Solution of the Geodetic Boundary-value Problem in Case of a Reference Ellipsoid


Book Description

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).




Geodetic Boundary Value Problem: the Equivalence between Molodensky’s and Helmert’s Solutions


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.










Geodetic Boundary Value Problems in View of the One Centimeter Geoid


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.










Principles of the Gravitational Method


Book Description

This self-contained monograph gives a thorough introduction to the theory of gravity which is used as the basis for developing applications in exploration and geodesy. In addition, a survey of gravity instrumentation is given, with emphasis on the theory of underlying these instruments. The book finishes with an exposition of forward modeling and inverston, again emphasizing fundamental principles. *Surveys gravity instrumentation with emphasis on the theory of why certain instrumentation is used *Presents thorough developments of the theory of gravity to aid in creating applications in exploration and geodesy *Emphasizes the fundamental principles of forward modeling and inversion in the gravitational method







Geodesy


Book Description

The fifth edition of this textbook has been completely revised and significantly extended in order to reflect the revolution of geodetic technologies, methods and applications during the last decade. 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. The societal importance of geodetic products was highlighted by the UN resolution on the Global Geodetic Reference Frame. In this context, both space and terrestrial techniques play a fundamental role. Recent space missions are monitoring climate-relevant processes such as mass transport in the Earth system and sea level changes. The analysis of the time variation of the geodetic products provides the link to neighboring geosciences and contributes to proper modelling of geodynamic processes. New satellite mission concepts and novel technologies such as quantum gravimetry and optical clocks show great potential to further improve the geodetic observing system in the future. The book especially addresses graduate students in the fields of geodesy, geophysics, surveying engineering, geomatics, and space navigation. It should also serve as a reference for geoscientists and engineers facing geodetic problems in their professional work. The book follows the principal directions of geodesy, providing the theoretical background as well as the principles of measurement and evaluation methods, which is enriched with numerous figures. An extensive reference list supports further studies.