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  • 1
    Electronic Resource
    Electronic Resource
    Theory for the stochastic gravity field
    Amsterdam : Elsevier
    Physics Letters A 31 (1970), S. 7-8 
    Details
    ISSN: 0375-9601
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://linkinghub.elsevier.com/retrieve/pii/0375-9601(70)90556-6
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  • 2
    Electronic Resource
    Electronic Resource
    The gravitational field of topographic-isostatic masses and the hypothesis of mass condensation II-the topographic-isostatic geoid (1996)
    Springer
    Surveys in geophysics 17 (1996), S. 41-66 
    Details
    ISSN: 1573-0956
    Keywords: Gravity ; Topographic Masses ; Isostatic compensation ; Geoidal undulations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract In Part I we focussed on a convergent representation of the gravitational potential generated bytopographic masses on top of the equipotential surface atMean Sea Level, thegeoid, and by those masses which compensate topography. Topographic masses have also been condensated, namely represented by a “single layer”. Part II extends the computation of the gravitational field of topographic-isostatic masses by a detailed analysis of itsforce field in terms ofvector-spherical harmonic functions. In addition, the discontinuous mass-condensated topographic gravitational force vector (“head force”) is given. Once we identify theMoho discontinuity asone interface of isostatically compensated topographical masses, we have computed the topographic potential and the gravitational potential which is generated by isostatically compensated masses atMean Sea Level, the geoid, and illustrated by various figures of geoidal undulations. In comparison to a data oriented global geoid computation ofJ. Engels (1991) the conclusion can be made that the assumption of aconstant crustal mass density, the basic condition for isostatic modeling, does not apply. Insteaddensity variations in the crust, e.g. betweenoceanic and continental crust densities, have to be introduced in order to match the global “real” geoid and its topographic-isostatic model. The performed analysis documents that thestandard isostatic models based upon aconstant crustal density areunreal.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01904474
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  • 3
    Electronic Resource
    Electronic Resource
    The Hammer projection of the ellipsoid of revolution (azimuthal, transverse, rescaled equiareal) (1997)
    Springer
    Journal of geodesy 71 (1997), S. 736-748 
    Details
    ISSN: 1432-1394
    Keywords: Key words. Hammer Projection ; Ellipsoid of revolution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract. The classical Hammer projection of the sphere, which is azimuthal transverse rescaled equiareal, is generalized to the ellipsoid of revolution. Its first constituent, the azimuthal transverse equiareal projection of the biaxial ellipsoid, is derived giving equations for an equiareal transverse azimuthal projection. The second constituent, the equiareal mapping of the biaxial ellipsoid with respect to a transverse frame of reference and a change of scale, is then considered; results give collections of the general mapping equations generating the ellipsoidal Hammer projection, which lead to a world map.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001900050140
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  • 4
    Electronic Resource
    Electronic Resource
    Closed-form solution of P4P or the three-dimensional resection problem in terms of Möbius barycentric coordinates (1997)
    Springer
    Journal of geodesy 71 (1997), S. 217-231 
    Details
    ISSN: 1432-1394
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract.  The perspective 4 point (P4P) problem - also called the three-dimensional resection problem - is solved by means of a new algorithm: At first the unknown Cartesian coordinates of the perspective center are computed by means of Möbius barycentric coordinates. Secondly these coordinates are represented in terms of observables, namely space angles in the five-dimensional simplex generated by the unknown point and the four known points. Substitution of Möbius barycentric coordinates leads to the unknown Cartesian coordinates (2.8)–(2.10) of Box 2.2. The unknown distances within the five-dimensional simplex are determined by solving the Grunert equations, namely by forward reduction to one algebraic equation (3.8) of order four and backward linear substitution. Tables 1.–4. contain a numerical example. Finally we give a reference to the solution of the 3 point (P3P) problem, the two-dimensional resection problem, namely to the Ansermet barycentric coordinates initiated by C.F. Gauß (1842), A. Schreiber (1908) and A.␣Ansermet (1910).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001900050089
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  • 5
    Electronic Resource
    Electronic Resource
    The oblique Mercator projection of the ellipsoid of revolution IE a 2 ,b (1995)
