Download or read book Geodetic Boundary Value Problem the Equivalence between Molodensky s and Helmert s Solutions written by Fernando Sansò and published by Springer. This book was released on 2016-11-09 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Geodetic Boundary Value Problem written by Fernando Sansò and published by . This book was released on 2017 with total page 81 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonlinear Solutions of the Geodetic Boundary Value Problem written by Helmut Moritz and published by . This book was released on 1969 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt: A complete series solution of Molodensky's boundary value problem is derived using, instead of an integral equation, analytical continuation by means of power series. This solution is shown to be equivalent, term by term, to the Molodensky-Brovar series, but is simpler and practically more convenient. This equivalence gives a physical explanation of the divergence of the Molodensky series. The exclusion of topographic masses to improve convergence is discussed, and computational formulas for height anomalies and deflections of the vertical are given. In the Appendix, structural similarities between the series of celestial mechanics and of physical geodesy are used to get an insight into the convergence behavior of these series. Another argument for the divergence of series of Molodensky type is given. (Author).
Download or read book Model Computations for Different Solutions of the Geodetic Boundary value Problem written by Karl-Rudolf Koch and published by . This book was released on 1968 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).
Download or read book Solution of the Geodetic Boundary value Problem in Case of a Reference Ellipsoid written by Karl-Rudolf Koch and published by . This book was released on 1968 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: The solution of the boundary-value problem of physical geodesy in the case of a reference ellipsoid is given with a relative error of the order of the square of the flattening of the earth. The solution is obtained by representing the disturbing potential at the earth's surface as the potential of a simple layer and by introducing this expression into the boundary condition. If the earth's topography is neglected in the derived solution, a new solution of Stokes' problem for a reference ellipsoid is obtained. As an example, the geodetic boundary-value problem is solved for a mathematical model of the earth. (Author).
Download or read book Geodetic Boundary Value Problems in View of the One Centimeter Geoid written by Fernando Sansò and published by Springer. This book was released on 1997-06-25 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Numerical Results for Correction Terms Used in the Solution of the Geodetic Boundary Value Problem written by David Russell Robinson and published by . This book was released on 1970 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book VII Hotine Marussi Symposium on Mathematical Geodesy written by Nico Sneeuw and published by Springer Science & Business Media. This book was released on 2012-02-02 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book X Hotine Marussi Symposium on Mathematical Geodesy written by Jeffrey T. Freymueller and published by Springer Nature. This book was released on with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Geodetic Boundary Value Problem in Two Dimensions and Its Iterative Solution written by Martin van Gelderen and published by . This book was released on 1991 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geodetic Boundary Value Problems in View of the One Centimeter Geoid written by Fernando Sansò and published by Springer. This book was released on 2014-03-12 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Simulation Study of the Overdetermined Geodetic Boundary Value Problem Using Collocation written by Lucia S. Tsaoussi and published by . This book was released on 1989 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Linear Solutions of the Geodetic Boundary value Problem written by Helmut Moritz and published by . This book was released on 1968 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Geodetic Boundary Value Problem in Two Dimensions and Its Iterative Solutions written by M. van Gelderen and published by . This book was released on 1991 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Recent Developments in the Geodetic Boundary value Problem written by Helmut Moritz and published by . This book was released on 1977 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: The report reviews progress in the mathematical formulation and treatment of the geodetic boundary-value problem, in particular, the existence and uniqueness theorems of L. Hormander and the gravity space approach due to F. Sanso. The method of Hormander uses a very advanced inverse function theorem of nonlinear functional analysis. Sanso has transformed Molodensky's free boundary-value problem into a fixed boundary-value problem in gravity space, thereby essentially reducing the mathematical complexity. As a linear approximation, the gravity space approach gives identical superior for treating questions of existence and uniqueness of the solution, although it is restricted to the pure gravitational case without centrifugal force. (Author).
Download or read book The Geodetic Boundary Value Problem and the Coordinate Choice Problem written by Fernando Sansò and published by . This book was released on 1981 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Solution of the Geodetic Boundry Value Problem to Order E3 written by Ronald S. Mather and published by . This book was released on 1973 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt:
