GOCE Gravity Field Processing Strategy

A processing strategy and the corresponding software architecture for the processing of GOCE (Gravity field and steady-state Ocean Circulation Explorer) observables is presented and described, with the major objective to compute a high-accuracy, high-resolution spherical harmonic model of the Earth's gravity field. The combination of two numerical solution strategies, i.e. the rigorous solution of the corresponding large normal equation systems applying parallel processing (on a PC cluster) as the core solver, and the fast semianalytic approach as a quick-look gravity field analysis (QL-GFA) tool, is proposed. Such a method fusion benefits from the advantages of the individual components: the rigorous inversion of the system providing also the full variance-covariance information, and the quickness enabling the consecutive production of intermediate gravity field solutions, for the purpose to analyse partial and incomplete data sets and to derive a diagnosis of the performance of the GOCE measurement system. The functionality and operability of the individual components are demonstrated in the framework of a closed loop simulation, which is based on a realistic mission scenario both in terms of the orbit configuration and the coloured measuring noise. Special concern is given to the accuracy of the recovered coefficients, the numerical behaviour, the required computing time, and the particular role of the individual modules within the processing chain. In the case of the core solver, it is demonstrated that the assembling and rigorous solution of large normal equation systems can be handled by using Beowulf clusters within a reasonable computing time. The application of the quick-look tool to partial data sets with short-term data gaps is demonstrated on the basis of several case studies. Additionally, the spectral analysis of the residuals of the adjustment is presented as a valuable tool for the verification of the noise characteristics of the GOCE gradiometer.     

Volatile loss from melt inclusions in pyroclasts of differing sizes

We have investigated the loss of H₂O from olivine-hosted melt inclusions (MIs) by designing an experiment using tephra samples that cooled at different rates owing to their different sizes: ash, lapilli, and bomb samples that were deposited on the same day (10/17/74) of the sub-Plinian eruption of Volcán de Fuego in Guatemala. Ion microprobe, laser ablation-ICPMS, and electron probe analyses show that MIs from ash and lapilli record the highest H₂O contents, up to 4.4 wt%. On the other hand, MIs from bombs indicate up to 30 % lower H₂O contents (loss of ~1 wt% H₂O) and 10 % post-entrapment crystallization of olivine. This evidence is consistent with the longer cooling time available for a bomb-sized clast, up to 10 min for a 3–4-cm radius bomb, assuming conductive cooling and the fastest H diffusivities measured in olivine (D~10^?9 to 10^?10 m²/s). On the other hand, several lines of evidence point to some water loss prior to eruption, during magma ascent and degassing in the conduit. Thus, results point to both slower post-eruptive cooling and slower magma ascent affecting MIs from bombs, leading to H₂O loss over the timescale of minutes to hours. The important implication of this study is that a significant portion of the published data on H₂O concentrations in olivine-hosted MIs may reflect unrecognized H₂O loss via diffusion. This work highlights the importance of reporting clast and MI sizes in order to assess diffusive effects and the potential benefit of using water loss as a chronometer of magma ascent.     

Spatially restricted data distributions on the sphere: the method of orthonormalized functions and applications

 In many geoscientific applications data are irregularly distributed and not globally available, e.g. caps around the poles which are uncovered due to non-polar satellite orbits, or signals being defined solely on bounded regions on the globe. Starting from a sequence of base functions with global support, which in the present case is composed of spherical harmonics being initially non-orthogonal on a bounded subdomain, a set of functions is generated that constitutes an orthonormal basis. Different approaches to realize this transformation are studied and compared with respect to numerical stability and computational effort, and the corresponding effects on the coefficient recovery are investigated. A number of synthetic tests demonstrate the applicability, the benefit, but also the limitations, of this method. Received: 24 March 2000 / Accepted: 9 October 2000     

PEPSI: The high‐resolution échelle spectrograph and polarimeter for the Large Binocular Telescope

