LEADER 04836nam 2200577Ia 450 001 9910437943503321 005 20200520144314.0 010 $a3-540-74700-1 024 7 $a10.1007/978-3-540-74700-0 035 $a(CKB)3400000000125624 035 $a(EBL)1206005 035 $a(SSID)ssj0000878965 035 $a(PQKBManifestationID)11482792 035 $a(PQKBTitleCode)TC0000878965 035 $a(PQKBWorkID)10850356 035 $a(PQKB)10635128 035 $a(DE-He213)978-3-540-74700-0 035 $a(MiAaPQ)EBC1206005 035 $a(PPN)168307901 035 $a(EXLCZ)993400000000125624 100 $a20130705d2013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aGeoid determination $etheory and methods /$fFernando Sanso, Michael Sideris, editors 205 $a1st ed. 2013. 210 $aHeidelberg ;$aNew York $cSpringer$dc2013 215 $a1 online resource (734 p.) 225 0$aLecture notes in earth system sciences 300 $aDescription based upon print version of record. 311 $a3-540-74699-4 320 $aIncludes bibliographical references and index. 327 $aPart I: 1. The forward modelling of the gravity field -- 2. Observable of physical geodesy and their analytical representation -- 3. Harmonic calculus and global gravity models -- 4. The local modellling of the gravity field: terrain effects -- 5. The local modelling of the gravity field by collocation.-  Part II: 6. Global gravitational Models -- 7. Geoid determination by 3D least squares collaction -- 8. Mass reductions in geoid modelling -- 9. Marine gravity and geoid from satellite altimetry -- 10. Geoid determination by fast Fourier transform techniques -- 11 -- Combination of heights -- Part III: 12. Hilbert spaces and deterministic collacation -- 13. On potential theory and HS of harmonic functions -- 14. A quick look to classical BVP solutions -- 15. The analysis of geodetic boundary value problems (BVP) in linear form. 330 $aKnowledge 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. 410 0$aLecture Notes in Earth System Sciences,$x2193-8571 606 $aGeodesy$xMathematics 607 $aEarth (Planet)$xFigure$xMeasurement 607 $aEarth (Planet)$xFigure$xMathematical models 615 0$aGeodesy$xMathematics. 676 $a526.1 701 $aSanso$b F$g(Fernando),$f1945-$0422254 701 $aSideris$b Michael G.$f1958-$01761682 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910437943503321 996 $aGeoid determination$94201280 997 $aUNINA