paper with LaTex

xiao jia xiao
chhina university of geosciences wuhan


In this paper, eigenvalues of the full gravity gradient tensor (GGT) are used to detect edges of geological structure. First, the solving of GGT eigenvalues is discussed; then a new edge detection method is proposed by using the eigenvalues of GGT. Comparing with the pervious edge detection method based on curvature gravity gradient tensor (CGGT), the full gravity gradient tensor containsmore independent gradient components that are helpful to detect more subtle structures of the sources. The proposed method is applied to the synthetic data with and without noise to determine the locations of the edges of the mixed positive/negative contract density bodies. It has also been tested on real field data. All of the experimental results have shown that the newly proposed method is effective for edge detection.


Edge detection is Boldface the wordsrequired for interpretation of gravity field data,and has been widely used in tectonic studies and mineral explorations(Paterson 1985). To gain a better understanding of gravity sources,Italic some words; a variety of methods based on the use of directional derivatives aureplacedverbaa of different orders have been developed to locate anomalous source boundaries.

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In this paper,

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we propose an edge detection method based on the analysis of eigenvalues of GGT.

All things in their being are good for something.–nobody

Considering the actual geological situation, the positive and negative density bodies usually coexist simultaneously. The proposed has designed to outline the positive/negative density bodies with the corresponding values.

Full gravity gradient tensor and its eigenvalue analysis

Theory of GGT

The practical gradio meter systems for rapidly measuring GGT have been developed. Mikus and Hinojosa propose the method of approximating of the GGT from measured gravity data. The full gravity gradient tensor, symbol T, can be written in the form[eq.(1)] :
\[\label{eq.(1)} T = \begin{bmatrix} \frac{\partial^{2}U}{\partial_x^{2}} & \frac{\partial^{2}U}{\partial_ x\partial_y} & \frac{\partial^{2}U}{\partial_x\partial_x} \\ \frac{\partial^{2}U}{\partial_y\partial_x} & \frac{\partial^{2}U}{\partial_y^{2}} & \frac{\partial^{2}U}{\partial_y\partial_z} \\ \frac{\partial^{2}U}{\partial_z\partial_x} & \frac{\partial^{2}U}{\partial_z\partial_y} & \frac{\partial^{2}U}{\partial_z^{2}} \end{bmatrix} = \begin{bmatrix} g_{xx} & g_{xy} & g_{xz} \\ g_{yx} & g_{yy} & g_{yz}\\g_{zx} & g_{zy} & g_{zz} \end{bmatrix}\]

some eq or figure

in this subsection I will show a equation about GGT。
\[\label{eq.2} p = g_{xx}g_{yy} + g_{xx}g_{zz} + g_{yy}g_{zz}−g_{zx}g_{xz}−g_{xy}g_{yx}−g_{zy}g_{yz};\] \[\label{eq.3} q = g_{xy}g_{yz}g_{zx} + g_{xz}g_{yx}g_{zy} + g_{zx}g_{yy}g_{xz} + g_{xy}g_{yx}g_{zz} + g_{xx}g_{zy}g_{yz};\]

show fig

in this paragraph I will show how to create a fig . now I will create a fig in the next.

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Now we almost finish this manual.