Research On Inversion Algorithm Of Phase Induction Logging

The inhomogeneous inversion method on the phase induction logging has been studied in this dissertation. The inversion simulation is performed from the phase difference △φ and amplitude ratio B of the two receiver coils in one-dimensional and two-dimensional inverse modeling, respectively.Firstly, the theories and methods of electromagnetic scattering and inverse scattering are reviewed in this paper. The high-dimensional electromagnetic inverse scattering method is introduced mainly.The efficiency of the data inversion highly depends on the speed of the forward modeling. The subsurface structure is modeled as a one-dimension horizontally layered medium, the inversion equation of the phase induction logging is obtained by applying the variation principal. The algorithm is applied to pretreat phase difference △φ logging data, and the formation resistivity distribution of one-dimensional modeling is obtained.Following, in the two-dimensional inverse modeling, the numerical mode-matching (NMM) method as an efficient algorithm is used to model various multiregion vertically and cylindrically stratified inhomogeneous media. The inversion equation is obtained by applying the variation principal in a two-dimensional axisymmetrical inhomogeneous medium, which is solved by using the conjugate gradient (CG) method. The convergence speed, precision and tolerance to noise of the inversion method are discussed, it is found that the accuracy of formation boundary location influents the inversion precision of formation resistivity. The initial value of formation resistivity and boundary location are obtained from phase difference △φ logging response curve, then the formation resistivity and boundary location per bed are simultaneously reconstructed from the phase induction logging data. In order to investigate radial resolution, the formation resistivity is inverted from logging data with mud invasion.The formation resistivity and permittivity are inverted by using the conjugate gradient (CG) method from the phase difference △φ and amplitude ratio B logging data, the convergence speed and tolerance to noise of the inversion method are investigated. The accuracy of formation boundary location influents the inversion precision of formation resistivity and permittivity, the accuracy of boundary location should be paid much attention. The initial value of formation boundary location is obtained from phase difference △φ and amplitude ratio B logging response curves,...