【摘要】 针对实际反射式超声波测井 ,把套管与地层环空间单层介质的波阻抗和厚度作为两个待反演参数 ,分别将相移正切函数及反正切函数形式下的方程作为目标函数 ,提出了对波阻抗和厚度反演的线性化最小二乘法 .通过对两种反演方程误差函数的数值考察和对合成数据反演结果的分析 ,发现相移反正切函数形式下方程的线性化最小二乘法是较为稳定有效的方法 ,能够完全消除多极值的缺点 ,反演结果对波阻抗和厚度初值不敏感更多还原

【Abstract】 Impedance and thickness of one\|layered medium in annular space between casing pipe and formation are selected as two inversion parameters.Equations with the tangent function form of phase\|shift and equations with the arctangent function form of phase\|shift are regarded as the target functions, respectively.Linear least\|square inversion method of impedance and thickness is established.Investigation of error functions and inversion results of synthetical data are given.It is found that linear least square inversion method with the arctangent function form of phase\|shift is a stable and effective method which can avoid multi\|minimal points and the error function only has one minimum value corresponding to the true value of impedance and thickness.Reversion results are not sensitive to the initial value of impedance and thickness. [更多还原