B0 is the loop.

An increasing number of measurement electrodes have been designed to satisfy the demand for high-resolution detection using galvanic logging technology in complex formations. The forward modeling response analysis of logging tools has important guiding significance in the design of galvanic logging tools. Based on a three-dimensional finite element numerical simulation method, we established a forward model of galvanic multi-electrodes in a complex formation. We also designed a symmetrical resistance network model of the formation with equivalent resistance between two electrodes. A symmetrical resistance network was derived using the balanced bridge method. The asymmetrical admittance matrix was extended to a symmetrical extended admittance matrix to realize a convenient calculation of the equivalent symmetrical resistance network in complex formations. Verification of the microcolumn-focused logging tool, with nine electrodes in a simulated standard well, and an evaluation of the degree of invasion in an actual oil well indicate that this calibration method can improve the measurement accuracy of galvanic logging instruments.为满足复杂地层中电流测井（galvanic logging）技术高分辨率探测的需求，越来越多的测量电极被研发设计。测井仪器的正演响应分析，对电流测井仪器的设计具有重要指导意义。本文基于三维有限元数值模拟（three-dimensional finite element numerical simulation）方法，构建了复杂地层下电流式多电极测井的正演模型；同时设计了一种以两电极间等效电阻（equivalent resistance）为核心参数的地层对称电阻网络（symmetrical resistance network）模型。研究采用电桥平衡法（balanced bridge method）推导得到该对称电阻网络的解析形式，并将非对称导纳矩阵（asymmetrical admittance matrix）拓展为对称扩展导纳矩阵（symmetrical extended admittance matrix），以实现复杂地层下等效对称电阻网络的便捷计算。通过在模拟标准井中对搭载9根电极的微柱聚焦测井仪（microcolumn-focused logging tool）开展性能验证，并在实际油井中进行地层侵入程度评估，结果表明该校准方法可有效提升电流测井仪器的测量精度。