样条函数在补偿中子算法中的应用

Application of Spline Function to Algorithm of Compensated Neutron Log

本文从对补偿中子测井实验刻度点的讨论出发,提出用样条插值方法而不是通常回归拟合方法来构造补偿中子响应方程。样条函数采用分段的多项式。文中指出,四点三次样条插值是其较为实用的形式,这时插值多项式参数计算的解析式容易导出,实时处理中求视孔隙度的计算量完全可为一般采用软件作数值运算的微处理机系统所接受;并提出补偿中子测井的刻度方法,这种算法极大地简化了井下仪的调校;对水点取值也进行了讨论。附录中给出求解参数的具体计算公式,可以此作为上机编程的依据。

Starting discussion on calibration points of Compensated Neutron Log,this paper proposes that spline interpolation, instead of conventional regression fitting,is used to build the response equation of CNL. The favorate spline function is polynomial in a segment of the domain. The author points out four-point third-order polynomial is a practical formula of the spline interpolation. The coefficients of the polynomial are easy to derive. The realtime processing parameters in porosity equation can be accepted by a digital computer system supported by ordinary software. A new calibration method is proposed for CNL. The test of downhole tools is much more simplified. Determination of water point value is discussed. The concrete formula for calculating parameters is provided in the appendix,and can be used as the basis for computer programming.