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The deployment of electromagnetic (EM) induction tools while drilling is oneof the standard routines for assisting the geosteering decision-making process.The conductivity distribution obtained through the inversion of the EMinduction log can provide important information about the geological structurearound the borehole. To image the 3D geological structure in the subsurface, 3Dinversion of the EM induction log is required. Because the inversion process ismainly dependent on forward modelling, the use of fast and accurate forwardmodelling is essential. In this paper, we present an improved version of theintegral equation (IE) based modelling technique for general anisotropic mediawith domain decomposition preconditioning. The discretised IE after domaindecomposition equals a fixed-point equation that is solved iteratively witheither the block Gauss-Seidel or Jacobi preconditioning. Within each iteration,the inverse of the block matrix is computed using a Krylov subspace methodinstead of a direct solver. An additional reduction in computational time isobtained by using an adaptive relative residual stopping criterion in theiterative solver. Numerical experiments show a maximum reduction incomputational time of 35 per cent compared to solving the full-domain IE with aconventional GMRES solver. Additionally, the reduction of memory requirementfor covering a large area of the induction tool sensitivity enablesacceleration with limited GPU memory. Hence, we conclude that the domaindecomposition method is improving the efficiency of the IE method by reducingthe computation time and memory requirement.

3D induction log modelling with integral equation method and domain decomposition preconditioning