Regularized integral equation based inversion of tensor induction logging data in three-dimensional formations

There is growing interest in developing a three-dimensional (3-D) inversion and imaging technique from a single borehole. This problem can be solved by using tensor (multi-component) induction welllogging – TIWL. This method was originally introduced to resolve formation anisotropy. However, it was demonstrated in several publications that the TIWL instrument has sensitivity to 3-D conductivity distribution in the borehole vicinity. In previous works we introduced a method of fast 3-D imaging from a single borehole based on the localized quasi-linear (LQL) approximation. In the current paper we introduce a combined method of iterative LQL inversion of the TIWL data and rigorous integral equation (IE)-based inversion. Addition of the rigorous inversion stage improves the LQL inversion result significantly, and provides more accurate inversion error estimation. A new algorithm of 3-D TIWL data interpretation is tested for several models of typical 3-D structures located in the vicinity of the borehole.