Design considerations for a dedicated gravity recovery satellite mission consisting of two pairs of satellites

Future satellite missions dedicated to measuring time-variable gravity will need to address the concern of temporal aliasing errors; i.e., errors due to high-frequency mass variations. These errors have been shown to be a limiting error source for future missions with improved sensors. One method of reducing them is to fly multiple satellite pairs, thus increasing the sampling frequency of the mission. While one could imagine a system architecture consisting of dozens of satellite pairs, this paper explores the more economically feasible option of optimizing the orbits of two pairs of satellites. While the search space for this problem is infinite by nature, steps have been made to reduce it via proper assumptions regarding some parameters and a large number of numerical simulations exploring appropriate ranges for other parameters. A search space originally consisting of 15 variables is reduced to two variables with the utmost impact on mission performance: the repeat period of both pairs of satellites (shown to be near-optimal when they are equal to each other), as well as the inclination of one of the satellite pairs (the other pair is assumed to be in a polar orbit). To arrive at this conclusion, we assume circular orbits, repeat groundtracks for both pairs of satellites, a 100-km inter-satellite separation distance, and a minimum allowable operational satellite altitude of 290 km based on a projected 10-year mission lifetime. Given the scientific objectives of determining time-variable hydrology, ice mass variations, and ocean bottom pressure signals with higher spatial resolution, we find that an optimal architecture consists of a polar pair of satellites coupled with a pair inclined at 72°, both in 13-day repeating orbits. This architecture provides a 67% reduction in error over one pair of satellites, in addition to reducing the longitudinal striping to such a level that minimal post-processing is required, permitting a substantial increase in the spatial resolution of the gravity field products. It should be emphasized that given different sets of scientific objectives for the mission, or a different minimum allowable satellite altitude, different architectures might be selected.     

Ophiolites and the oceanic crust: New evidence from the Tyrrhenian sea and the Western Alps

The succession recovered in ODP hole 107–651 in the young oceanic Vavilov basin (Tyrrhenian Sea) comprises, beneath a thick Pleistocene to Upper Pliocene sedimentary cover (chiefly volcanoclastics), four basement units: (1) MORB-type basaltic pillows and breccias; (2) a complex succession made of dolerites, albitites, basaltic breccias, metadolerite pebbles (including an intercalated sandy layer with periodotite clasts); (3) MORB-type basaltic pillows and breccias; (4) highly serpentinized peridotite. Between units 3 and 4, granitoid pebbles occur.This sequence is surprisingly similar to successions known in the Western Alps' Tethyan ophiolites. There, the sediments (Callovian-Oxfordian radiolarian cherts) lie stratigraphically upon breccias mostly derived from underlying serpentinite, and sometimes gabbroic basement. At some places, thin basaltic (tholeiitic) pillows and breccias occur between the radiolarian cherts and the breccias.From the comparison between a present day setting (the central Tyrrhenian Sea) and a formerly emplaced basement succession (the Western Alps), we stress the following (a) both the here-discussed ophiolites and oceanic basement are different from classical ophiolite sequences; (b) both occurrences imply unroofing of mantle rocks that therefore were directly outcropping on the seafloor; (c) such a comparison may indicate a very slow spreading rate for the Alpine Tethyan ocean.     

Long-wavelength global gravity field models: GRIM4-S4, GRIM4-C4

Summary.  GFZ Potsdam and GRGS Toulouse/Grasse jointly developed a new pair of global models of the Earth's gravity field to satisfy the requirements of the recent and future geodetic and altimeter satellite missions. A precise gravity model is a prerequisite for precise satellite orbit restitution, tracking station positioning and altimeter data reduction. According to different applications envisaged, the new model exists in two parallel versions: the first one being derived exclusively from satellite tracking data acquired on 34 satellites, the second one further incorporating satellite altimeter data over the oceans and terrestrial gravity data. The most recent “satellite-only” gravity model is labelled GRIM4-S4 and the “combined” gravity model GRIM4-C4. The models are solutions in spherical harmonics and have a resolution up to degree and order 60 plus a few resonance terms in the case of GRIM4-S4, and up to degree/order 72 in the case of GRIM4-C4, corresponding to a spatial resolution of 555 km at the Earth's surface. The gravitational coefficients were estimated in a rigorous least squares adjustment simultaneously with ocean tidal terms and tracking station position parameters, so that each gravity model is associated with a consistent ocean tide model and a terrestrial reference frame built up by over 300 optical, laser and Doppler tracking stations. Comprehensive quality tests with external data and models, and test arc computations over a wide range of satellites have demonstrated the state-of-the-art capabilities of both solutions in long-wavelength geoid representation and in precise orbit computation. Received 1 February 1996; Accepted 17 July 1996     

The International DORIS Service: genesis and early achievements

All space-geodetic techniques are now organized as separate services of the International Association of Geodesy (IAG), supporting the first pilot project “Global Geodetic Observing System (GGOS)”. The International DORIS (Détermination d’Orbite et Radiopositionnement Intégrés par Satellite) Service (IDS) was created in mid-2003 to organize a DORIS contribution to this project and to foster a larger international cooperation on this topic. The goal of this paper is to summarize the key steps that were taken to create this structure and to present its current organization and recent results. At present, more than 50 groups from 35 different countries participate in the IDS at various levels, including 43 groups hosting DORIS stations in 32 countries all around the globe. Four Analysis Centres (ACs) provide results, such as estimates of weekly or monthly station coordinates, geocentre variations or Earth polar motion, that will soon be used to generate IDS-combined products for geodesy and geodynamics. As a first test, a preliminary combination was performed for all the 2004 data from these four ACs. Three of them show RMS of weighted station residuals with respect to this combination solution between 1 and 2 cm. The main topic under investigation is a discrepancy in the scale factor of the terrestrial reference frame (TRF) to map the individual solutions into the combination solution, which reaches 6 cm (multiplying the unit-less scale factor by the Earth radius to get convert scale to millimetre in vertical at the Earth’s surface). Finally, foreseen improvements of the DORIS technology are discussed as well as future improvements concerning the service organization itself and the accuracy and reliability of its scientific products.     

