沃尔什函数法测井曲线高分辨率反演

HIGH-RESOLUTION INVERSION OF WELL LOGS USING WALSH FUNCTIONS

沃尔什（Ｗａｌｓｈ）函数法首先将地层物理量展开成沃尔什级数，其次利用线性模型参数估计法由测井曲线和响应方程估计出展开系数，进而求出地层物理量的真值．本文介绍了该方法的原理、参数估计和误差控制的方法，并对深感应测井的模型数据和实际资料进行了试算，获得了满意的效果．该方法具有３个特点：１．使常规测井曲线的垂向分辨率提高到两个深度采样间隔（０．２５ｍ）；２．反演结果的误差不超过反演前数据本身的误差；３．无需迭代算法，处理资料速度快．

Walsh functions are used to express a petrophyslcal quantity in an interval of laminated formation, shch as conductivity. The unknown coefficients in the expression can be found from the well-logging measurement corresponding to the quantity by means of the tool response equation and the parameter estimation theory of linear model.The methedology,parameter estimation and error control are discribed. As an example, we apply the method proposed here to modeling data and field data of deep induction log. The results show that the method can enhance the vertical resolution of logs to two intervals of depth (0. 25 m),that the inversion does not expand the error of the log, and that the method is very efficient.