Model Computations for Different Solutions of the Geodetic Boundary-value Problem PDF Download
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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: 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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Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 1572
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Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 1264
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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: Fernando Sansò
Publisher:
ISBN: 9783319463599
Category : Physical geography
Languages : en
Pages : 81
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Author: Helmut Moritz
Publisher:
ISBN:
Category : Earth (Planet)
Languages : en
Pages : 434
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Author: Helmut Moritz
Publisher:
ISBN:
Category : Boundary value problems
Languages : en
Pages : 107
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Author: Air Force Cambridge Research Laboratories (U.S.)
Publisher:
ISBN:
Category : Atmosphere, Upper
Languages : en
Pages : 84
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Author: Athanasios Dermanis
Publisher:
ISBN:
Category : Artificial satellites
Languages : en
Pages : 316
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Book Description