Problems in data compilation

Concepts involved in the estimation of target quantities and other adjustment parameters are critically discussd. We point out that one can find more accurate precepts for the reduction of data by utilizing all available constraints on all available data in the derivation of the reduction precepts. We introduce a measure for theefficiency of a set of adjustment parameters such that adjustments carried out using different precepts can be objectively compared. Finally, having applied our suggestions to a specific problem, we show that we have obtained estimates of a set of target quantities (in our case, star positions and proper motions) which have smaller formal errors than estimates of the same target quantities derived from the same input material but following traditional procedures.     

The GeoForschungsZentrum Potsdam/Groupe de Recherche de Gèodésie Spatiale satellite-only and combined gravity field models: EIGEN-GL04S1 and EIGEN-GL04C

The recent improvements in the Gravity Recovery And Climate Experiment (GRACE) tracking data processing at GeoForschungsZentrum Potsdam (GFZ) and Groupe de Recherche de Géodésie Spatiale (GRGS) Toulouse, the availability of newer surface gravity data sets in the Arctic, Antarctica and North-America, and the availability of a new mean sea surface height model from altimetry processing at GFZ gave rise to the generation of two new global gravity field models. The first, EIGEN-GL04S1, a satellite-only model complete to degree and order 150 in terms of spherical harmonics, was derived by combination of the latest GFZ Potsdam GRACE-only (EIGEN-GRACE04S) and GRGS Toulouse GRACE/LAGEOS (EIGEN-GL04S) mean field solutions. The second, EIGEN-GL04S1 was combined with surface gravity data from altimetry over the oceans and gravimetry over the continents to derive a new high-resolution global gravity field model called EIGEN-GL04C. This model is complete to degree and order 360 and thus resolves geoid and gravity anomalies at half- wavelengths of 55 km at the equator. A degree-dependent combination method has been applied in order to preserve the high accuracy from the GRACE satellite data in the lower frequency band of the geopotential and to form a smooth transition to the high-frequency information coming from the surface data. Compared to pre-CHAMP global high-resolution models, the accuracy was improved at a spatial resolution of 200 km (half-wavelength) by one order of magnitude to 3 cm in terms of geoid heights. The accuracy of this model (i.e. the commission error) at its full spatial resolution is estimated to be 15 cm. The model shows a reduced artificial meridional striping and an increased correlation of EIGEN-GL04C-derived geostrophic meridional currents with World Ocean Atlas 2001 (WOA01) data. These improvements have led to select EIGEN-GL04C for JASON-1 satellite altimeter data reprocessing. Electronic Supplementary Material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Numerical simulation of a stratigraphic model

A multi-lithology diffusive stratigraphic model is considered, which simulates at large scales in space and time the infill of sedimentary basins governed by the interaction between tectonics displacements, eustatic variations, sediment supply, and sediment transport laws. The model accounts for the mass conservation of each sediment lithology resulting in a mixed parabolic, hyperbolic system of partial differential equations (PDEs) for the lithology concentrations and the sediment thickness. It also takes into account a limit on the rock alteration velocity modeled as a unilaterality constraint. To obtain a robust, fast, and accurate simulation, fully and semi-implicit finite volume discre tization schemes are derived for which the existence of stable solutions is proved. Then, the set of nonlinear equations is solved using a Newton algorithm adapted to the unilaterality constraint, and preconditioning strategies are defined for the solution of the linear system at each Newton iteration. They are based on an algebraic approximate decoupling of the sediment thickness and the concentration variables as well as on a proper preconditioning of each variable. These algorithms are studied and compared in terms of robustness, scalability, and efficiency on two real basin test cases.     

Generalized ‘dependencies’ and parameter variance

The autodependence, (a special case of the — now quite obsolete — dependences, which had been introduced for very specialized astrometric purposes) is proportional to the parameter variance which is the expectation of the variance of the systematic error of a function evaluated with estimated parameters.     

