用样条函数建立位场转换系统的研究

Constructing a potential field conversion system by spline function.

本文提出一种基于样条函数的空间域位场转换方法。首先应用位场延拓基本公式建立一个第一类弱奇异性积分方程,求解该方程可得到边界上位场值的法向导数;然后求得积分表达式的值,它与基于样条函数的反演方法形成一个系统,从而实现位场转换。模型试算和实例处理结果显示,本方法原理简单、精度高、受地形坡度影响不大,因此为这一领域的探索提供了一个新思路。

A method for space domain potential field conversion based on spline function is advanced here. It includes the following essential points. ·The basic formula for potential field continuation is used to construct first type of weak oddness integral equation. ·This integral equation is solved to have normal derivative of boundary potential field. ·The integral expression is evaluated then. ·The method matches the inversion based on spline function to form a system for potential field conversion. Modeling computation and real processing result show that the method is characterized by simple principle, high accuracy, and slight influence due to terrain slope. It is thus a new way in this realm.