二维密度界面正反演的样条函数法

Spline function method for forward and inverse problems of 2-D density interface

本文从重力场基本公式出发，研究了节点任意分划的二元三次样条函数的插值、求导和求积方法，并提出了常密度二维单一界面及多界面正反演的样条函数方法。该方法将形体正反演与界面正反演统一起来，使计算灵活方便。文中给出的理论模型和实际数据算例证明了该方法的实用性；该方法与其它正反演方法（线元法正演、方柱体组合法正演、压缩质面法反演、Parker公式正反演）相比，计算结果更加精确。

On the basis of fundamental formulas of gravitational field,we describe the interpolation, derivation and integration of two-variable cubic spline function whose knots are arbitrarily distributed. Then we advance the spline function method for forward and inverse problems of single (multiple) 2D constant density interface.This method identifies forward and inverse problems of density body with those of density interface, making the computation nimble and convenient. Its feasibility is proved by theoretical model and real examples- This method is more accurate than others (such as forward problem using linear method,forward problem using rectangular-prism combination method,forward and inverse problems using Parker formula, etc.).