A crustal suture and lineament in North Africa

A possible suture between an old craton in West Africa and the Arabian—Nubian shield is marked by a persistent zone of Phanerozoic weakness. This zone extends between the Nile and Niger deltas and passes through the Qattara embayment, along the Bahariya fault, through the Kufra basin, between the Tibesti and Jabal al Uwaynat massifs, through the Bahr el Ghazal and Lake Chad areas, and along the Benoue trough.     

Automated mapping of rock slope geometry,kinematics and stability with RSS-GIS

A GIS-implemented, deterministic approach for the automated spatial evaluation of geometrical and kinematical properties of rock slope terrains is presented. Based on spatially distributed directional information on planar geological fabrics and DEM-derived topographic attribute data, the internal geometry of rock slopes can be characterized on a grid cell basis. For such computations, different approaches for the analysis and regionalization of available structural directional information applicable in specific tectonic settings are demonstrated and implemented in a GIS environment. Simple kinematical testing procedures based on feasibility criteria can be conducted on a pixel basis to determine which failure mechanisms are likely to occur at particular terrain locations. In combination with hydraulic and strength data on geological discontinuities, scenario-based rock slope stability evaluations can be performed. For conceptual investigations on rock slope failure processes, a GIS-based specification tool for a 2-D distinct element code (UDEC) was designed to operate with the GIS-encoded spatially distributed rock slope data. The concepts of the proposed methodology for rock slope hazard assessments are demonstrated at three different test sites in Germany.     

An integrated wavelet concept of physical geodesy

For the determination of the earth's gravity field many types of observations are nowadays available, including terrestrial gravimetry, airborne gravimetry, satellite-to-satellite tracking, satellite gradio-metry, etc. The mathematical connection between these observables on the one hand and gravity field and shape of the earth on the other is called the integrated concept of physical geodesy. In this paper harmonic wavelets are introduced by which the gravitational part of the gravity field can be approximated progressively better and better, reflecting an increasing flow of observations. An integrated concept of physical geodesy in terms of harmonic wavelets is presented. Essential tools for approximation are integration formulas relating an integral over an internal sphere to suitable linear combinations of observation functionals, i.e. linear functionals representing the geodetic observables. A scale discrete version of multiresolution is described for approximating the gravitational potential outside and on the earth's surface. Furthermore, an exact fully discrete wavelet approximation is developed for the case of band-limited wavelets. A method for combined global outer harmonic and local harmonic wavelet modelling is proposed corresponding to realistic earth's models. As examples, the role of wavelets is discussed for the classical Stokes problem, the oblique derivative problem, satellite-to-satellite tracking, satellite gravity gradiometry and combined satellite-to-satellite tracking and gradiometry. Received: 28 February 1997 / Accepted: 17 November 1997     

Airborne gravimetry used in precise geoid computations by ring integration

Two detailed geoids have been computed in the region of North Jutland. The first computation used marine data in the offshore areas. For the second computation the marine data set was replaced by the sparser airborne gravity data resulting from the AGMASCO campaign of September 1996. The results of comparisons of the geoid heights at on-shore geometric control showed that the geoid heights computed from the airborne gravity data matched in precision those computed using the marine data, supporting the view that airborne techniques have enormous potential for mapping those unsurveyed areas between the land-based data and the off-shore marine or altimetrically derived data. Received: 7 July 1997 / Accepted: 22 April 1998     

The determination of potential difference by the joint application of measured and synthetical gravity data: a case study in Hungary

In an elementary approach every geometrical height difference between the staff points of a levelling line should have a corresponding average g value for the determination of potential difference in the Earth’s gravity field. In practice this condition requires as many gravity data as the number of staff points if linear variation of g is assumed between them. Because of the expensive fieldwork, the necessary data should be supplied from different sources. This study proposes an alternative solution, which is proved at a test bed located in the Mecsek Mountains, Southwest Hungary, where a detailed gravity survey, as dense as the staff point density (~1 point/34 m), is available along a 4.3-km-long levelling line. In the first part of the paper the effect of point density of gravity data on the accuracy of potential difference is investigated. The average g value is simply derived from two neighbouring g measurements along the levelling line, which are incrementally decimated in the consecutive turns of processing. The results show that the error of the potential difference between the endpoints of the line exceeds 0.1 mm in terms of length unit if the sampling distance is greater than 2 km. Thereafter, a suitable method for the densification of the decimated g measurements is provided. It is based on forward gravity modelling utilising a high-resolution digital terrain model, the normal gravity and the complete Bouguer anomalies. The test shows that the error is only in the order of 10⁻³mm even if the sampling distance of g measurements is 4 km. As a component of the error sources of levelling, the ambiguity of the levelled height difference which is the Euclidean distance between the inclined equipotential surfaces is also investigated. Although its effect accumulated along the test line is almost zero, it reaches 0.15 mm in a 1-km-long intermediate section of the line.     

