采用递推方法得到柱状成层各向异性介质(横向各向同性)中并矢Green函数的解析表达式。该表达式可用于模拟柱状成层各向异性地层中任意点源(包括电流源和磁流源)的响应，地层数目可以任意，源点和场点的位置可以在任意地层中。利用上述表达式模拟含金属心轴和绝缘保护层多分量感应测井仪器在有井眼和侵入带各向异性地层中的响应。为提高模拟精度，考虑各分量线圈系的具体形状。将金属心轴作为一层介质处理，既可以考虑其电导率有限，也可以考虑其电导率为无穷大的情况。数值模拟结果表明，共面线圈系具有与共轴线圈系完全不同的响应特性。共面线圈系的响应特性更为复杂，对钻井液电导率、侵入带电导率、地层电导率、地层各向异性的变化更为敏感，且在很多情况下其响应会随这些参数的变化出现符号改变。此外，由于共面线圈系的同一响应可对应各向同性地层或各向异性地层的不同电导率，从而使得对测量数据的解释处理变得复杂。%An analytical expression of dyadic Green's functions in cylindrically stratified anisotropic media ( transversely iso-tropic media) was obtained using a recursive method. The expression can be used to simulate the response of an arbitrary point source ( including electric source and magnetic source) in cylindrically stratified anisotropic formations. The expression can be applied to any number of formation layers, and with the source location and field location in any of the layers. Using the method, the responses of multi-component induction logging tools with a metal mandrel and an insulating protection layer were simulated in anisotropic formations with a borehole and an invasion zone. The shape of each component's coils was taken into account in order to increase the simulating precision, and the metal mandrel was taken as a layer whose conductivity can be both finite and infinite. The simulation results show that the response of coplanar coil system has entirely different charac-teristics from that of coaxial coil system:the response of coplanar coil system is often more complex and more sensitive to the change in drilling liquid conductivity, invasion zone's conductivity, formation conductivity, and formation anisotropy. These parameters may even cause sign flip in the response under many conditions. Furthermore, since the same response of copla-nar coil system may be produced by entirely different formation conductivities in isotropic or anisotropic formations, it will be-come much complicated to interpret or process the measured data.
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