Sequential multi‐dimensional parameter inversion of induction logging data

Abstract Structural information about the subsurface near the borehole can be obtained from reconstructed conductivity distributions. These distributions may be reconstructed via the inversion of deep‐sensing electromagnetic induction log data. Unfortunately, these complex media often display anisotropy and structural variations in both horizontal and vertical directions, making the three‐dimensional inversion computationally demanding and ill‐posed. To address these challenges, we introduce a sequential inversion strategy of deep‐sensing electromagnetic induction logging data that is measured while drilling. For the inversion at each logging position, we employ a matrix‐free implementation of the adjoint integral equation method and a quasi‐Newton algorithm. To tackle the ill‐posed nature of the problem, we regularize the inverse problem by employing a multi‐dimensional inversion parameter technique that shifts from zero‐ to three‐dimensional parameterization. The model derived from the inversion of the data at multiple positions is incrementally integrated by utilizing the sensitivity data at each logging position. To validate our approach, we tested our method on simulated data using an anisotropic model. These experiments show that this approach produces a good reconstruction of the true conductivity for the whole track while only doing the inversion at a single position at a time.