PEPSI is the bench‐mounted, two‐arm, fibre‐fed and stabilized Potsdam Echelle Polarimetric and Spectroscopic Instrument for the 2×8.4 m Large Binocular Telescope (LBT). Three spectral resolutions of either 43 000, 120 000 or 270 000 can cover the entire optical/red wavelength range from 383 to 907 nm in three exposures. Two 10.3k×10.3k CCDs with 9‐µm pixels and peak quantum efficiencies of 94–96 % record a total of 92 échelle orders. We introduce a new variant of a wave‐guide image slicer with 3, 5, and 7 slices and peak efficiencies between 92–96 %. A total of six cross dispersers cover the six wavelength settings of the spectrograph, two of them always simultaneously. These are made of a VPH‐grating sandwiched by two prisms. The peak efficiency of the system, including the telescope, is 15 % at 650 nm, and still 11 % and 10 % at 390 nm and 900 nm, respectively. In combination with the 110 m² light‐collecting capability of the LBT, we expect a limiting magnitude of ≈20th mag in V in the low‐resolution mode. The R = 120 000 mode can also be used with two, dual‐beam Stokes IQUV polarimeters. The 270 000‐mode is made possible with the 7‐slice image slicer and a 100‐µm fibre through a projected sky aperture of 0.74″, comparable to the median seeing of the LBT site. The 43 000‐mode with 12‐pixel sampling per resolution element is our bad seeing or faint‐object mode. Any of the three resolution modes can either be used with sky fibers for simultaneous sky exposures or with light from a stabilized Fabry‐Pérot étalon for ultra‐precise radial velocities. CCD‐image processing is performed with the dedicated data‐reduction and analysis package PEPSI‐S4S. Its full error propagation through all image‐processing steps allows an adaptive selection of parameters by using statistical inferences and robust estimators. A solar feed makes use of PEPSI during day time and a 500‐m feed from the 1.8 m VATT can be used when the LBT is busy otherwise. In this paper, we present the basic instrument design, its realization, and its characteristics. Some pre‐commissioning first‐light spectra shall demonstrate the basic functionality. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Monitoring GOCE gradiometer calibration parameters using accelerometer and star sensor data: methodology and first results

The Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite, launched on 17 March 2009, is designed to measure the Earth’s mean gravity field with unprecedented accuracy at spatial resolutions down to 100?km. The accurate calibration of the gravity gradiometer on-board GOCE is of utmost importance for achieving the mission goals. ESA’s baseline method for the calibration uses star sensor and accelerometer data of a dedicated calibration procedure, which is executed every 2?months. In this paper, we describe a method for monitoring the evolution of calibration parameter during that time. The method works with star sensor and accelerometer data and does not require gravity field models, which distinguishes it from other existing methods. We present time series of calibration parameters estimated from GOCE data from 1 November 2009 to 17 May 2010. The time series confirm drifts in the calibration parameters that are present in the results of other methods, including ESA’s baseline method. Although these drifts are very small, they degrade the gravity gradients, leading to the conclusion that the calibration parameters of the ESA’s baseline method need to be linearly interpolated. Further, we find a correction of ?36 × 10^?6 for one calibration parameter (in-line differential scale factor of the cross-track gradiometer arm), which improves the gravity gradient performance. The results are validated by investigating the trace of the calibrated gravity gradients and comparing calibrated gravity gradients with reference gradients computed along the GOCE orbit using the ITG-Grace-2010s gravity field model.     

Assessment of three numerical solution strategies for gravity field recovery from GOCE satellite gravity gradiometry implemented on a parallel platform

 The recovery of a full set of gravity field parameters from satellite gravity gradiometry (SGG) is a huge numerical and computational task. In practice, parallel computing has to be applied to estimate the more than 90 000 harmonic coefficients parameterizing the Earth's gravity field up to a maximum spherical harmonic degree of 300. Three independent solution strategies (preconditioned conjugate gradient method, semi-analytic approach, and distributed non-approximative adjustment), which are based on different concepts, are assessed and compared both theoretically and on the basis of a realistic-as-possible numerical simulation regarding the accuracy of the results, as well as the computational effort. Special concern is given to the correct treatment of the coloured noise characteristics of the gradiometer. The numerical simulations show that the three methods deliver nearly identical results—even in the case of large data gaps in the observation time series. The newly proposed distributed non-approximative adjustment approach, which is the only one of the three methods that solves the inverse problem in a strict sense, also turns out to be a feasible method for practical applications. Received: 17 December 2001 / Accepted: 17 July 2002 Acknowledgments. We would like to thank Prof. W.-D. Schuh, Institute of Theoretical Geodesy, University of Bonn, for providing us with the serial version of the PCGMA algorithm, which forms the basis for the parallel PCGMA package developed at our institute. This study was partially performed in the course of the GOCE project `From E?tv?s to mGal+', funded by the European Space Agency (ESA) under contract No. 14287/00/NL/DC. Correspondence to: R. Pail     

