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 will be based on the material of the lecture noties in several International Schools for the Determination and Use of the Geoid, organized by the International Geoid Serivice of the International Association of Geodesy. It consolidates, unifies, and streamlines this material in a unique way not covereed by the few other books that exist on this subjext. More specifically, the book presents (for the first time in a single volume) the theory and methodology of the most common technique used for precise determination of the geoid, including the computation of the marine geoid from satellite altimetry data. These are illustrated by specific examples and actual computations of local geoids. In addition, the book provides the fundamentals of estimating orthometric heights without spirit levelling, by properly combining a geoid with heights from GPS. Besides the geodectic and geophysical uses, this last application has made geoid computation methods very popular in recent years because the entire GPS and GIS user communities are interested in estimating geoid undulations in order to convert GPS heights to physically meaningful orthometric heights (elevations above mean sea level). The overall purpose of the book is, therefore, to provide the user community (academics, graduate students, geophysicists, engineers, oceanographers, GIS and GPS users, researchers) with a self-contained textbook, which will supply them with the complete roadmap of estimating geoid undulations, from the theoretical definitions and formulas to the available numerical methods and their implementation and the test in practice.

At the XXIV General Assembly of the International Union of Geodesy and Geophysics (IUGG), held July 2 13, 2007 in Perugia, Italy, the International As- ciation of Geodesy (IAG) also had its quadrennial General Assembly. The IAG - organized and contributed to several Union Symposia, as well as to Joint Symposia with other Associations. It also organized ve Symposia of its own, one dedicated to eachofitsfourCommissionsanda fthonededicatedtotheGlobalGeodeticObse- ing System (GGOS). This volume contains the proceedings of these ve Symposia, which are listed below: Symposium GS001: Reference Frames Convener: H. Drewes Co-convener: A. Dermanis Symposium GS002: Gravity Field Convener: C. Jekeli Co-conveners: U. Marti, S. Okubo, N. Sneeuw, I. Tziavos, G. Vergos, M. Vermeer, P. Visser Symposium GS003: Earth Rotation and Geodynamics Convener: V. Dehant Co-convener: Chengli Huang Symposium GS004: Positioning and Applications Convener: C. Rizos Co-convener: S. Verhagen Symposium GS005: The Global Geodetic Observing System (GGOS) Conveners: M. Rothacher Co-conveners: R. Neilan, H. -P. Plag The Symposia were organized based on the structure of the IAG (i. e., one per Commission) and covered the there pillars of geodesy, namely geometry, Earth ro- tion, and gravity eld, plus their applications. The inclusion of the Symposium on GGOS which is no longer a project but a major component of the IAG integrated all geodetic areas and highlighted the importance of multidisciplinarity in, and for, geodetic research."

This book will be based on the material of the lecture noties in several International Schools for the Determination and Use of the Geoid, organized by the International Geoid Serivice of the International Association of Geodesy. It consolidates, unifies, and streamlines this material in a unique way not covereed by the few other books that exist on this subjext. More specifically, the book presents (for the first time in a single volume) the theory and methodology of the most common technique used for precise determination of the geoid, including the computation of the marine geoid from satellite altimetry data. These are illustrated by specific examples and actual computations of local geoids. In addition, the book provides the fundamentals of estimating orthometric heights without spirit levelling, by properly combining a geoid with heights from GPS. Besides the geodectic and geophysical uses, this last application has made geoid computation methods very popular in recent years because the entire GPS and GIS user communities are interested in estimating geoid undulations in order to convert GPS heights to physically meaningful orthometric heights (elevations above mean sea level). The overall purpose of the book is, therefore, to provide the user community (academics, graduate students, geophysicists, engineers, oceanographers, GIS and GPS users, researchers) with a self-contained textbook, which will supply them with the complete roadmap of estimating geoid undulations, from the theoretical definitions and formulas to the available numerical methods and their implementation and the test in practice.

The IAG International Symposium on Gravity, Geoid and Geodynamics 2000 (GGG2000) took place in Banff, Alberta, Canada, from July 31 to August 4, 2000. This symposium continued the tradition of mid-term meetings ("GraGeoMar96: Gravity, Geoid and Marine Geodesy," Tokyo, Japan, Sept. 30 - Oct. 5,1996) held between the joint symposia of the International Geoid and Gravity Commissions ("1st Joint Meeting of the International Gravity Commission and the International Geoid Commission," Graz, Austria, Sept. 11-17, 1994 and "2nd Joint Meeting of the International Gravity Commission and the International Geoid Commission," Trieste, Italy, Sept. 7-12, 1998). This time, geodynamics was chosen as the third topic to accompany the of gravity and geoid. The symposium thus aimed and succeeded at bringing traditional topics together geodesists and geophysicists working in the general areas of gravity, geoid and geodynamics. Besides covering the traditional research areas, special attention was paid to the use of geodetic methods for geodynamics studies, dedicated satellite missions, airborne surveys, arctic regions geodesy and geodynamics, new mathematical methods and the integration of geodetic and geophysical information. The Scientific Committee members (Jean Dickey, Martine Feissel, Rene Forsberg, Petr Holota, Inginio Marson, Masao Nakada, Richard W. Peltier, Reiner Rummel, Burkhard Schaffrin, Klaus Peter Schwarz, Michael G. Sideris, DetlefWolf and Patrick Wu) are sincerely thanked for selecting the session topics, which resulted in such an exciting scientific event. More specifically, the following ten sessions were organized: 1. Reference Frames and the Datum Problem C.

The IAG International Symposium on Gravity, Geoid and Geodynamics 2000 (GGG2000) took place in Banff, Alberta, Canada, from July 31 to August 4, 2000. This symposium continued the tradition of mid-term meetings ("GraGeoMar96: Gravity, Geoid and Marine Geodesy," Tokyo, Japan, Sept. 30 - Oct. 5,1996) held between the joint symposia of the International Geoid and Gravity Commissions ("1st Joint Meeting of the International Gravity Commission and the International Geoid Commission," Graz, Austria, Sept. 11-17, 1994 and "2nd Joint Meeting of the International Gravity Commission and the International Geoid Commission," Trieste, Italy, Sept. 7-12, 1998). This time, geodynamics was chosen as the third topic to accompany the of gravity and geoid. The symposium thus aimed and succeeded at bringing traditional topics together geodesists and geophysicists working in the general areas of gravity, geoid and geodynamics. Besides covering the traditional research areas, special attention was paid to the use of geodetic methods for geodynamics studies, dedicated satellite missions, airborne surveys, arctic regions geodesy and geodynamics, new mathematical methods and the integration of geodetic and geophysical information. The Scientific Committee members (Jean Dickey, Martine Feissel, Rene Forsberg, Petr Holota, Inginio Marson, Masao Nakada, Richard W. Peltier, Reiner Rummel, Burkhard Schaffrin, Klaus Peter Schwarz, Michael G. Sideris, DetlefWolf and Patrick Wu) are sincerely thanked for selecting the session topics, which resulted in such an exciting scientific event. More specifically, the following ten sessions were organized: 1. Reference Frames and the Datum Problem C.