Development and research of geometric inversion of induction logging data measured in vertical wells

The paper considers the software which implements the geometric-2D inversion of induction logging data in vertical wells. In solving the direct problem the electromagnetic field simulation is carried out by the finite element method in cylindrical domain. As unknown parameters which are to be recovered during the inversion, we take the values of conductivity, the horizontal boundaries of the layers as well as the vertical boundaries within these layers. The vertical boundaries may be related to the boundaries of the invasion, annulus, and others. In the inversion process adaptive choice of regularization parameters is used. This ensures a stable convergence of the inversion process. Testing and studying the workability of software developed for the data interpretation were carried out using the synthetic data with and without noise generated for a geoelectrical model, which is typical of electromagnetic logging problems in vertical wells. As the data to be measured we take phase difference and amplitude ratio for different frequencies and spans of a logging tool. Computational experiments have shown that the use of geometric 2D inversion allows us to recover quite accurately all parameters of the geoelectrical model. The increase in the noise level may slightly decrease the accuracy of recovering the vertical boundaries locations in the environment around the borehole walls, but the conductivity of the formation is recovered with good accuracy.