Radar Campaign to Determine the Dependence of Initial Radii of Meteor Plasma Trains on Trajectory and Orbit

Experimental and theoretical work on the transverse dimensions of meteoric plasma trains have not converged to provide generally accepted values especially uncertain is the dependence of the train radii on meteor speeds. The roles of the meteoroid structure, fragmentation and plasma processes such as ion–electron instabilities need establishing. Knowledge of the quantitative spatial distribution of plasma in meteor trains is essential for a correct interpretation of fluxes and orbital characteristics. A current project is described which employs the AMOR 26 MHz radar facility in conjunction with a frequency managed radar operating at longer wavelengths designed to measure the ionization train radii, heights, atmospheric speeds and orbits of individual meteors.     

An evaluation of the global variations in the major element chemistry of arc basalts

Arc volcanoes occur at convergent margins with a wide range in subduction parameters, and variations in these parameters might be expected to lead to variations in the chemistry of magmas parental to arcs. Major element analyses from approximately 100 volcanic centers within 30 arcs, normalized to 6% MgO to minimize the effects of crystal fractionation, display wide variations. Na₂O and CaO at 6% MgO (Na_6.0 and Ca_6.0) correlate remarkably well with the thickness of the overlying crust. These systematics are consistent with two possible models. In the first model, the crust behaves as a chemical filter; where the crust is thick, magmas crystallize at higher pressure and interact more extensively with the arc crust. Modeling of high-pressure crystallization and assimilation, however, does not reproduce the associated variations in Na_6.0 and Ca_6.0 without calling upon complicated combinations of fractionating phases and assimilants. In the second model, crustal thickness determines the height of the mantle column available for melting beneath arc volcanoes. If melting begins beneath arcs at similar depths, then the column of mantle that undergoes decompression melting is much shorter beneath the thickest arc crust. The shorter mantle column for arcs built on thick crust will lead to smaller extents of melting in the mantle, and hence higher Na_6.0 and lower Ca_6.0 in the parental magmas. Modeling shows that variations in the extent of melting in the mantle can easily account for the associated variations in Ca_6.0 and Na_6.0. The abundances of the other major elements at 6% MgO do not correlate well with crustal thickness, or any other subduction parameter. Co-variation of some of these other major elements (e.g., Si_6.0 and Fe_6.0) within individual arcs suggests that they are strongly influenced by local crustal level processes that obscure partial melting systematics. Correction for the crustal processes improves the relationship between Na_6.0 and Ca_6.0 that is so readily explained by partial melting. The extents of melting in the mantle beneath arc volcanoes estimated from the ranges in Na_6.0 and Ca_6.0 are remarkably similar to those estimated beneath mid-ocean ridges. This observation provides further evidence that the mantle wedge, and not the slab, melts beneath arc volcanic fronts.     

The AUSTRAL VLBI observing program

The AUSTRAL observing program was started in 2011, performing geodetic and astrometric very long baseline interferometry (VLBI) sessions using the new Australian AuScope VLBI antennas at Hobart, Katherine, and Yarragadee, with contribution from the Warkworth (New Zealand) 12 m and Hartebeesthoek (South Africa) 15 m antennas to make a southern hemisphere array of telescopes with similar design and capability. Designed in the style of the next-generation VLBI system, these small and fast antennas allow for a new way of observing, comprising higher data rates and more observations than the standard observing sessions coordinated by the International VLBI Service for Geodesy and Astrometry (IVS). In this contribution, the continuous development of the AUSTRAL sessions is described, leading to an improvement of the results in terms of baseline length repeatabilities by a factor of two since the start of this program. The focus is on the scheduling strategy and increased number of observations, aspects of automated operation, and data logistics, as well as results of the 151 AUSTRAL sessions performed so far. The high number of the AUSTRAL sessions makes them an important contributor to VLBI end-products, such as the terrestrial and celestial reference frames and Earth orientation parameters. We compare AUSTRAL results with other IVS sessions and discuss their suitability for the determination of baselines, station coordinates, source coordinates, and Earth orientation parameters.