对重力势二阶垂直偏导数的一种新的取样方法

A new simple equation to second vertical derivative of gravitational potential field's determination

从目前的研究来看,二阶垂直导数(X和Y两个方向)的求解方法较简单,它采用的五个因子的数字滤波的最小二乘法来优化数据。但是在较小区域面积时(对工程和环境应用中的重力数据),重力异常很容易放大和被区域重力场掩盖,我们认为产生的缘由是表示重力场的x和y方向上的二次多项式引起的。因此,为了逼近重力水平方向的偏导可以设计一个好的滤波器来拟合在xy平面的重力场值,再得出想要的重力垂直方向偏导,文中最后对提出的方法在前人经典模型上和野外实践进行了验证。

The present work proposed a simple computation of the second horizontal derivatives of gravitational potential fields （in both X and Y directions）using a digital filter of five operators that is designed to fit the data in the least-square concept. In relatively small areas （gravity data collected in engineering and environmental applications） the anomalies have small amplitudes and are easily obscured by the regional gravity field,we consider that it is caused due to a second order polynomial along X and Y axis which represents the gravity field. Thus, in order to approximate the horizontal derivatives, a digital filter has been well designed to fit the gravity values on the X -Y plane and thus yield the desired vertical variation. The proposed equation has been tested and verified on the predecessors＇theoretical models as well as by the field practises.