Gravity Anomaly of Polyhedral Bodies Having a Polynomial Density Contrast
Gravity Anomaly of Polyhedral Bodies Having a Polynomial Density Contrast
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DOI：
10.1007/s10712-017-9411-9
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发表时间：
2017-04
影响因子：
4.6
通讯作者：
M. D'Urso;S. Trotta
中科院分区：
文献类型：
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作者：
M. D'Urso;S. Trotta
我们分析评估重力异常与多面体体具有任意的几何形状和多项式密度对比在水平和垂直方向。重力异常在任意点处进行评估，该任意点不一定与分配密度函数的参考系的原点重合。密度对比度被假设为三阶多项式作为最大值，但在本文中利用的一般方法可以很容易地扩展到高阶多项式函数。与位势理论的最新结果相反，本文所导出的解是无奇异性的，并表示为仅依赖于多面体顶点的三维坐标和多项式密度函数的代数量之和.所提出的方法的准确性，鲁棒性和有效性的数值比较来自现有文献的例子说明。
We analytically evaluate the gravity anomaly associated with a polyhedral body having an arbitrary geometrical shape and a polynomial density contrast in both the horizontal and vertical directions. The gravity anomaly is evaluated at an arbitrary point that does not necessarily coincide with the origin of the reference frame in which the density function is assigned. Density contrast is assumed to be a third-order polynomial as a maximum but the general approach exploited in the paper can be easily extended to higher-order polynomial functions. Invoking recent results of potential theory, the solution derived in the paper is shown to be singularity-free and is expressed as a sum of algebraic quantities that only depend upon the 3D coordinates of the polyhedron vertices and upon the polynomial density function. The accuracy, robustness and effectiveness of the proposed approach are illustrated by numerical comparisons with examples derived from the existing literature.