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Optimized formulas for the gravitational field of a tesseroid

Grombein, Thomas; Seitz, Kurt; Heck, Bernhard

Various tasks in geodesy, geophysics, and related geosciences require precise information on the impact of mass distributions on gravity field-related quantities, such as the gravitational potential and its partial derivatives. Using forward modeling based on Newton's integral, mass distributions are generally decomposed into regular elementary bodies. In classical approaches, prisms or point mass approximations are mostly utilized. Considering the effect of the sphericity of the Earth, alternative mass modeling methods based on tesseroid bodies (spherical prisms) should be taken into account, particularly in regional and global applications. Expressions for the gravitational field of a point mass are relatively simple when formulated in Cartesian coordinates. In the case of integrating over a tesseroid volume bounded by geocentric spherical coordinates, it will be shown that it is also beneficial to represent the integral kernel in terms of Cartesian coordinates. This considerably simplifies the determination of the tesseroid's potential derivatives in comparison with previously published methodologies that make use of integral kernels expressed in spherical coordinates. ... mehr

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DOI: 10.5445/IR/1000035020
DOI: 10.1007/s00190-013-0636-1
Zitationen: 75
Web of Science
Zitationen: 72
Cover der Publikation
Zugehörige Institution(en) am KIT Geodätisches Institut (GIK)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2013
Sprache Englisch
Identifikator ISSN: 0949-7714
KITopen-ID: 1000035020
Erschienen in Journal of Geodesy
Band 87
Heft 7
Seiten 645-660
Nachgewiesen in Web of Science
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