论文部分内容阅读
曲面位场导数的换算方法大多基于调和函数的积分方程数值解。本文提出了基于B样条函数的曲面上位场导数直接计算法。引入按弧长S作变量的三次样条插值,得出了位场水平导数的计算式。该方法还有一个特点,那就是可以用一元样条来实现曲面上的求导。这些,都决定了该方法的简便性和精确性。利用曲线上和曲面上的两种理论模型进行试算,分别计算了Zα/x和Δg/Z~2计算和理论的结果对比表明,符合很好。误差主要取决于曲面起伏大小,异常变化陡度和取样的间隔。
Most of the conversion methods of the surface field derivatives are based on the numerical solution of the integral equation of the harmonic function. In this paper, we propose a direct method of calculating the field derivative on a surface based on B-spline function. The cubic spline interpolation according to the arc length S is introduced to obtain the formula of horizontal derivative of the field. Another characteristic of this method is that it is possible to use one-dimensional splines for derivation on surfaces. All of these determine the simplicity and accuracy of the method. The two theoretical models on the curve and on the surface were used for trial calculation. Comparing the calculation results of Zα / x and Δg / Z ~ 2 and the theoretical results respectively, the results were in good agreement. The error depends on the size of the surface undulation, the steepness of the anomaly, and the sampling interval.