Influence Fields Calculation in Problems of Induction Logging by the Finite Element Method

The paper presents the software and algorithms for solving forward problems and calculating the influence fields during the induction logging data inversion. The algorithm for the direct problem solving is based on the finite element method. Grouping the positions of the receiving-generator set was used: the same finite element mesh was built for each group. As a result, the finite element SLAEs in the group differed in the right hand side vector (in accordance with the source position). The use of the grouping increases the direct methods efficiency of SLAE solving. The P ARDISO program was used to solve the finite element SLAE. With the help of the developed software and mathematical apparatus, research were carried out to determine the minimal changes in the geoelectric medium properties (both geoelectric and geometric) that significantly (greater than the noise level) affect the signals in the receivers. The results obtained are applicable when setting the increments of the unknown parameters of the medium for calculating the influence fields by the Gauss-Newton method, as well as when analyzing the well log for setting the starting model for of the induction logging data inversion.