Alternative expressions for gravity gradients in local north-oriented frame and tensor spherical harmonics

Eshagh, Mehdi

doi:10.2478/s11600-009-0048-z

Cited by 38 publications

(25 citation statements)

References 14 publications

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“…Since the local gravitational gradient changes are of interest here, the local north-east-down (NED) frame at a point with spherical coordinates (r, h, k) is introduced: the x-axis is directed to the north, the y-axis to the east and the z-axis downwards. The full gravitational gradient tensor (second derivatives of the gravitational potential) in this local NED frame is represented in Eshagh (2009) and Eshagh and Abdollahzadeh (2012). Because of the correlated errors in the high-frequency components of GRACE data, 'destriping' and filtering techniques are commonly applied to obtain estimates of the timevariable signals.…”

Section: Gravitational Gradient Changes Using Grace Coefficientsmentioning

confidence: 99%

Computation of the changes in gravitational gradient components from GRACE observations and analytical model

2015

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In this study the gravitational gradient changes caused by faulting on a finite rectangular plane buried in a homogenous half-space are computed using an analytical model which is a function of fault parameters. The sensitivity analysis of the analytical model with optional parameters revealed that the model is sensitive to the most of the fault parameters such as slip, depth, dip and is not sensitive to the strike. Also the results show that the model is sensitive to the length and the width of the fault. Moreover, the gravitation and gravitational gradient changes for the case of the Maule earthquake on 27 February 2010 are directly computed by GRACE observations without need to fault parameters information. Since the high-frequency contents in gravitational field variation can be amplified by deriving the gravitational gradients, the GRACE-derived coseismic gravitational gradient changes clearly delineate the fault lines and better define the extent of the coseismic deformation.

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Section: Gravitational Gradient Changes Using Grace Coefficientsmentioning

confidence: 99%

Computation of the changes in gravitational gradient components from GRACE observations and analytical model

2015

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“…Here, Fennoscandia, limited between latitudes of 50 N to 75 N and longitudes of 0 N to 35 N, is considered as the test area. We use the nonsingular expressions of the gravity gradients presented by Eshagh (2009b) as well as the vectorised models presented for their programming by Abdollahzadeh (2010, 2011). We considered a larger area by 9 than Fennoscandia as required for integration.…”

Section: Numerical Studiesmentioning

confidence: 99%

From Tensor to Vector of Gravitation

Eshagh

2014

Artificial Satellites

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Different gravitational force models are used for determining the satellites' orbits. The satellite gravity gradiometry (SGG) data contain this gravitational information and the satellite accelerations can be determined from them. In this study, we present that amongst the elements of the gravitational tensor in the local north-oriented frame, all of the elements are suitable for this purpose except Txy. Three integral formulae with the same kernel function are presented for recovering the accelerations from the SGG data. The kernel of these integrals is well-behaving which means that the contribution of the far-zone data is not very significant to their integration results; but this contribution is also dependent on the type of the data being integrated. Our numerical studies show that the standard deviations of the differences between the accelerations recovered from Tzz, Txz and Tyz and those computed by an existing Earth´s gravity model reduce by increasing the cap size of integration. However, their root mean squared errors increase for recovering Ty from Tyz. Larger cap sizes than 5 on is recommended for recovering Tx and Tz but smaller ones for Ty.

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“…In this study we consider the local north-oriented frame which is defined as one whose z-axis is pointing upwards in geocentric radial direction, x-axis towards the north and the frame is righthanded, implying that y-axis is directed to the west. The non-singular expressions for the gradients in such a frame are (Eshagh 2009c):…”

Section: Synthesis Of Gravity Gradients In Local Framementioning

confidence: 99%

“…Three combinations of the gradients are used and called vertical-vertical, vertical-horizontal and horizontalhorizontal GBVP (VVGBVP, VHGBVP and HHGBVP). Based on these boundary values three sets of solutions for the geopotential coefficients are obtained (Martinec 2003 andEshagh 2009c):…”

Section: Synthesis Of Gravity Gradients In Local Framementioning

confidence: 99%

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Semi-vectorization: an efficient technique for synthesis and analysis of gravity gradiometry data

Eshagh

Abdollahzadeh

2010

Earth Sci Inform

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The harmonic synthesis and analysis of the elements of gravitational tensor can be done in few minutes if a suitable programming algorithm is used. Vectorization is an efficient technique for such processes, but the size of matrices will increase when the resolution of synthesis or analysis is high; say higher than 0.5°×0.5°. Here, we present a technique to manage the computer memory and computational time by excluding one computational loop from the matrix products and we call this method semivectorization. Based on this technique, we synthesize the gravitational tensor using the EGM96 geopotential model and after that we analyze the tensor for recovering the geopotential coefficients. MATLAB codes are provided which are able to analyze 224 millions gradiometric data, corresponding to a global grid of 2.5′×2.5′ on a sphere in 1,093 s by a personal computer with 2 Gb RAM.

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Alternative expressions for gravity gradients in local north-oriented frame and tensor spherical harmonics

Cited by 38 publications

References 14 publications

Computation of the changes in gravitational gradient components from GRACE observations and analytical model

Computation of the changes in gravitational gradient components from GRACE observations and analytical model

From Tensor to Vector of Gravitation

Semi-vectorization: an efficient technique for synthesis and analysis of gravity gradiometry data

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