Phase center modeling for LEO GPS receiver antennas and its impact on precise orbit determination

Most satellites in a low-Earth orbit (LEO) with demanding requirements on precise orbit determination (POD) are equipped with on-board receivers to collect the observations from Global Navigation Satellite systems (GNSS), such as the Global Positioning System (GPS). Limiting factors for LEO POD are nowadays mainly encountered with the modeling of the carrier phase observations, where a precise knowledge of the phase center location of the GNSS antennas is a prerequisite for high-precision orbit analyses. Since 5 November 2006 (GPS week 1400), absolute instead of relative values for the phase center location of GNSS receiver and transmitter antennas are adopted in the processing standards of the International GNSS Service (IGS). The absolute phase center modeling is based on robot calibrations for a number of terrestrial receiver antennas, whereas compatible antenna models were subsequently derived for the remaining terrestrial receiver antennas by conversion (from relative corrections), and for the GNSS transmitter antennas by estimation. However, consistent receiver antenna models for space missions such as GRACE and TerraSAR-X, which are equipped with non-geodetic receiver antennas, are only available since a short time from robot calibrations. We use GPS data of the aforementioned LEOs of the year 2007 together with the absolute antenna modeling to assess the presently achieved accuracy from state-of-the-art reduced-dynamic LEO POD strategies for absolute and relative navigation. Near-field multipath and cross-talk with active GPS occultation antennas turn out to be important and significant sources for systematic carrier phase measurement errors that are encountered in the actual spacecraft environments. We assess different methodologies for the in-flight determination of empirical phase pattern corrections for LEO receiver antennas and discuss their impact on POD. By means of independent K-band measurements, we show that zero-difference GRACE orbits can be significantly improved from about 10 to 6 mm K-band standard deviation when taking empirical phase corrections into account, and assess the impact of the corrections on precise baseline estimates and further applications such as gravity field recovery from kinematic LEO positions.     

Classical globally reflected gravity field determination in modern locally oriented multiscale framework

The purpose of this paper is the canonical connection of classical global gravity field determination following the concept of Stokes (Trans Camb Philos Soc 8:672–712, 1849), Bruns (Die Figur der Erde, Publikation Königl. Preussisch. Geodätisches Institut, P. Stankiewicz Buchdruckerei, Berlin, 1878), and Neumann (Vorlesungen über die Theorie des Potentials und der Kugelfunktionen. Teubner, Leipzig, pp 135–154, 1887) on the one hand and modern locally oriented multiscale computation by use of adaptive locally supported wavelets on the other hand. The essential tools are regularization methods of the Green, Neumann, and Stokes integral representations. The multiscale approximation is guaranteed simply as linear difference scheme by use of Green, Neumann, and Stokes wavelets. As an application, gravity anomalies caused by plumes are investigated for the Hawaiian and Iceland areas.     

On the topographic bias in geoid determination by the external gravity field

The topographic bias is defined as the error/bias committed by continuing the external gravity field inside the topographic masses by a harmonic function. We study the topographic bias given by a digital terrain model defined by a spherical template, and we show that the topographic bias is given only by the potential of an inner-zone cap, and it equals the bias of the Bouguer shell, independent of the size of the cap. Then we study the effect on the real Earth by decomposing its topography into a template, and we show also in this case that the topographic bias is that of the Bouguer shell, independent of the shape of the terrain. Finally, we show that the topographic potential of the terrain at the geoid can be determined to any precision by a Taylor expansion outside the Earth’s surface. The last statement is demonstrated by a Taylor expansion to fourth order.