The Discrete Newton Method of the Three Parameters Inversion in Electrical Logging

Abstract

Abstract Log analysts are always interested in the problem of determining the invaded zone resistivity, Rxo, the virgin formation resistivity and the diameter of the invaded zone, D, simultaneously, using the logging tool responses of the deep and shallow laterolog 3. In this paper, the problem of multiple parameter identification in electrical logging is reduced to a partial differential equation. Using the Discrete Newton method and the regularization method, the mathematical formulas of inverting three parameters are derived. Thus, an iterative method of simultaneously solving Rxo, RT and D is obtained. To test this method, some numerical computations have been made. The computational results show that when no noise is added, the mean relative errors of inverting Rxo, RT and D are 0.67%, 0.47%, and 2.28%, respectively. When 10% noise is added to the resistivities of the adjacent formation, the mean relative errors are 2.65%, 0.92%, and 5.39%, respectively. This method has been used to deal with the real measured data. This method can be used widely to direct log interpretation and eliminate the interpretation chart.