电法测井的快速整体反演及其应用

Rapid whole inversion and its application in electric well logging

为了提高电法测井反演的速度,提出了一种快速计算雅可比矩阵的方法,即只考虑每个待反演参数的微小改变对其所在层及其邻层视电阻率有影响,而对其他层的视电阻率没有影响,从而节约了大量计算雅可比矩阵的时间,其反演的时间与待反演的参数个数基本上呈线性关系。在计算精度基本不受影响的情况下,使得应用阻尼最小二乘方法反演侵入半径和原状地层真电阻率的速度提高了至少一个数量级。人工模型和实际资料的处理结果表明,该方法能有效地消除环境因素的影响,恢复地层的实际电阻率。同时也证实了阵列感应测井数据具有探测深度大、分辨率高的特点,在层不太薄(层厚超过1 m)、侵入不太深(侵入半径不超过0.25 m)时,深探测数据能较准确地反映地层真电阻率。

To improve the speed of inversion algorithm in electric well logging, a rapid algorithm for Jacobi matrix computation was proposed. It only computes the effects of inversion parameters on apparent resistivity of object bed and adjacent bed when these parameters have small.changes. The effects on the apparent resistivity of other beds can be neglected approximately. Therefore, the large time on Jacobi matrix computation was saved and the time of the inversion is linearly depen dent on the number of inversion parameters. When it is applied in the invasion radius and virgin resistivity inversion by damped least .square method, the speed is improved at least 10 times and the precision is not affected markedly. So the total inversion for electric well logging becomes realizable. Synthetical model and field data procession show that the method can eliminate efficiently the environmental effects and resume the virgin resistivity. The deep array induction well logging data can give a good approximation to the virgin resistivity when the thickness of the layer is over 1 m and the invasion radius is no more than 0.25 m.