On the Linearized Boundary Value Problems of Physical Geodesy PDF Download
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Author: Bernhard Heck
Publisher:
ISBN:
Category : Geodesy
Languages : en
Pages : 74
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Book Description
Author: Bernhard Heck
Publisher:
ISBN:
Category : Geodesy
Languages : en
Pages : 74
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Book Description
Author: Fernando Sansò
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 620
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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.
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: Helmut Moritz
Publisher:
ISBN:
Category :
Languages : en
Pages : 48
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Book Description
Author: Peter Meissl
Publisher:
ISBN:
Category : Boundary value problems
Languages : en
Pages : 138
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Book Description
The geodetic boundary value problem consists in determining an unknown closed surface from the boundary values of an external potential and its gradient. A rigorous mathematical formulation of this problem is given leading to a system of non-linear integro-differential equations. The formalism of differentiation in function spaces is applied yielding a linearized version which involves no further neglections and approximations. Tensor calculus is used in linearizing the various differential geometric quantities. The results are specialized to a linearization with respect to the equipotential sphere in which case the formulas of Stokes and Vening Meinesz are simultaneously obtained. (Author).
Author: Helmut Moritz
Publisher:
ISBN:
Category : Geodesy
Languages : en
Pages : 552
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Book Description
Author: Erik Grafarend
Publisher: Springer Science & Business Media
ISBN: 3662052962
Category : Science
Languages : en
Pages : 460
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Book Description
Geodesy as the science which determines the figure of the earth, its orientation in space and its gravity field as well as its temporal changes, produces key elements in describing the kinematics and the dynamics of the deformable body "earth". It contributes in particular to geodynamics and opens the door to decode the complex interactions between components of "the system earth". In the breathtaking development recently a whole arsenal of new terrestrial, airborne as well as satelliteborne measurement techniques for earth sciences have been made available and have broadened the spectrum of measurable earth parameters with an unforeseen accuracy and precision, in particular to resolve the factor time. The book focusses on these topics and gives a state of the art of modern geodesy.
Author: Arne Bjerhammar
Publisher:
ISBN:
Category : Geodesy
Languages : en
Pages : 122
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Book Description
Author: F. Sacerdote
Publisher:
ISBN:
Category :
Languages : en
Pages : 20
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Book Description
Author: Helmut Moritz
Publisher:
ISBN:
Category : Boundary value problems
Languages : en
Pages : 135
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Book Description
The report is concerned with formulas for the determination of the earth's physical surface and external gravity field from free-air gravity anomalies to an approximation linear in the elevation and its derivatives. Part A considers integral equations and their linear solutions; Part B gives an elementary deduction of these solutions from the geometrically evident gradient solution; and the subject of Part C is an application to various gravity-dependent quantities and an evaluation of different solutions. (Author).
