The Gravity Anomaly of a 2D Polygonal Body Having Density Contrast Given by Polynomial Functions
The Gravity Anomaly of a 2D Polygonal Body Having Density Contrast Given by Polynomial Functions
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DOI：
10.1007/s10712-015-9317-3
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发表时间：
2015-01
影响因子：
4.6
通讯作者：
M. D'Urso
中科院分区：
文献类型：
--
作者：
M. D'Urso
本文给出了任意几何形状的二维物体产生的重力异常的解析解，其中密度差在水平和垂直方向上均为多项式函数。近似的真实的形状的身体的多边形，解决方案表示为代数量的总和，只依赖于坐标的顶点的多边形和多项式密度函数。本文中提出的解决方案，它是指一个三阶多项式函数作为最大值，表现出内在的对称性，自然表明其扩展到高阶多项式描述的密度对比度的情况下。此外，在任意点处评估重力异常，该任意点不一定与分配密度函数的参考框架的原点重合。与位势理论的最新结果相比较，本文所导出的解是无奇异性的，数值上是稳健的。与现有文献中的算例进行了数值比较，证明了该方法的准确性和有效性。
An analytical solution is presented for the gravity anomaly produced by a 2D body whose geometrical shape is arbitrary and where the density contrast is a polynomial function in both the horizontal and vertical directions. Approximating the real shape of the body by a polygon, the solution is expressed as sum of algebraic quantities that depend only upon the coordinates of the vertices of the polygon and upon the polynomial density function. The solution presented in the paper, which refers to a third-order polynomial function as a maximum, exhibits an intrinsic symmetry that naturally suggests its extension to the case of higher-order polynomials describing the density contrast. Furthermore, 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. Invoking recent results of potential theory, the solution derived in the paper is shown to be singularity-free and numerically robust. The accuracy and effectiveness of the proposed approach is witnessed by the numerical comparisons with examples derived from the existing literature.