Optimum expression for computation of the gravity field of a polyhedral body with linearly increasing density

Pohánka, V.

doi:10.1046/j.1365-2478.1998.960335.x

Cited by 65 publications

(46 citation statements)

References 2 publications

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“…Currently, the 3D interpretive methods using the so-called polyhedrons (i.e. the bodies bounded by a polygonal surfaces (facets)) are applied frequently (e.g., Bott 1963;Nagy 1966;Okabe 1979;Hansen & Wang 1988in Blakely 1996Pohánka 1988Pohánka , 1998. This category also includes the software IGMAS (Interactive Gravity and Magnetics Application System), which is a tool applied for the interpretation of observed gravity and magnetic fields.…”

Section: Introductionmentioning

confidence: 99%

3D density modelling of Gemeric granites of the Western Carpathians

Šefara¹,

Bielik²,

Vozár³

et al. 2017

Geologica Carpathica

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Abstract:The position of the Gemeric Superunit within the Western Carpathians is unique due to the occurrence of the Lower Palaeozoic basement rocks together with the autochthonous Upper Palaeozoic cover. The Gemeric granites play one of the most important roles in the framework of the tectonic evolution of this mountain range. They can be observed in several small intrusions outcropping in the western and south-eastern parts of the Gemeric Superunit. Moreover, these granites are particularly interesting in terms of their mineralogy, petrology and ages. The comprehensive geological and geophysical research of the Gemeric granites can help us to better understand structures and tectonic evolution of the Western Carpathians. Therefore, a new and original 3D density model of the Gemeric granites was created by using the interactive geophysical program IGMAS. The results show clearly that the Gemeric granites represent the most significant upper crustal anomalous low-density body in the structure of the Gemeric Superunit. Their average thickness varies in the range of 5-8 km. The upper boundary of the Gemeric granites is much more rugged in comparison with the lower boundary. There are areas, where the granite body outcrops and/or is very close to the surface and places in which its upper boundary is deeper (on average 1 km in the north and 4-5 km in the south). While the depth of the lower boundary varies from 5-7 km in the north to 9-10 km in the south. The northern boundary of the Gemeric granites along the tectonic contact with the Rakovec and Klátov Groups (North Gemeric Units) was interpreted as very steep (almost vertical). The results of the 3D modelling show that the whole structure of the Gemeric Unit, not only the Gemeric granite itself, has an Alpine north-vergent nappe structure. Also, the model suggests that the Silicicum-Turnaicum and Meliaticum nappe units have been overthrusted onto the Golčatov Group.

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Section: Introductionmentioning

confidence: 99%

3D density modelling of Gemeric granites of the Western Carpathians

Šefara¹,

Bielik²,

Vozár³

et al. 2017

Geologica Carpathica

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“…Artemjev et al 1994). Combining the benefits of using more generalized geometrical bodies and taking into account density variation models, Pohánka (1998) introduced the expression for the attraction of an arbitrary polyhedral body having a linearly varying density by means of line integrals. The alternative expression was derived by Hansen (1999).…”

Section: Introductionmentioning

confidence: 99%

“…Holstein (2003) generalized their work deriving the formulae also for the potential and its second derivatives. To avoid singular terms and obtain a maximal numerical efficiency, Pohánka (1998) in his study derived the optimum expression and proposed a simple computational algorithm for computing the gravitational attraction.…”

Section: Introductionmentioning

confidence: 99%

“…Following the concept used by Pohánka (1988Pohánka ( , 1998 in this study we derive the optimum expression for computing the gravitational potential of an arbitrary polyhedral body having a linearly varying density. The optimum expression for the gravitational potential of the polyhedral body having a homogeneous density is given in Pohánka (1988).…”

Section: Introductionmentioning

confidence: 99%

“…In comparison to the formula for the potential given by Holstein (2003), the main advantage of adopting the computational strategy developed by Pohánka (1988Pohánka ( , 1998) is that our expression does not have the singular terms. We also demonstrate that the computational algorithm for computing the attraction proposed by Pohánka (1998) can directly be applied for computing the potential. The potential of an arbitrary polyhedral body having a linearly varying density by means of line integrals is derived in Sect.…”

Section: Introductionmentioning

confidence: 99%

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The optimum expression for the gravitational potential of polyhedral bodies having a linearly varying density distribution

Hamayun

Prutkin

Tenzer

2009

J Geod

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When topography is represented by a simple regular grid digital elevation model, the analytical rectangular prism approach is often used for a precise gravity field modelling at the vicinity of the computation point. However, when the topographical surface is represented more realistically, for instance by a triangular irregular network (TIN) model, the analytical integration using arbitrary polyhedral bodies (the analytical line integral approach) can be implemented directly without additional data pre-processing (gridding or interpolation). The analytical line integral approach can also facilitate 3-D density models created for complex geometrical bodies. For the forward modelling of the gravitational field generated by the geological structures with variable densities, the analytical integration can be carried out using polyhedral bodies with a varying density. The optimal expression for the gravitational attraction vector generated by an arbitrary polyhedral body having a linearly varying density is known. In this article, the corresponding optimal expression for the gravitational potential is derived by means of line integrals after applying the Gauss divergence theorem.

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A Remark on the Computation of the Gravitational Potential of Masses with Linearly Varying Density

D’Urso

2015

VIII Hotine-Marussi Symposium on Mathematical Geodesy

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Optimum expression for computation of the gravity field of a polyhedral body with linearly increasing density

Abstract: The formula for the computation of the gravity field of a polyhedral body with density linearly depending on some coordinate is derived and transformed in the optimum form for numerical calculation.

Cited by 65 publications

References 2 publications

3D density modelling of Gemeric granites of the Western Carpathians

3D density modelling of Gemeric granites of the Western Carpathians

The optimum expression for the gravitational potential of polyhedral bodies having a linearly varying density distribution

A Remark on the Computation of the Gravitational Potential of Masses with Linearly Varying Density

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