用边界单元法计算任意形体的重力异常及其导数

THE CALCULATION OF THE GRAVITATIONAL ANOMALY AND ITS DERIVATIVE OF THE GEOLOGIC BODY WITH ABITRARY CONFIGURATION BY BOUNDARY-ELEMENTS METHOD

中国科学技术大学

任意形体的重力异常的计算通常用量板法或积分法进行。量板法的效率和精度都较低。用积分法计算时,二维形体用面积分,三维形体用体积分。本文提出用边界单元法计算重力异常,二维形体用线积分,三维形体用表面积分。由于积分阶数降低,计算时间缩短,计算精度将提高,而且边界单元法也便于计算重力位的高阶导数。

The conventional way of calculation of the gravitational anomals of the geologic body with arbitrary figuration is performed by template or integration process. The efficiency and the accuracy of the template process are not so high as reguired. As for the integration, the surface integral is used if the geological body is a 2-D object and the volume integral is used if it is a 3-D object. Tt is suggested in this paper that the calculation of the gravitational anomaly is performed by boundary elements method,curvilinear integral is for 2-D object and surface integral for 3-D object. Because of less integral order and timesaving, so that we can expect better accuracy. In addition, the boundary elements method is available to the high-order derivatives of the gravitational potential.