0422−476: a shell galaxy with azimuthally distributed shells

A morphological and two-colour charge-coupled device photometry study of the shell galaxy 0422−476, one of the richest known azimuthally distributed shell galaxies, is presented. Taking this galaxy as a prototype, a general method for reducing observational data of these objects is defined and quantitative parameters for use in further theoretical studies are derived.
According to some recent models (e.g. that of Thomson and Wright in 1990), the shells in such a galaxy could be density waves induced in a thick disc population of dynamically cold stars by a weak interaction with another galaxy. In 0422−476 there is no evidence of either a conventional exponential disc or a thick disc. Although it is not possible to rule out the weak interaction model, the observations continue to favour the merger model (e.g. that of Quinn from 1984).     

Quantifying FES2004 S<Subscript>2</Subscript> tidal model from multiple space-geodesy techniques,GPS and GRACE,over North West Australia

Unmodeled sub-daily ocean S₂ tide signals that alias into lower frequencies have been detected in the analysis of gravity recovery and climate experiment (GRACE) space gravity fields of GRGS. The most significant global S₂ aliased signal occurs off the northwest coast of Australia in a shallow continental shelf zone, a region with high tidal amplitudes at a period of 161 days. The GRACE S₂ aliased equivalent water height grids are convolved with Green’s functions to produce GRACE aliased tidal loading (GATL) vertical displacements. The analysis of hourly global positioning system (GPS) vertical coordinate estimates at permanent sites in the region confirms the presence of spectral power at the S₂ frequency when the same ocean tide model (FES2004) was used. Thus, deficiencies in the FES2004 ocean tide model are detected both directly and indirectly by the two independent space geodetic techniques. Through simulation, the admittance (ratio of amplitude of spurious long-wavelength output signal in the GRACE time-series to amplitude of unmodeled periodic signals) of the GRACE unmodeled S₂ tidal signals, aliased to a 161-day period, is found to have a global average close to 100%, although with substantial spatial variation. Comparing GATL with unmodeled S₂ tidal sub-daily signals in the vertical GPS time-series in the region of Broome in NW Australia suggests an admittance of 110–130%.     

The effect of seasonal and long-period geopotential variations on the GPS orbits

We examine the impact of using seasonal and long-period time-variable gravity field (TVG) models on GPS orbit determination, through simulations from 1994 to 2012. The models of time-variable gravity that we test include the GRGS release RL02 GRACE-derived 10-day gravity field models up to degree and order 20 (grgs20x20), a 4 × 4 series of weekly coefficients using GGM03S as a base derived from SLR and DORIS tracking to 11 satellites (tvg4x4), and a harmonic fit to the above 4 × 4 SLR–DORIS time series (goco2s_fit2). These detailed models are compared to GPS orbit simulations using a reference model (stdtvg) based on the International Earth Rotation Service (IERS) and International GNSS Service (IGS) repro1 standards. We find that the new TVG modeling produces significant along, cross-track orbit differences as well as annual, semi-annual, draconitic and long-period effects in the Helmert translation parameters (Tx, Ty, Tz) of the GPS orbits with magnitudes of several mm. We show that the simplistic TVG modeling approach used by all of the IGS Analysis Centers, which is based on the models provided by the IERS standards, becomes progressively less adequate following 2006 when compared to the seasonal and long-period TVG models.     

The metamorphic history of rocks buried,accreted and exhumed in an accretionary prism: an example from the Otago Schist,New Zealand

Although subgreenschist facies metamorphic rocks are widespread in the upper crust, mineralogical processes affecting these rocks are poorly understood. Subgreenschist mineralogical transitions have been invoked as critical controls on the mechanical behaviour of rocks within the crustal seismogenic zone, calling for further study of very low‐grade metamorphic assemblages. In this study a multi‐technique thermobarometric study of the Chrystalls Beach Complex mélange, which is located within the Otago Schist accretion‐collision assemblage of the South Island of New Zealand, is presented. The Chrystalls Beach Complex comprises highly sheared trench‐fill sedimentary rocks and scattered pillow basalts, and is inferred to have formed during Jurassic subduction under the paleo‐Pacific Gondwana margin. Equilibrium mineral assemblages indicate peak P–T conditions in the range 400–550 MPa and 250–300 °C, which is supported by chlorite thermometry. Relatively high pressures of burial and accretion during foliation development are inferred from phengite content and b₀ spacing analyses of white mica. Rare lawsonite occurs in a post‐foliation vein, and illite ‘crystallinity’ measurements indicate a thermal overprint during exhumation. These P–T estimates and their relative chronology indicate that the mineral assemblages developed along a clockwise P–T path. Based on variability in P–T estimates from different techniques, mineral assemblages developed during burial are largely overprinted during exhumation at similar or higher‐T than experienced along the prograde path. Observed subduction‐related subgreenschist assemblages are therefore likely to indicate lower‐P than experienced during subduction, as higher‐P mineral compositions re‐equilibrate during exhumation. The P–T path inferred in this study is similar in shape to P–T paths for higher grade parts of the Otago Schist, and other exhumed accretionary prisms around the world, and is therefore probably common for rocks buried, accreted and exhumed in accretionary prisms.     

Thermische Klärschlammbehandlung

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