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This volume includes a selection of papers presented at the IAG international symposium "Gravity, Geoid and Height Systems 2012" (GGHS2012), which was organized by IAG Commission 2 “Gravity Field” with the assistance of the International Gravity Field Service (IGFS) and GGOS Theme 1 “Unified Global Height System”. The book summarizes the latest results on gravimetry and gravity networks, global gravity field modeling and applications, future gravity field missions. It provides a detailed compilation on advances in precise local and regional high-resolution geoid modeling, the establishment and unification of vertical reference systems, contributions to gravity field and mass transport modeling as well as articles on the gravity field of planetary bodies.
Detailed information on the gravitational effect of the Earth's topographic and isostatic masses can be calculated by gravity forward modeling. Within this book, the tesseroid-based Rock-Water-Ice (RWI) approach is developed, which allows a rigorous separate modeling of the Earth's rock, water, and ice masses with variable density values. Besides a discussion and evaluation of the RWI approach, applications in the context of the GOCE satellite mission and height system unification are presented.
This book contains a selection of peer-reviewed papers presented at the VIII Hotine-Marussi Symposium on Mathematical Geodesy in Rome, 17-21 June, 2013. The scientific sessions focused on global reference systems, geodetic data analysis, geopotential modelling, gravity field mapping as well as digital terrain modelling. A special chapter is dedicated to understand the generation of Flash.
These Proceedings include the written version of papers presented at the IAG International Symposium on "Gravity, Geoid and Earth Observation 2008". The Symposium was held in Chania, Crete, Greece, 23-27 June 2008 and organized by the Laboratory of Geodesy and Geomatics Engineering, Technical University of Crete, Greece. The meeting was arranged by the International Association of Geodesy and in particular by the IAG Commission 2: Gravity Field. The symposium aimed at bringing together geodesists and geophysicists working in the general areas of gravity, geoid, geodynamics and Earth observation. Besides covering the traditional research areas, special attention was paid to the use of geodetic methods for: Earth observation, environmental monitoring, Global Geodetic Observing System (GGOS), Earth Gravity Models (e.g., EGM08), geodynamics studies, dedicated gravity satellite missions (i.e., GOCE), airborne gravity surveys, Geodesy and geodynamics in polar regions, and the integration of geodetic and geophysical information.
This book offers extensive information on the operation of gravimeters, including airborne, marine and terrestrial ones, and on the associated data processing methods such as optimal and adaptive filtering, smoothing, structural and parametric identification. Further, it describes specific features relating to the study of the gravitational field in remote areas of the Earth, with the necessary modifications of equipment and software for all-latitude applications. Findings from gravity studies in such remote areas are also presented. Advanced methods for studying the gravitational field, including those for simultaneous determination of gravity anomalies and deflection of the vertical are described and analyzed in detail. Gravity gradiometers and cold atom gravimeters are also covered. Last but not least, the book deals with the development of Earth’s gravity field models and their various applications, including map-aided navigation, with a special attention to model accuracy estimation. Gathering research findings and best practice recommendations relating to Earth’s gravity field measurements, collected by a team of researchers and professionals, the book offers a unique guide for engineers, scientists and graduate students dealing with terrestrial, marine and airborne gravimetry. It will also help other specialists involved in developing and using navigation systems in practice, including designers of gravimetric equipment and navigators.
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.
Modelling the gravity field of the Earth is important for many scientific disciplines. Global gravity models allow for the investigation of long-wavelength properties of the gravity field. Global models derived from satellite observations provide an additional benefit: they are uncorrelated with any error contaminating regional terrestrial gravity information; this makes them ideal for combination with terrestrial gravity data in order to formulate high-precision regional geoid models. This dissertation investigates several possible areas of improvement to both the formulation and evaluation of satellite-only global gravity models. The first major barrier is due to what is known to the geodetic community as the “polar-gap problem”: the lack of data collected by the satellites over the poles due to the inclination angle of their orbit. The second is the rigorous application of these models inside of the topographical masses (and most pertinent, on the surface of the geoid). These problems are addressed in three articles. The first presents a mathematical tool that can be used in order to address the polar-gap problem by performing the global integration making use of the additivity property of Riemann integrals. The second article presents a computational scheme that allows for the evaluation of various quantities derived from global gravity models inside the topographical masses. Finally, the third article describes the production and validation of a 2D global topographical density model that is required for the rigorous evaluation of the gravity field as prescribed in the second article.
Contents 1. Introduction 1 2. Estimation of the Earth's gravity field 9 3. Augmentation of the functional model 35 4. Stochastic model validation 49 5. Monte Carlo implementation 83 6. Outlier detection and robust estimation 97 7. Application 1: CHAMP satellite gravity data 115 8. Application 2: Joint inversion of global GPS time-series with GRACE gravity models 141 9. Application 3: Temporal aliasing of hydrological signals in a simulated GRACE recovery 165 10. Application 4: The computation of a height reference surface in Switzerland 177 11. Conclusions and recommendations 191 References 197 A. Series expansion into spherical harmonics 217 B. Matrix algebra and matrix analysis 219 C. Some standard distributions 221 Summary 223 Samenvatting 227 Curriculum Vitae 231