Complete gravity field of an ellipsoidal prism by Gauss–Legendre quadrature
| Autor: | José Cali, Clément Roussel, Jérôme Verdun, Frédéric Masson |
|---|---|
| Přispěvatelé: | Laboratoire Géomatique et foncier (GeF), Conservatoire National des Arts et Métiers [CNAM] (CNAM), Institut de physique du globe de Strasbourg (IPGS), Université de Strasbourg (UNISTRA)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS), Ecole et Observatoire des Sciences de la Terre (EOST) |
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
Physics
Gravity anomalies and Earth structure 010504 meteorology & atmospheric sciences Satellite geodesy Discretization [SDU.STU.GP]Sciences of the Universe [physics]/Earth Sciences/Geophysics [physics.geo-ph] Figure of the Earth Geometry 010502 geochemistry & geophysics Geodesy 01 natural sciences Physics::Geophysics Geopotential theory Gravitation symbols.namesake Geophysics Gravitational field Geochemistry and Petrology Numerical approximations and analysis Theoretical gravity symbols Gaussian quadrature Prism 0105 earth and related environmental sciences |
| Zdroj: | Geophysical Journal International Geophysical Journal International, Oxford University Press (OUP), 2015, 203 (3), pp.2220-2236. ⟨10.1093/gji/ggv438⟩ Geophysical Journal International, Oxford University Press (OUP), 2015, ⟨10.1093/gji/ggv438⟩ |
| ISSN: | 0956-540X 1365-246X |
| DOI: | 10.1093/gji/ggv438⟩ |
| Popis: | International audience; The increasing availability of geophysical models of the Earth's lithosphere and mantle has generated renewed interest in computation of theoretical gravity effects at global and regional scales. At the same time, the increasing availability of gravity gradient anomalies derived from satellite measurements, such as those provided by GOCE satellite, requires mathematical methods that directly model the gravity gradient anomalies in the same reference frame as GOCE gravity gradients. Our main purpose is to interpret these anomalies in terms of source and density distribution. Numerical integration methods for calculating gravity gradient values are generally based on a mass discretization obtained by decomposing the Earth's layers into a finite number of elementary solid bodies. In order to take into account the curvature of the Earth, spherical prisms or 'tesseroids' have been established unequivocally as accurate computation tools for determining the gravitational effects of large-scale structures. The question which then arises from, is whether gravity calculation methods using spherical prisms remain valid when factoring in the ellipticity of the Earth. In the paper, we outline a comprehensive method to numerically compute the complete gravity field with the help of the Gauss-Legendre quadrature involving ellipsoidal shaped prisms. The assessment of this new method is conducted by comparison between the gravity gradient values of simple sources obtained by means of numerical and analytical calculations, respectively. A comparison of the gravity gradients obtained from PREM and LITHO1.0 models using spherical-and ellipsoidal-prism-based methods is also presented. Numerical results indicate that the error on gravity gradients, caused by the use of the spherical prism instead of its ellipsoidal counterpart to describe an ellipsoidally shaped Earth, is useful for a joint analysis with those deduced from GOCE satellite measurements. Provided that a suitable scaling of prism densities has been performed, the spherical approximation error at GOCE height hardly reaches 1 mE for the entire Earth's lithosphere. The error attains 6 mE at a peak for a complete modeling of the Earth, from the crust down to the internal core. |
| Databáze: | OpenAIRE |
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