层状各向异性地层中含环状天线槽随钻方位电磁波测井几何因子算法

本文基于感应测井中的几何因子与一阶Born近似理论,通过柱坐标系下耦合势Helmholtz方程三维有限体积法研究建立了各向异性地层中含环状天线槽的随钻方位电磁波测井几何因子.首先,通过引入环状电流源与径向磁偶极子源电磁场Green函数,并结合Green第二积分公式,推导出随钻方位电磁波测井仪器中环形电场和横向磁场微小变化与各向异性地层中水平和垂直电导率相对摄动量之间的关系,得到轴向和横向感应电动势微小变化量计算方法与柱坐标系中轴向和横向分量空间灵敏度函数(三维几何因子)表达式.在此基础上,进一步给出径向和纵向微分几何因子计算公式.然后,应用耦合势三维有限体积法确定发射线圈产生的感应电磁场以及环状电流源与径向磁偶极子源电磁场Green函数的数值解.最后,给出不同频率、不同倾角、不同各向异性系数等多种情况下该仪器的空间灵敏度函数与微分几何因子的数值结果,用于分析考查仪器的响应特征与空间探测能力.

Perturbation to Unified Symmetry and Adiabatic Invariants for Relativistic Hamilton Systems

Based on the concept of adiabatic invariant, the perturbation to unified symmetry and adiabatic invariants for relativistic Hamilton systems are studied. The definition of the perturbation to unified symmetry for the system is presented, and the criterion of the perturbation to unified symmetry is given. Meanwhile, the Noether adiabatic invariants, the generalized Hojman adiabatic invariants, and the Mei adiabatic invariants for the perturbed system are obtained.