    Springer
    Journal of geodesy 70 (1995), S. 38-50 
    Details
    ISSN: 1432-1394
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract While the standardMercator projection / transverse Mercator projecton maps the equator / the transverse metaequator equivalent to the meridian of referenceequidistantly, theoblique Mercator projection aims at aconformal mapping of the ellipsoid of revolution constraint to anequidistant mapping of an oblique metaequator. Obliqueness is determined by the extension of the area to be mapped, e.g. determined by the inclination of satellite orbits: Satellite cameras map the area just under the orbit geometry. Here we derive themapping equations of theoblique Mercator projection being characterized to beconformal andequidistant on the oblique metaequator extending results ofM. Hotine (1946, 1947).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00863417
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  • 6
    Electronic Resource
    Electronic Resource
    W0: an estimate in the Finnish Height Datum N60, epoch 1993.4, from twenty-five GPS points of the Baltic Sea Level Project (1997)
    Springer
    Journal of geodesy 71 (1997), S. 673-679 
    Details
    ISSN: 1432-1394
    Keywords: Key words. Gauge of geoid ; Geoid datum ; Gravitational potential ; Spheroidal harmonics ; Spheroidal coordinates
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract. Based upon a data set of 25 points of the Baltic Sea Level Project, second campaign 1993.4, which are close to mareographic stations, described by (1) GPS derived Cartesian coordinates in the World Geodetic Reference System 1984 and (2) orthometric heights in the Finnish Height Datum N60, epoch 1993.4, we have computed the primary geodetic parameter W 0(1993.4) for the epoch 1993.4 according to the following model. The Cartesian coordinates of the GPS stations have been converted into spheroidal coordinates. The gravity potential as the additive decomposition of the gravitational potential and the centrifugal potential has been computed for any GPS station in spheroidal coordinates, namely for a global spheroidal model of the gravitational potential field. For a global set of spheroidal harmonic coefficients a transformation of spherical harmonic coefficients into spheroidal harmonic coefficients has been implemented and applied to the global spherical model OSU 91A up to degree/order 360/360. The gravity potential with respect to a global spheroidal model of degree/order 360/360 has been finally transformed by means of the orthometric heights of the GPS stations with respect to the Finnish Height Datum N60, epoch 1993.4, in terms of the spheroidal “free-air” potential reduction in order to produce the spheroidal W 0(1993.4) value. As a mean of those 25 W 0(1993.4) data as well as a root mean square error estimation we computed W 0(1993.4)=(6 263 685.58 ± 0.36) kgal × m. Finally a comparison of different W 0 data with respect to a spherical harmonic global model and spheroidal harmonic global model of Somigliana-Pizetti type (level ellipsoid as a reference, degree/order 2/0) according to The Geodesist's Handbook 1992 has been made.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001900050134
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  • 7
    Electronic Resource
    Electronic Resource
    Closed form solution to the twin P4P or the combined three dimensional resection-intersection problem in terms of Möbius barycentric coordinates (1997)
    Springer
    Journal of geodesy 71 (1997), S. 232-239 
    Details
    ISSN: 1432-1394
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract. The twin perspective 4 point (twin P4P) problem – also called the combined three dimensional resection-intersection problem – is the problem of finding the position of a scene object from 4 correspondence points and a scene stereopair. While the perspective centers of the left and right scene image are positioned by means of a double three dimensional resection, the position of the scene object imaged on the left and right photograph is determined by a three dimensional intersection based upon given resected perspective centers. Here we present a new algorithm solving the twin P4P problem by means of Möbius barycentric coordinates. In the first algorithmic step we determine the distances between the perspective centers and the unknown intersected point by solving a linear system of equations. Typically, area elements of the left and right image build up the linear equation system. The second algorithmic step allows for the computation of the Möbius barycentric coordinates of the unknown intersected point which are thirdly converted into three dimensional object space coordinates {X,Y,Z} of the intersected point. Typically, this three-step algorithm based upon Möbius barycentric coordinates takes advantage of the primary double resection problem from which only distances from four correspondence points to the left and right perspective centre are needed. No orientation parameters and no coordinates of the left and right perspective center have to be made available.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001900050090
