Inversion of resistivity and permittivity using phase induction logging data
用相位感应测井数据反演地层电阻率和介电常数

An inverse method is presented to inverse the permittivity and resistivity of the formation in a two_dimensional axisymmetric inhomogeneous media. The measured data of phase induction logging is the phase difference and amplitude ratio of the two receiving coils. The initial value of the formation geometrical parameter is determined by phase difference and amplitude ratio logging curves. The inverse equation is derived by the logging response equation and the variation principle. The conjugate gradient (CG) method is used to solve this inverse equation. Simultaneous inversion is performed to obtain the resistivity, permittivity and geometrical parameter of the multi_layer formation. The numerical results show that this method is effective.