任意曲线上二维重磁位场转换的B样条函数法

CONVERSION OF TWO-DIMENSIONAL POTENTIAL USING B-SPLINE FUNCTIONS ALONG IRREGULAR CURVE

重磁位场转换在重磁资料解释中是十分重要和必要的。随着物探仪器的改进和资料解释精度要求的提高,人们对位场转换方法的研究越来越深入。本文提出一种原理简单、计算精度高的新方法——B样条函数法,应用其插值、求导、求积的性质,以解决曲线上二维重磁位场转换的两类问题。一是Z_α分量向H_α分量的转换及向上延拓,二是水平和垂向导数的换算及磁位的计算。 样条函数为分段多项式函数。B样条函数是用σ函数逼近的一类样条函数。

B-spline functions are used to complete upward-continuation,component conver-tion of two-dimensional potential along irregular curve and to get second-order derivative,magnetic potential.From Laplace's equation,applying variational principle,continuation and component conversion can be achieved with quadrature through using B-spline functions:(u:gravity or magnetic anomalies,B-spline functions)In order to count derivative and magnetic potential of two-dimensional potential field on a curve,it is necessary and reasonable for us to count the arc-length as the parameter to describe B-spline functions.