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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 this paper, according to the Lagrange equation, the B-spline function with arbitrary distribution of nodes is applied to calculate the even-even derivative. The advantages of the method are unity and flexibility. Using Curve Interpolation instead of Surface Interpolation Not only is the interpolation program easier to write, it also saves computer memory. In this paper, three theoretical models and one example are used to calculate and test the second and fourth vertical derivatives. The results show that the method is very effective. Compared with other methods in the space domain (including ordinary Bivariate Spline Function method), the accuracy is improved by more than one level, and the fourth-order vertical derivative is easier to divide the local abnormal body than the second-order vertical derivative.