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如何准确地求取位场观测异常ΔT及其垂直梯度沿地形切线方向的导数是综合利用ΔT及其垂直梯度进行曲化平的关键。为此本文提出应用三次样条函数及其求导的方法进行曲化平。该法的基本思路是：选择双三次样条曲线函数代替样条曲面函数，即对测线方向和基线方向分别用三次样条函数进行拟合；再利用样条函数求导求得观测场的垂向二阶和三阶导数；最后利用泰勒级数计算出某一平面上的近似场值，达到曲化平的目的。模型计算表明，该法理论正确、精度较高、运算速度较快、能充分发挥梯度测量的效果。
How to accurately calculate the derivative of ΔT and its vertical gradient along the tangential direction of the terrain is the key to the smoothing of ΔT and its vertical gradient. For this reason, this paper proposes to apply the cubic spline function and its derivation method to smooth the curve. The basic idea of this method is to select the bi-cubic spline curve function instead of the spline curve function, that is, to fit the measured line direction and the baseline direction respectively to cubic spline function; then use the spline function to derive the observed field Vertical second order and third order derivatives; Finally, the use of Taylor series to calculate the approximate field value in a plane, to achieve the purpose of flattening. The model calculation shows that the theory of the law is correct, the precision is high, the calculation speed is fast, and the effect of gradient measurement can be brought into full play.