Fernando Sanso Livres

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.

This book consolidates and streamlines material from lectures at International Schools for the Determination and Use of the Geoid, organized by the International Geoid Service of the International Association of Geodesy. It uniquely presents the theory and methodology of the most common techniques for precise geoid determination, including marine geoid computation from satellite altimetry data, all in a single volume. Specific examples and actual computations of local geoids are included. Additionally, it covers the fundamentals of estimating orthometric heights without spirit leveling by effectively combining geoid data with GPS heights. This method has gained popularity due to its relevance for the GPS and GIS user communities, who seek to convert GPS heights into meaningful orthometric elevations above mean sea level. The book aims to serve a diverse user community, including academics, graduate students, geophysicists, engineers, oceanographers, and researchers, by providing a comprehensive roadmap for estimating geoid undulations. It encompasses theoretical definitions, formulas, available numerical methods, implementation strategies, and practical testing, making it a self-contained resource for those interested in this field.

Geodesy is the science dealing with the determination of the position of points in space, the shape and gravity field of the Earth and with their time variations. A consequence is that geodesists feel as a permanent subject of research, the detection, analysis and interpretation of spatial deformation as well as gravity field variation. This book collects 36 selected papers from the International Symposium on Geodetic Deformation Monitoring held in Jaén (Spain) from 17 th to 19 th March 2005. The main topics covered in the symposium were: mathematical and statistical models for crustal deformation analysis, deformation monitoring from GPS and InSAR data: analysis and geophysical interpretation, geodetic monitoring of movements in civil engineering, integration of spatial and terrestrial techniques in deformation studies, geodynamical applications of gravimetric observations and present-day geodetic instrumentation for deformation monitoring. This volume is a good overview of theoretical matters, models and results.

Every four years the International Association of Geodesy meets at the IUGG General Assembly and this has always been an important event for IAG to make the point on where are we going as geodesists both in terms of scientific production as well as in terms of organization. The proceedings of IAG at the Sapporo 2003 General Assembly are the mirror of our scientific achievements, and, as Geodesy is a living entity like any other science, we could say it is a way to see the picture of what we consider our field of applications as well as of theoretical speculations. Let us examine this aspect in terms of what are: the object of our research, the methods we use, the general scientific results we can produce. • Our object: here I would like to use a pseudo-Helmert definition; the object of Geodesy is knowing the surfaces of the earth: the geometric surface by positioning and e. m. surveying, and the physical surface, i. e the gravity field, by land, marine or satellite gravimetry, and their time variations. This „object“ is naturally interlaced with other physical properties of the earth both through deep processes affecting its surface and through the gravity field at all different scales from the global to the regional and local, where most engineering applications take place.

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.

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.

In 1954, Antonio Marussi started a series of symposia in Venice. The first three of these covered the entire theoretical definition of 3-D geodesy as delineated in discussions with renowned contemporary scientists, particularly Martin Hotine. After Marussi's death, the symposia were finally named the Hotine-Marussi Symposia and were continued in Italy. The Third Hotine-Marussi Symposium was held in L'Aquila from May 30 to June 3, 1994. It provided geodesists interested in theory and methodology with the opportunity to discuss their theoretical achievements, as well as new topics in the geodetic sciences. This book thus provides an updated overview of the main geodetic theories in various fields of application.