The gravitational potential and its derivatives for the prism

Nagy, D.; Papp, Gábor; Benedek, Judit

doi:10.1007/s001900000116

Cited by 347 publications

(203 citation statements)

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“…Over 65,000 terrain-corrected Bouguer gravity measurements for this region were obtained from the Pan-American Center for Earth and Environmental Studies (PACES) U.S. gravity database [Keller et al, 2006]. Bouguer gravity at each surface location is predicted from the density model by first calculating the vertical gravitation due to each model block with the analytic solution for a rectangular prism [Nagy et al, 2000], which reduces near-surface discretization effects. Numeric volume integration is then performed to obtain total gravitation.…”

Section: Flexure and Gravity Modelingmentioning

confidence: 99%

“…calculating the vertical gravitation due to each model block with the analytic solution for a rectangular prism [Nagy et al, 2000]: where x ¼ x y ½ is the horizontal position vector of the model block relative to the observation location where g z is measured, G is the gravitational constant, and r¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x 2 þ y 2 þ z 2 p is the block distance. Numeric volume integration is then performed to obtain total gravitation.…”

Section: A12 Gravity Modelingmentioning

confidence: 99%

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A rootless rockies—Support and lithospheric structure of the Colorado Rocky Mountains inferred from CREST and TA seismic data

Hansen

Dueker

Stachnik

et al. 2013

Geochem Geophys Geosyst

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[1] Support for the Colorado high topography is resolved using seismic data from the Colorado Rocky Mountain (CRM) Experiment and Seismic Transects. The average crustal thickness, derived from P wave receiver function imaging, is 48 km. However, a negative correlation between Moho depth and elevation is observed, which negates Airy-Heiskanen isostasy. Shallow Moho (<45 km depth) is found beneath some of the highest elevations, and therefore, the CRM are rootless. Deep Moho (45-51 km) regions indicate structure inherited from the Proterozoic assembly of the continent. Shear wave velocities from surface wave tomography are mapped to density employing empirical velocity-to-density relations in the crust and mantle temperature modeling. Predicted elastic plate flexure and gravity fields derived from the density model agree with observed long-wavelength topography and Bouguer gravity. Therefore, lowdensity crust and mantle are sufficient to support much of the CRM topography. Centers of Oligocene volcanism, e.g., the San Juan Mountains, display reduced crustal thicknesses and lowest average crustal velocities, suggesting that magmatic modification strongly influenced modern lithospheric structure and topography. Mantle velocities span 4.02-4.64 km/s at 73-123 km depth, and peak lateral temperature variations of 600 C are inferred. S wave receiver function imaging suggests that the lithosphereasthenosphere boundary is 100-150 km deep beneath the Colorado Plateau, and 150-200 km deep beneath the High Plains. A region of negative arrivals beneath the CRM above 100 km depth correlates with low mantle velocities and is interpreted as thermally modified/metasomatized lithosphere resulting from Cenozoic volcanism.

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Section: Flexure and Gravity Modelingmentioning

confidence: 99%

Section: A12 Gravity Modelingmentioning

confidence: 99%

A rootless rockies—Support and lithospheric structure of the Colorado Rocky Mountains inferred from CREST and TA seismic data

Hansen

Dueker

Stachnik

et al. 2013

Geochem Geophys Geosyst

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“…The first term on the right-hand side of equation (4) is equivalent to the contribution of a constant density prism [Nagy et al, 2000]. The second term is related to the density gradient g. Similarly, the corresponding geoid anomaly for the same prism is [Fullea, 2008]:…”

Section: Gravity and Geoid Anomaliesmentioning

confidence: 99%

LitMod3D: An interactive 3‐D software to model the thermal, compositional, density, seismological, and rheological structure of the lithosphere and sublithospheric upper mantle

Fullea¹,

Afonso

Connolly

et al. 2009

Geochem Geophys Geosyst

123

166

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[1] We present an interactive 3-D computer program (LitMod3D) developed to perform combined geophysical-petrological modeling of the lithosphere and sublithospheric upper mantle. In contrast to other available modeling software, LitMod3D is built within an internally consistent thermodynamicgeophysical framework, where all relevant properties are functions of temperature, pressure, and composition. By simultaneously solving the heat transfer, thermodynamic, rheological, geopotential, and isostasy (local and flexural) equations, the program outputs temperature, pressure, surface heat flow, density (bulk and single phase), seismic wave velocities, geoid and gravity anomalies, elevation, and lithospheric strength for any given model. These outputs can be used to obtain thermal and compositional models of the lithosphere and sublithospheric upper mantle that simultaneously fit all available geophysical and petrological observables. We illustrate some of the advantages and limitations of LitMod3D using synthetic models and comparing our predictions with those from other modeling methods. In particular, we show that (1) temperature at midlithosphere depths may be overestimated by as much as 200 K when compositional heterogeneities in the mantle and T-P effects are not considered in lithospheric models and (2) the neglect of mantle phase transformations on gravity-based models in thin-crust settings can result in a significant overestimation and underestimation of the derived crustal thickness and its internal density distribution, respectively.

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“…Then the strict formulas of rectangular prisms (c.f., Holstein 2003, Nagy et al 2000 were simplified to simple point masses, and Eq. (3) was used.…”

Section: Calculations For Metromentioning

confidence: 99%

Various parameterizations of “latitude” equation – Cartesian to geodetic coordinates transformation

Ligas

2013

Journal of Geodetic Science

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Abstract:The paper presents a solution to one of the basic problems of computational geodesy -conversion between Cartesian and geodetic coordinates on a biaxial ellipsoid. The solution is based on what is known in the literature as "latitude equation". The equation is presented in three different parameterizations commonly used in geodesy -geodetic, parametric (reduced) and geocentric latitudes. Although the resulting equations may be derived in many ways, here, we present a very elegant one based on vectors orthogonality. As the "original latitude equations" are trigonometric ones, their representation has been changed into an irrational form after Fukushima (1999Fukushima ( , 2006. Furthermore, in order to avoid division operations we have followed Fukushima's strategy again and rewritten the equations in a fractional form (a pair of iterative formulas). The resulting formulas involving parametric latitude are essentially the same as those introduced by

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The gravitational potential and its derivatives for the prism

Cited by 347 publications

References 0 publications

A rootless rockies—Support and lithospheric structure of the Colorado Rocky Mountains inferred from CREST and TA seismic data

A rootless rockies—Support and lithospheric structure of the Colorado Rocky Mountains inferred from CREST and TA seismic data

LitMod3D: An interactive 3‐D software to model the thermal, compositional, density, seismological, and rheological structure of the lithosphere and sublithospheric upper mantle

Various parameterizations of “latitude” equation – Cartesian to geodetic coordinates transformation

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