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During the last thirty years a great advancement in low energy physics, particularly interactions of atoms with the electromagnetic field, has been achieved and the development of electronics and laser techniques has allowed to implement a fine manipulation of atoms with photons. A wealth of important applications has sprung out from the ability of manipulating large samples of cold atoms. Among them, the improvement of atomic clocks and the creation of atomic gyroscopes and of atomic gravity meters, which is obviously of great interest for geodesists and geophysicists, particularly for potential applications in satellite geodesy. This book explains the fundamental concepts necessary to understand atom manipulation by photons, including the principles of quantum mechanics. It is conceived as a road that leads the reader from classical physics (mechanics and electromagnetism, considered as a common scientific background of geodesists and geophysicists), to the basics of quantum mechanics in order to understand the dynamics of atoms falling in the gravity field, while interacting with suitably resonant laser beams. There are different types of measurements of gravity based on the manipulation of ultra-cold atoms; the book presents the principles of the instruments based on stimulated Raman transition, which can be easily worked out analytically. However, the concepts explained in the text can provide a good starting point to understand also the applications based on the so-called Block oscillations or on the Bose–Einstein condensation. .

Geophysics. --- Quantum physics. --- Magnetism. --- Magnetic materials. --- Geophysics/Geodesy. --- Quantum Physics. --- Magnetism, Magnetic Materials. --- Materials --- Mathematical physics --- Physics --- Electricity --- Magnetics --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Mechanics --- Thermodynamics --- Geological physics --- Terrestrial physics --- Earth sciences --- Gravity --- Measurement. --- Gravimetry

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This textbook presents a comprehensive treatment of the theory and implementation of inverse methods in the analysis and interpretation of Earth's gravity field. By restricting their consideration to a local rather than global level, the authors focus on the use of observations and data that are more sensitive to local mass anomalies. All necessary theoretical aspects are reformulated in terms of a Euclidean framework so that less complex tools from mathematical analysis can be utilized. Divided into three parts, the text begins with a review of basic mathematical properties of gravitation, computing gravity from mass distributions, and relevant methods from Fourier analysis. In the second part of the text, the Earth's gravity field and its properties are introduced, and the preprocessing and processing of gravity data are explored. Finally, elementary inverse theory is discussed, after which the general inversion problem is considered via application of both the Tikhonov deterministic approach and a stochastic MCMC model. Throughout, examples and exercises are provided to both clarify material and to illustrate real-word applications for readers. Analysis of the Gravity Field: Direct and Inverse Problems is carefully written to be accessible to both mathematicians and geophysicists without sacrificing mathematical rigor. Readers should have a familiarity with the basics of mathematical analysis, as well as some knowledge of statistics and probability theory. Detailed proofs of more advanced results are relegated to appendices so that readers can concentrate on solution algorithms. .

Harmonic analysis. Fourier analysis --- Geophysics --- Computer. Automation --- Fourieranalyse --- informatica --- wiskunde --- geofysica

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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.

Geophysics --- Mining industry --- mijnbouw --- geofysica

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Knowledge of the Earth’s gravity field is an essential component for understanding the physical system of the Earth. Inside the masses, the field interacts with many other fields, according to complicated processes of physical and chemical nature; the study of these phenomena is the object of geophysics. Outside the masses, the gravity field smoothes out in agreement with the “harmonic” character of gravitation, while preserving, particularly close to the Earth’s surface, the signature of the internal processes; the study of the gravity field on the boundary and in the external space is the object of physical geodesy. It is necessary to define a separation surface between the masses and the “free” space. This surface is the geoid, an equipotential surface of the gravity field in a stack of such surfaces, close to the surface of the sea. Determining the geoid, or some other surface closer to the Earth's surface, has become synonymous to modelling the gravity field in physical geodesy; this is the subject of this book. Nowadays, this knowledge has become a practical issue also for engineering and other applications, because the geoid is used as a reference surface (datum) of physical heights that is very important in order to relate such heights to purely geometric ones obtained, for example, from GNSS. The methods currently used to produce the geoid at the centimetre level require significant mathematical, stochastic and numerical analysis. The book is structured in such a way as to provide self consistently all the necessary theoretical concepts, from the most elementary ones, such as Newton’s gravitation law, to the most complicated ones dealing with the stability of solutions of boundary value problems. It also provides a full description of the available numerical techniques for precise geoid and quasi-geoid determination. In this way, the book can be used by both students at the undergraduate and graduate level, as well as by researchers engaged in studies in physical geodesy and in geophysics. The text is accompanied by a number of examples, from most elementary to more advanced, as well as by exercises that illustrate the main concepts and computational methods.

Geodesy. Cartography --- Electromagnetism. Ferromagnetism --- Geophysics --- Geology. Earth sciences --- Mining industry --- Physical geography --- Geography --- geodesie --- GIS (geografisch informatiesysteem) --- mijnbouw --- geografie --- fysische geografie --- geofysica --- magnetisme