Non-Singular Expressions for the Gravity Gradients in the Local North-Oriented and Orbital Reference Frames

Petrovskaya, M. S.; Vershkov, A. N.

doi:10.1007/s00190-006-0031-2

Cited by 64 publications

(10 citation statements)

References 11 publications

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“…These linear anomalies are most visible when plotting horizontal gradients of the gravity tensor (cf. Petrovskaya and Vershkov, 2006) and are plausibly the expression of ancient magmatic dikes that formed when the lunar lithosphere was in a state of extension.…”

Section: The Moonmentioning

confidence: 98%

Gravity and Topography of the Terrestrial Planets

Wieczorek¹

2015

Treatise on Geophysics

131

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Section: The Moonmentioning

confidence: 98%

Gravity and Topography of the Terrestrial Planets

Wieczorek¹

2015

Treatise on Geophysics

131

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“…In LNOF, where z has the geocentric radial downward direction, x points to the north, and y is directed to the east with a right-handed system, relationship between the LNOF and GSF can be described as in Eq. (2) (Reed 1973;Petrovskaya and Vershkov 2006).…”

Section: Ggt In the Spherical Coordinate Systemmentioning

confidence: 99%

3D inversion of full gravity gradient tensor data in spherical coordinate system using local north-oriented frame

Zhang

Yan

et al. 2018

Earth Planets Space

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In this paper, we propose an inverse method for full gravity gradient tensor data in the spherical coordinate system. As opposed to the traditional gravity inversion in the Cartesian coordinate system, our proposed method takes the curvature of the Earth, the Moon, or other planets into account, using tesseroid bodies to produce gravity gradient effects in forward modeling. We used both synthetic and observed datasets to test the stability and validity of the proposed method. Our results using synthetic gravity data show that our new method predicts the depth of the density anomalous body efficiently and accurately. Using observed gravity data for the Mare Smythii area on the moon, the density distribution of the crust in this area reveals its geological structure. These results validate the proposed method and potential application for large area data inversion of planetary geological structures.

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“…In the computations with a simulated input, the EGM2008 gravitational field model (Pavlis et al 2008) and the GRS80 ellipsoid (Moritz 2000) are used. Thus, we will move from the gravitational potential to the disturbing potential defined as T = W (EGM2008) − U (GRS80), where the centrifugal part in W is considered to be equal to that of GRS80.…”

Section: Numerical Investigationsmentioning

confidence: 99%

“…The standard procedure usually neglects the specific orientation of data and reduces measured values for the dominant ellipsoidal effects (Pavlis 1988). The resulting spherical data such as the gravity anomaly or disturbance are then inverted to the geopotential coefficients.…”

Section: Introductionmentioning

confidence: 99%

“…The first is a closed-loop test with simulated data and as such it confirms the concept and the codes. In the second test, we discuss the ellipsoidal correction that usually compensates the problem of the vertical when the gravity anomaly/disturbance is to be processed with standard formula in the spherical approximation (Jekeli 1981;Cruz 1986;Pavlis 1988;Najafi-Alamdari et al 2006). The accuracy of this correction is verified through the least squares spherical harmonic analysis (LS SHA) of data on the reference ellipsoid.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Short guide to direct gravitational field modelling with Hotine’s equations

Sebera

Wagner

Bezděk

et al. 2012

J Geod

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This paper presents a unified approach to the least squares spherical harmonic analysis of the acceleration vector and Eötvös tensor (gravitational gradients) in an arbitrary orientation. The Jacobian matrices are based on Hotine's equations that hold in the Earth-fixed Cartesian frame and do not need any derivatives of the associated Legendre functions. The implementation was confirmed through closedloop tests in which the simulated input is inverted in the least square sense using the rotated Hotine's equations. The precision achieved is at the level of rounding error with RMS about 10 −12 −10 −14 m in terms of the height anomaly. The second validation of the linear model is done with help from the standard ellipsoidal correction for the gravity disturbance that can be computed with an analytic expression as well as with the rotated equations. Although the analytic expression for this correction is only of a limited accuracy at the submillimeter level, it was used for an independent validation. Finally, the equivalent of the ellipsoidal correction, called the effect of the normal, has been numerically obtained also for other gravitational functionals and some of their combinations. Most of the numerical investigations are provided up to spherical harmonic degree 70, with degree 80 for the computation time comparison using real GRACE data. The relevant Matlab source codes for the design matrices are provided.

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Non-Singular Expressions for the Gravity Gradients in the Local North-Oriented and Orbital Reference Frames

Cited by 64 publications

References 11 publications

Gravity and Topography of the Terrestrial Planets

Gravity and Topography of the Terrestrial Planets

3D inversion of full gravity gradient tensor data in spherical coordinate system using local north-oriented frame

Short guide to direct gravitational field modelling with Hotine’s equations

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