直流电测井响应的二阶几何因子逼近计算

Approximate Computation of Electrode type Resistivity by 2nd Order Geometrical Factor in Inhomogeneous Medium

张庚骥等：直流电测井响应的二阶几何因子逼近计算，测井技术，１９９６（５）２０，３２０～３２４。对直流电测井几何因子理论及逐次逼近解法进行了进一步的推导论证，同时给出了电极条件下二阶直流电几何因子逼近的具体计算方法和数值分析结果。计算结果显示，较一阶几何因子逼近结果有明显改进，已经基本接近真值，进一步证明了直流电几何因子理论在电测井数值模拟方面的有效性。

On the basis of the successive approximation method and the geometrical factor theory proposed by Zhang Gengji, some new modifications are presented in this paper in order to make the computation of the electrode type resistivity accurate and efficient. Thus, the 2nd order geometrical factor is used to meet the need of accuracy. However, when it is treated as the integrand, the computation of five dimensional numerical integral is involved, which is known to be difficult, As a result, one method employed to convert 5D numerical integration into 2D one solvesthe problem and accelerates the computation of electrical logging response. At last, two simple examples are provided, and the comparison between the result by the first order geometrical factor and that by the second order geometrical factor shows that the latter approximates the analytical solution much closer than the former. Therefore, the geometrical factor theory and the successive approximation method could be workable in the simulation and inversion of electric logging.