Spacetime Modeling of the Earth’s Gravity Field by Ellipsoidal Harmonics

Erik W. Grafarend, Matthias Klapp and Zdeněk Martinec
Additional contact information
Erik W. Grafarend: Stuttgart University, Department of Geodesy and Geoinformatics
Matthias Klapp: Dublin Institute for Advanced Studies
Zdeněk Martinec: Charles University, Department of Geophysics, Faculty of Mathematics and Physics

Chapter 7 in Handbook of Geomathematics, 2010, pp 159-252 from Springer

Abstract: Abstract All planetary bodies like the Earth rotate causing centrifugal effect! The result is an equilibrium figure of ellipsoidal type. A natural representation of the planetary bodies and their gravity fields has therefore to be in terms of ellipsoidal harmonics and ellipsoidal wavelets, an approximation of its gravity field which is three times faster convergent when compared to the “ruling the world” spherical harmonics and spherical wavelets. Freeden et al. (1998, 2004). Here, various effects are treated when considering the Earth to be “ellipsoidal”: > Sections 2 and > 3 start the chapter with the celebrated ellipsoidal Dirichlet and ellipsoidal Stokes (to first order) boundary-value problems. > Section 4 is devoted to the definition and representation of the ellipsoidal vertical deflections in gravity space, extended in > Sect. 5 to the representation in geometry space. The potential theory of horizontal and vertical components of the gravity field, namely, in terms of ellipsoidal vector fields, is the target of > Sect. 6. > Section 7 is concentrated on the reference potential of type Somigliana–Pizzetti field and its tensor-valued derivatives. > Section 8 illustrates an ellipsoidal harmonic gravity field for the Earth called SEGEN (Gravity Earth Model), a set-up in ellipsoidal harmonics up to degree/order 360/360. Five plates are shown for the West–East/North–South components of type vertical deflections as well as gravity disturbances refering to the International Reference Ellipsoid 2000. The final topic starts with a review of the curvilinear datum problem refering to ellipsoidal harmonics. Such a datum transformation from one ellipsoidal representation to another one in > Sect. 9 is a seven-parameter transformation of type (i) translation (three parameters), (ii) rotation (three parameters) by Cardan angles, and (iii) dilatation (one parameter) as an action of the conformal group in a three-dimensional Weitzenbäck space W(3) with seven parameters. Here, the chapter is begun with an example, namely, with a datum transformation in terms of spherical harmonics in > Sect. 10. The hard work begins with > Sect. 11 to formulate the datum transformation in ellipsoidal coordinates/ellipsoidal harmonics! The highlight is > Sect. 12 with the characteristic example in terms of ellipsoidal harmonics for an ellipsoid of revolution transformed to another one, for instance, polar motion or gravitation from one ellipsoid to another ellipsoid of reference. > Section 13 reviews various approximations given in the previous three sections.

Keywords: Gravity Field; Geoidal Height; Gravity Vector; Gravity Disturbance; Vertical Deflection (search for similar items in EconPapers)
Date: 2010
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-01546-5_7

Ordering information: This item can be ordered from
http://www.springer.com/9783642015465

DOI: 10.1007/978-3-642-01546-5_7

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().