用B样条函数计算位场垂向高偶阶导数

CALCULATION OF HIGHER EVEN VERTICAL DERIVATIVES OF POTENTIAL FIELD BY SPLINE FUNCTION B

山东海洋学院

本文根据拉氏方程,应用了结点任意分布的B样条函数来计算高偶阶导数。方法的优点是统一和灵活。使用曲线插值代替曲面插值不仅插值程序更易于编写,而且节省计算机内存。本文中用三个理论模型和一个实例作了二阶、四阶垂向导数的计算和检验。结果表明,方法非常有效。与其它空间域方法相比较(包括普通二元样条函数法)精度提高了一个级次以上,其中四阶垂向导数比二阶垂向导数更易于划分局部异常体。

In line with the Laplace equation and by using the spline function B with arbitrary distribution nodes, the calculation of the higher even derivatives were get through with. The advantage of this technique is its uniqueness and flexibilities. The use of the curveline interpolation instead of the surface interpolation not only makes the programming more easier but it has the advantage of internal storage saving. In this paper, the second and the quartic vertical derivatives were calculated and verified by three theoretical models and a field example. Results show that the technique recommended is highly effective, its accuracy is at least one order of magnitude higher than those obtained from other spatial domain techniques (including the method of binary spline function). In local-anomaly determination and location, the use of quartic derivatives seems to be more simple than that of the second derivatives.