Gravity field determination using boundary element methods

The Boundary Element Method (BEM), a numerical technique for solving boundary integral equations, is introduced to determine the earth's gravity field. After a short survey on its main principles, we apply this method to the fixed gravimetric boundary value problem (BVP), i.e. the determination of the earth's gravitational potential from measurements of the intensity of the gravity field in points on the earth's surface. We show how to linearize this nonlinear BVP using an implicit function theorem and how to transform the linearized BVP into a boundary integral equation using the single layer representation. A Galerkin method is used to transform the boundary integral equation using the single layer representation. A Galerkin method is used to transform the boundary integral equation into a linear system of equations. We discuss the major problems of this approach for setting up and solving the linear system. The BVP is numerically solved for a bounded part of the earth's surface using a high resolution reference gravity model, measured gravity values of high density, and a 50 50 m² digital terrain model to describe the earth's surface. We obtain a gravity field resolution of 1 1 km² with an accuracy of the order 10^–3 to 10^–4 in about 1 CPU-hour on a Siemens/Fujitsu SIMD vector pipeline machine using highly sophisticated numerical integration techniques and fast equation solvers. We conclude that BEM is a powerful numerical tool for solving boundary value problems and may be an alternative to classical geodetic techniques.     

Intercomparison of measurements of stratospheric hydrogen fluoride

Observations of the vertical profile of hydrogen fluoride (HF) vapor in the stratosphere and of the vertical column amounts of HF above certain altitudes were made using a variety of spectroscopic instruments in the 1982 and 1983 Balloon Intercomparison Campaigns. Both emission instruments working in the far infrared spectral region and absorption instruments using solar occultation in the 2.5m region were employed. No systematic differences were seen in results from the two spectral regions. A mean profile from 20–45 km is presented, with uncertainties ranging from 20% to 50%. Total columns measured from ground and from 12 km are consistent with the profile if the mixing ratio for HF is small in the tropophere and low stratosphere.     

Measurements of the light flash produced by high velocity particle impact

The impact light flash produced by electrostatically accelerated iron particles with diameters meters ranging from 5 to 0.05 μm and velocities lying between 1 km/sec and 30 km/sec has been investigated by means of photomultipliers. As target materials mainly gold and tungsten were used. The pulse of the multiplier was registered directly and after electronic integration. The pulse height of the multiplier signal, the amplitude of the integrated signal as well as its rise time were found to be unique functions of the mass and velocity of the impacting particle. For the pulse height of the differential signal the relation I = c₁ × m^1.25 × v⁵ was obtained, and for the integrated signal the relation I = c₂ × m^1.25 × v^3.8, with only c₁ and C₂ depending on the target material. The rise time of the integrated signal follows the relation T = 2.2 × 10² × v^?0.4 using gold as target, and in the case of tungsten material follows the relation T = 9.8 × 10² × v^?1.2, where v is expressed in km/sec and T in μsec. Using the spectral distribution of the light intensity, measured by means of calibrated photomultipliers, the total amount of light energy emitted in the visible range could be calculated. As a result we obtained that for v = 4 km/sec and m = 10^?11 g about 3 × 10^?4 of the kinetic energy of the particle was converted into light energy. The variation of the impact flash intensity with the target material and the measured spectral distribution allowed the temperature of the crater after the impact to be estimated as between 2000 and 3000 K.     

Late Holocene sea-level changes and isostasy in western Denmark

Cores and exposed cliff sections in salt marshes around Ho Bugt, a tidal embayment in the northernmost part of the Danish Wadden Sea, were subjected to ¹⁴C dating and litho- and biostratigraphical analyses to reconstruct paleoenvironmental changes and to establish a late Holocene relative sea-level history. Four stages in the late Holocene development of Ho Bugt can be identified: (1) groundwater-table rise and growth of basal peat (from at least 2300 BC to AD 0); (2) salt-marsh formation (0 to AD 250); (3) a freshening phase (AD 250 to AD 1600?), culminating in the drying out of the marshes and producing a distinct black horizon followed by an aeolian phase with sand deposition; and (4) renewed salt-marsh deposition (AD 1600? to present). From 16 calibrated AMS radiocarbon ages on fossil plant fragments and 4 calibrated conventional radiocarbon ages on peat, we reconstructed a local relative sea-level history that shows a steady sea-level rise of 4 m since 4000 cal yr BP. Contrary to suggestions made in the literature, the relative sea-level record of Ho Bugt does not contain a late Holocene highstand. Relative sea-level changes at Ho Bugt are controlled by glacio-isostatic subsidence and can be duplicated by a glacial isostatic adjustment model in which no water is added to the world's oceans after ca. 5000 cal yr BP.