Borehole correction for array induction logging data with an invasion model and tomography technique

Routine borehole correction algorithms for array induction logging rely on non-invasion models, thus creating a theoretical mismatch when applied to invaded zones. To address this problem, we propose an adaptive method combining an invasion model for geometric factor correction with tomography. The proposed method introduces an innovative approach by decomposing an invasion profile into the linear combination of multiple step functions and establishing the tomographic relationships between sub-array log responses based on the geometric factor theory to accurately solve borehole effect parameters. Unlike conventional approaches that misinterpret mud invasion as borehole effects, the new algorithm effectively preserves formation invasion characteristics during correction, therefore significantly enhancing the radial resolution of log curves for invasion analysis. This advancement establishes a new theoretical framework for the accurate interpretation of complex invaded formations.