基于重力梯度张量曲率的边界识别

重力梯度张量曲率目前广泛用于重力数据的处理和解释中.为了拓宽重力梯度张量曲率的应用,本文回顾了重力梯度张量曲率的定义,从等位面的曲率定义出发,讨论了正确计算曲率的测量参考系及局部旋转的相关理论,并以单个球体和棱柱体为例来说明曲率的正确计算方式.然后,在正确计算重力梯度张量曲率的基础上,将重力梯度张量曲率应用到重力数据的边界识别中,通过理论模型和实际数据详细分析和比较了各种曲率在重力边界识别中的应用效果.结果表明:基于等位面的局部旋转坐标系是各种曲率正确计算的先决条件,纠正了曲率计算的误区;在边界识别中,局部坐标系下所计算的高斯曲率进行边界识别能够较好的圈定地下地质体的边界.

Edge detection based on curvature of gravity gradient tensors

Recently, the curvature of gravity gradient tensors is widely used in processing and interpretation of gravity data. In order to extend the application of this parameter, the local reference system based on the related theory of local rotation is discussed for the correct calculation of curvature using gravity vectors and gradient tensors. And a single sphere and prism as an example is taken to illustrate the correctness of this theory. Then, the correctly calculated curvature of gravity gradient tensors is applied to the edge detection of gravity data. Finally, using the synthetic models and real data, the application effect of various curvatures in edge detection was analyzed and discussed. The results show that the local rotation coordinate system based on the equipotential surface is a prerequisite for correct calculation of various curvatures, which corrects the misunderstanding in the calculation of the curvature. In the edge detection, the Gauss curvature calculated in the local coordinate system can better delineate the edge of the underground geological body.