Model Computations for Different Solutions of the Geodetic Boundary-value Problem PDF Download
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Author: Joseph E. Gross
Publisher:
ISBN:
Category : Aerial triangulation
Languages : en
Pages : 510
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Book Description
Author: Karl-Rudolf Koch
Publisher:
ISBN:
Category : Boundary value problems
Languages : en
Pages : 43
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Book Description
To solve the boundary-value problem of physical geodesy, the perturbing potential is usually expressed by the potential of a simple layer. By introducing this expression into the boundary condition, Molodensky's basic integral equation is obtained; the solution of which enables us to compute the perturbing potential and its first derivative. To check the results of this method, Green's formula can be used. After transforming this formula and its derivative by a method, due to Molodensky, a linear integral equation for the disturbing potential is obtained. With the solutions of this integral equation, the first derivative of the disturbing potential can be computed from the transformed derivative of Green's formula. For a model consisting of a cone on a plane the basic integral equation and the integral equation of Green's formula are solved by successive approximation with a computer. The solution of the basic integral equation is also obtained by Molodensky's method. These three solutions are compared for different inclination angles of the surface of the cone. The results agree very well for small inclination angles, but the approximations don't converge for greater inclination angles. The reason has to be sought in the errors of numerical integration, by which the integration over the surface of the model is solved. (Author).
Author: Joseph E. Gross
Publisher:
ISBN:
Category : Aerial triangulation
Languages : en
Pages : 510
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Book Description
Author: Fernando Sansò
Publisher: Springer
ISBN: 3319463586
Category : Science
Languages : en
Pages : 83
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Book Description
This book offers a new approach to interpreting the geodetic boundary value problem, successfully obtaining the solutions of the Molodensky and Stokes boundary value problems (BVPs) with the help of downward continuation (DC) based methods. Although DC is known to be an improperly posed operation, classical methods seem to provide numerically sensible results, and therefore it can be concluded that such classical methods must in fact be manifestations of different, mathematically sound approaches. Here, the authors first prove the equivalence of Molodensky’s and Stoke's approaches with Helmert’s reduction in terms of both BVP formulation and BVP solutions by means of the DC method. They then go on to show that this is not merely a downward continuation operation, and provide more rigorous interpretations of the DC approach as a change of boundary approach and as a pseudo BVP solution approach.
Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 1572
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Book Description
Author: Fernando Sansò
Publisher:
ISBN: 9783319463599
Category : Physical geography
Languages : en
Pages : 81
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Book Description
Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 1264
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Book Description
Author: Fernando Sansò
Publisher: Springer Science & Business Media
ISBN: 366210735X
Category : Science
Languages : en
Pages : 356
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Book Description
Just as in the era of great achievements by scientists such as Newton and Gauss, the mathematical theory of geodesy is continuing the tradition of producing exciting theoretical results, but today the advances are due to the great technological push in the era of satellites for earth observations and large computers for calculations. Every four years a symposium on methodological matters documents this ongoing development in many related underlying areas such as estimation theory, stochastic modelling, inverse problems, and satellite-positioning global-reference systems. This book presents developments in geodesy and related sciences, including applied mathematics, among which are many new results of high intellectual value to help readers stay on top of the latest happenings in the field.
Author: Nico Sneeuw
Publisher: Springer Science & Business Media
ISBN: 3642220789
Category : Science
Languages : en
Pages : 393
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Book Description
The Hotine-Marussi Symposium is the core meeting of a “think thank”, a group scientists in the geodetic environment working on theoretical and methodological subjects, while maintaining the foundations of geodesy to the proper level by corresponding to the strong advancements improved by technological development in the field of ICT, electronic computing, space technology, new measurement devices etc. The proceedings of the symposium cover a broad area of arguments which integrate the foundations of geodesy as a science. The common feature of the papers therefore is not on the object, but rather in the high mathematical standards with which subjects are treated.
Author: Wolfgang Torge
Publisher: Walter de Gruyter
ISBN: 3110250004
Category : Technology & Engineering
Languages : en
Pages : 444
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Book Description
The fourth edition of this textbook has been thoroughly revised in order to reflect the central role which geodesy has achieved in the past ten years. The Global Geodetic Observing System established by the IAG utilizes a variety of techniques to determine the geometric shape of the earth and its kinematics, the variations of earth rotation, and the earth’s gravity field. Space techniques play a fundamental role, with recent space missions also including gravity field recovery. Terrestrial techniques are important for regional and local applications, and for validating the results of the space missions. Global and regional reference systems are now well established and widely used. They also serve as a basis for geo-information systems. The analysis of the time variation of the geodetic products provides the link to other geosciences and contributes to proper modelling of geodynamic processes. The book follows the principal directions of geodesy, providing the theoretical background as well as the principles of measurement and evaluation methods. Selected examples of instruments illustrate the geodetic work. An extensive reference list supports further studies. The book is intended to serve as an introductory textbook for graduate students as well as a reference for scientists and engineers in the fields of geodesy, geophysics, surveying engineering and geomatics.
Author: Fernando Sansò
Publisher: Springer
ISBN: 9783662176047
Category : Science
Languages : en
Pages : 596
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Book Description
The precise determination of the figure of the earth and its exterior gravitational field requires the solution of the geodetic boundary value problem (GBVP). Recently, a whole series of new measurement techniques has became available, in particular air- and spaceborne methods. They will make its solution much more complete and accurate and will contribute to a better understanding of ocean circulation and of the earth's interior. The book consists of contributions from leading scientists presented at an international summer school. It covers all aspects of the solution of the GBVP, from a mathematical basis via geodetic modeling to its relationship with advanced measurements. It provides three foundations to determine the geoid at a 1-cm precision level.
