https://github.com/leouieda/agu2010

Abstract and slides of "Computation of the gravity gradient tensor due to topographic masses using tesseroids" presented at the 2010 AGU Meeting of the Americas
https://github.com/leouieda/agu2010

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Abstract and slides of "Computation of the gravity gradient tensor due to topographic masses using tesseroids" presented at the 2010 AGU Meeting of the Americas

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• URL: https://github.com/leouieda/agu2010
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Figures, abstract and slides for the presentation given at the 2010 AGU Meeting

of the Americas in Foz do Iguaçu, Brazil.

Slides in PDF format available on figshare:

[doi:10.6084/m9.figshare.156858](http://dx.doi.org/10.6084/m9.figshare.156858)

Citation:

Uieda, L., N. Ussami, and C. F. Braitenberg (2010), Computation of the

gravity gradient tensor due to topographic masses using tesseroids, Eos

Trans. AGU, Meet. Am. Suppl., vol. 91, Abstract G22A-04

# Computation of the gravity gradient tensor due to topographic masses using tesseroids

**Leonardo Uieda, Naomi Ussami, and Carla Braitenberg**

The GOCE satellite mission has the objective of measuring the Earth's

gravitational field with an unprecedented accuracy through the measurement of

the gravity gradient tensor (GGT).  One of the several applications of this new

gravity data set is to study the geodynamics of the lithospheric plates, where

the flat Earth approximation may not be ideal and the Earth's curvature should

be taken into account. In such a case,  the Earth could be modeled using

tesseroids, also called spherical prisms, instead of the conventional

rectangular prisms. The GGT due to a tesseroid is  calculated using numerical

integration methods, such as the Gauss-Legendre Quadrature (GLQ), as already

proposed by Asgharzadeh et al. (2007) and Wild-Pfeiffer (2008).  We present a

computer program for the direct computation of the GGT caused by a tesseroid

using the GLQ. The accuracy of this implementation was evaluated by comparing

its results with the result of analytical formulas for the special case of a

spherical cap with computation point located at one of the poles. The GGT due

to the topographic masses of the Parana basin (SE Brazil) was estimated at 260km

altitude in an attempt to quantify this effect on the GOCE gravity data. The

digital elevation model ETOPO1 (Amante and Eakins, 2009) between 40º W and 65º W

and 10º S and 35º S, which includes the  Paraná Basin, was  used to generate a

tesseroid model of the topography with grid spacing of 10' x 10' and a constant

density of 2670 kg/m3. The largest amplitude  observed was on the second

vertical derivative component (-0.05 to 1.20 Eötvos) in regions of rough

topography, such as that along the eastern Brazilian continental margins. These

results indicate that the GGT due to topographic masses may have amplitudes of

the same order of magnitude as the GGT due to density anomalies within  the

crust and mantle.

**References**

Amante, C., Eakins, B.W., 2009. ETOPO1 1 Arc-Minute Global Relief Model:

Procedures, Data Sources and Analysis. NOAA Technical Memorandum NESDIS

NGDC-24, p. 19.

Asgharzadeh, M.F.; Von Frese, R.R.B.; Kim, H.R.; Leftwich, T.E.; Kim, J.W.,

2007. Spherical prism gravity effects by Gauss-Legendre quadrature integration.

Geophysics Journal International, v. 169, p. 1 - 11.

Wild-Pfeiffer, F., 2008. A comparison of different mass elements for use in

gravity gradiometry. Journal of Geodesy, v. 82 (10), p. 637 - 653.