implies different wavelengths of the incoming and reflected Kelvin wave, leading to increased amplitudes in shallow regions and a shift of amphidromic points in the direction of the deeper part. Including the shallow parts near the basin’s closed end (thus capturing the Kelvin resonance mechanism) is essential to reproduce semi-diurnal and diurnal tide observations in the Gulf of California, the Adriatic Sea and the Persian Gulf.     

V oxidation state in Fe–Ti oxides by high-energy resolution fluorescence-detected X-ray absorption spectroscopy

The oxidation state of vanadium in natural and synthetic Fe–Ti oxides is determined using high-energy resolution fluorescence-detected X-ray absorption spectroscopy (HERFD-XAS). Eleven natural magnetite-bearing samples from a borehole of the Main Magnetite Layer of the Bushveld Complex (South Africa), five synthetic Fe oxide samples, and three natural hematite-bearing samples from Dharwar supergroup (India) are investigated. V K edge spectra were recorded on the ID26 beamline at the European Synchrotron Radiation Facility (Grenoble, France), and the pre-edge features were used to determine the local environment and oxidation state of vanadium. In the case of the magnetite samples (natural and synthetic), we show that vanadium is incorporated in the octahedral site of the spinel structure under two oxidation states: +III and +IV. The variations of the pre-edge area are interpreted as various proportions in V³⁺ and V⁴⁺ (between 9.5 and 16.3% of V⁴⁺), V³⁺ being the main oxidation state. In particular, the variations of the V⁴⁺/V³⁺ ratio along the profile of the Main Magnetite Layer seem to follow the crystallization sequence of the layer. In the case of the hematite samples from India, the pre-edge features indicate that vanadium is substituted to Fe and mainly incorporated as V⁴⁺ (between 40 and 72% of V⁴⁺). We also demonstrate the potentiality of HERFD-XAS for mineralogical studies, since it can filter out the unwanted fluorescence and give better resolved spectra than conventional XAS.