scholarly journals Interpreting the direction of the gravity gradient tensor eigenvectors: The main tidal force and its relation to the curvature parameters of the equipotential surface

2016 ◽  
Vol 2016 (1) ◽  
pp. 1-8
Author(s):  
Carlos Cevallos
Keyword(s):  
Equipotential Surface ◽  
Tidal Force ◽  
Gravity Gradient ◽  
Gradient Tensor ◽  
Gravity Gradient Tensor

Interpreting the direction of the gravity gradient tensor eigenvectors: Their relation to curvature parameters of the gravity field

Geophysics ◽  
2016 ◽  
Vol 81 (3) ◽  
pp. G49-G57 ◽  
Author(s):  
Carlos Cevallos
Keyword(s):  
Equipotential Surface ◽  
Vertical Axis ◽  
Tidal Force ◽  
Airborne Gravity ◽  
Gravity Gradient ◽  
Gravity Gradiometer ◽  
Model Data ◽  
Gradient Tensor ◽  
Gravity Gradient Tensor ◽  
Canning Basin

Rotating the gravity gradient tensor about a vertical axis by an appropriate angle allows one to express its components as functions of the curvatures of the equipotential surface. The description permits the identification of the gravity gradient tensor as the Newtonian tidal tensor and part of the tidal potential. The identification improves the understanding and interpretation of gravity gradient data. With the use of the plunge of the eigenvector associated with the largest eigenvalue or plunge of the main tidal force, it is possible to estimate the location and depth of buried gravity sources; this is developed in model data and applied to FALCON airborne gravity gradiometer data from the Canning Basin, Australia.

Understanding curvatures of the equipotential surface in gravity gradiometry

Geophysics ◽  
2018 ◽  
Vol 83 (4) ◽  
pp. G35-G45
Author(s):  
Yaoguo Li
Keyword(s):  
Coordinate System ◽  
Local Coordinate System ◽  
Practical Importance ◽  
Equipotential Surface ◽  
Vertical Axis ◽  
Gravity Gradient ◽  
Gravity Gradiometry ◽  
Gradient Tensor ◽  
Gravity Gradient Tensor ◽  
Equipotential Surfaces

The concept of curvatures of equipotential surfaces is of theoretical and practical importance in gravity gradiometry because curvatures describe the shape of equipotential surfaces, which can yield information about the shape of the source. Although the fundamentals of curvatures are well-established, their connection to modern gravity gradiometry and the associated applications in exploration geophysics remain areas of active research. In particular, there is a misunderstanding in the calculation of the said curvatures directly from measured gravity gradient data that are now widely used in exploration geophysics. The error stems from the incorrect use of the formulas in a fixed user coordinate system that are only valid in a rotated coordinate system. We demonstrate that the gravity gradient tensor must be rotated to a local coordinate system whose vertical axis is aligned with the local anomalous gravity field direction so that the curvatures of the anomalous equipotential surface can be calculated correctly using these classic formulas. To facilitate practical application, we present theoretical and practical aspects related to coordinate systems and rotations of the gravity gradient tensor. We have also developed an approach for estimating local gravity for use in the curvature calculation by wavenumber-domain conversion from gradient tensors. The procedure may form a basis for developing new interpretation techniques in gravity gradient gradiometry based on curvatures.

Speed and accuracy improvements in standard algorithm for prismatic gravitational field

2020 ◽  
Vol 222 (3) ◽  
pp. 1898-1908
Author(s):  
Toshio Fukushima
Keyword(s):  
Gravitational Field ◽  
Exact Formula ◽  
New Method ◽  
Gravity Gradient ◽  
Gradient Tensor ◽  
Gravity Gradient Tensor ◽  
Triple Difference ◽  
Transcendental Functions ◽  
Arctangent Function ◽  
Speed And Accuracy

SUMMARY By utilizing the addition theorems of the arctangent function and the logarithm, we developed a new expression of Bessel’s exact formula to compute the prismatic gravitational field using the triple difference of certain analytic functions. The use of the new expression is fast since the number of transcendental functions required is significantly reduced. The numerical experiments show that, in computing the gravitational potential, the gravity vector, and the gravity gradient tensor of a uniform rectangular parallelepiped, the new method runs 2.3, 2.3 and 3.7 times faster than Bessel’s method, respectively. Also, the new method achieves a slight increase in the computing precision. Therefore, the new method can be used in place of Bessel’s method in any situation. The same approach is applicable to the geomagnetic field computation.

Noise filtering of full-gravity gradient tensor data

2013 ◽  
Vol 10 (3) ◽  
pp. 241-250 ◽  
Author(s):  
Yuan Yuan ◽  
Da-Nian Huang ◽  
Qing-Lu Yu ◽  
Mei-Xia Geng
Keyword(s):  
Gravity Gradient ◽  
Noise Filtering ◽  
Gradient Tensor ◽  
Gravity Gradient Tensor ◽  
Tensor Data

Estimative of gravity-gradient tensor components via fast iterative equivalent-layer technique

2019 ◽  
Author(s):  
Larissa S. Piauilino ◽  
Fillipe C. L. Siqueira ◽  
Vanderlei C. Oliveira ◽  
Valeria C. F. Barbosa
Keyword(s):  
Gravity Gradient ◽  
Gradient Tensor ◽  
Gravity Gradient Tensor ◽  
Layer Technique ◽  
Equivalent Layer
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