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  • 8
    Electronic Resource
    Electronic Resource
    Construction of Green's function to the external Dirichlet boundary-value problem for the Laplace equation on an ellipsoid of revolution (1997)
    Springer
    Journal of geodesy 71 (1997), S. 562-570 
    Details
    ISSN: 1432-1394
    Keywords: Key words. Green's function ; Dirichlet boundary-value problem ; Ellipsoid of revolution ; ellipsoidal harmonics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract. Green's function to the external Dirichlet boundary-value problem for the Laplace equation with data distributed on an ellipsoid of revolution has been constructed in a closed form. The ellipsoidal Poisson kernel describing the effect of the ellipticity of the boundary on the solution of the investigated boundary-value problem has been expressed as a finite sum of elementary functions which describe analytically the behaviour of the ellipsoidal Poisson kernel at the singular point ψ = 0. We have shown that the degree of singularity of the ellipsoidal Poisson kernel in the vicinity of its singular point is of the same degree as that of the original spherical Poisson kernel.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001900050124
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  • 9
    Electronic Resource
    Electronic Resource
    The optimal Mercator projection and the optimal polycylindric projection of conformal type – case-study Indonesia (1998)
    Springer
    Journal of geodesy 72 (1998), S. 251-258 
    Details
    ISSN: 1432-1394
    Keywords: Key words Optimal Mercator projection ; Polycylindric projection ; Ellipsoid of revolution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract. As a conformal mapping of the sphere S 2 R or of the ellipsoid of revolution E 2 A , B the Mercator projection maps the equator equidistantly while the transverse Mercator projection maps the transverse metaequator, the meridian of reference, with equidistance. Accordingly, the Mercator projection is very well suited to geographic regions which extend east-west along the equator; in contrast, the transverse Mercator projection is appropriate for those regions which have a south-north extension. Like the optimal transverse Mercator projection known as the Universal Transverse Mercator Projection (UTM), which maps the meridian of reference Λ0 with an optimal dilatation factor &ρcirc;=0.999 578 with respect to the World Geodetic Reference System WGS 84 and a strip [Λ0−Λ W ,Λ0 + Λ E ]×[Φ S ,Φ N ]= [−3.5∘,+3.5∘]×[−80∘,+84∘], we construct an optimal dilatation factor ρ for the optimal Mercator projection, summarized as the Universal Mercator Projection (UM), and an optimal dilatation factor ρ0 for the optimal polycylindric projection for various strip widths which maps parallel circles Φ0 equidistantly except for a dilatation factor ρ0, summarized as the Universal Polycylindric Projection (UPC). It turns out that the optimal dilatation factors are independent of the longitudinal extension of the strip and depend only on the latitude Φ0 of the parallel circle of reference and the southern and northern extension, namely the latitudes Φ S and Φ N , of the strip. For instance, for a strip [Φ S ,Φ N ]= [−1.5∘,+1.5∘] along the equator Φ0=0, the optimal Mercator projection with respect to WGS 84 is characterized by an optimal dilatation factor &ρcirc;=0.999 887 (strip width 3∘). For other strip widths and different choices of the parallel circle of reference Φ0, precise optimal dilatation factors are given. Finally the UPC for the geographic region of Indonesia is presented as an example.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001900050165
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  • 10
    Electronic Resource
    Electronic Resource
    The spheroidal fixed–free two-boundary-value problem for geoid determination (the spheroidal Bruns' transform) (1999)
    Springer
    Journal of geodesy 73 (1999), S. 513-533 
    Details
    ISSN: 1432-1394
    Keywords: Key words. Two-boundary value problem ; Spheroidal boundary value problem ; Spheroidal Stokes' operator ; Spheroidal Bruns' formula ; Geoid determination
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract. The target of the spheroidal Gauss–Listing geoid determination is presented as a solution of the spheroidal fixed–free two-boundary value problem based on a spheroidal Bruns' transformation (“spheroidal Bruns' formula”). The nonlinear spheroidal Bruns' transform (nonlinear spheroidal Bruns' formula), the spheroidal fixed part and the spheroidal free part of the two-boundary value problem are derived. Four different spheroidal gravity models are treated, in particular to determine whether they pass the test to fit to the postulate of a level ellipsoidal gravity field, namely of Somigliana–Pizzetti type.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001900050263
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