Gravity anomalies of arbitrary 3D polyhedral bodies with horizontal and vertical mass contrasts up to cubic order
Gravity anomalies of arbitrary 3D polyhedral bodies with horizontal and vertical mass contrasts up to cubic order
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水平和垂直质量对比高达立方级的任意 3D 多面体的重力异常
DOI：
10.1190/geo2017-0219.1
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发表时间：
2018-01-01
期刊：
影响因子：
3.3
通讯作者：
Pan, Kejia
中科院分区：
文献类型：
--
作者：
Ren, Zhengyong;Zhong, Yiyuan;Pan, Kejia
利用三次多项式函数，推导出了具有水平和垂直变密度对比度的任意三维多面体质量体的重力场的新的无奇异性解析公式。首先，将观测点移动到坐标系的原点。然后，依次调用体积积分和曲面积分定理，将体积积分转化为多边形面上的表面积分和多面体质量体边缘上的线积分。在此基础上，给出了边界上这些线积分的无奇异性闭合解。因此，观察点可以位于3D分布的内部、之上或外部。采用一个合成的棱柱质量体来验证我们新发展的解析表达式的准确性和无奇异性。我们的解决方案与其他已发布的封闭形式解决方案之间获得了极好的一致，相对误差在10−12%到10−13%的量级。在一个……
ABSTRACTA new singularity-free analytical formula has been developed for the gravity field of arbitrary 3D polyhedral mass bodies with horizontally and vertically varying density contrast using third-order polynomial functions. First, the observation sites are moved to the origin of the coordinate system. Then, the volume and surface integral theorems are invoked successively to transform the volume integrals into surface integrals over polygonal faces and into line integrals over the edges of the polyhedral mass bodies. Furthermore, singularity-free closed-form solutions are derived for these line integrals over the edges. Thus, the observation sites can be located inside, on, or outside the 3D distributions. A synthetic prismatic mass body is adopted to verify the accuracy and singularity-free property of our newly developed analytical expressions. Excellent agreements are obtained between our solutions and other published closed-form solutions with relative errors in the order of 10−12% to 10−13%. In a...