用模式匹配算法研究层状各向异性倾斜地层中多分量感应测井响应

Study on the response of a multicomponent induction logging tool in deviated and layered anisotropic formations by using numerical mode matching method

利用数值模式匹配技术,研究并建立层状各向异性倾斜地层中多分量感应测井响应的快速数值模拟算法.首先将位于井轴上的三个相互正交磁偶极子转化成关于极角θ的三个谐变分量的叠加,以便将三个正交磁偶极子电磁场的正演问题完全简化成三个谐变分量电磁场的轴对称定解问题,并给出电磁场各个谐变分量在井轴上满足的边界条件,保证电磁场在井轴附近仍然可解.然后利用数值模式匹配技术建立电磁场各个谐变分量的正演过程,得到层状各向异性地层中磁流源并矢Green函数的半解析表达式,给出计算层状各向异性倾斜地层中多分量感应测井响应的具体方法,最后通过数值计算结果证明该算法的有效性并考察几种不同情况下多分量感应测井响应特征.

In this paper, we advance an efficient algorithm to compute the responses of multicomponent induction logging （MCIL） tool in deviated and layered anisotropic formation through a numerical mode matching method （NMM）. First, the three mutually orthogonal magnetic dipoles located at the borehole axis are represented as the sum of three harmonic components about the dipole angle 0 so that the electromagnetic （EM） fields produced by the dipoles can be transformed into three axisymmetrie problems. And new boundary conditions satisfied by every EM harmonic component at borehole axis are given to assure the EM field near the borehole axis can still be calculated. Then NMM is used to solve the three axisymmetric problems and obtain a semianalytic expression of a dyadic Green function by magnetic current source in the formation. Furthermore, the formula to compute the MCIL response is given. Numerical tests are carried out to validate the algorithm and investigate the characteristics of MCIL response in several different cases.