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

TL;DR

This paper introduces an improved integral equation-based modelling technique with domain decomposition preconditioning for 3D electromagnetic induction log inversion, significantly enhancing computational efficiency and reducing memory usage.

Contribution

The paper presents a novel domain decomposition preconditioning approach for integral equation modelling, enabling faster and more memory-efficient 3D inversion of electromagnetic induction logs.

Findings

Maximum 35% reduction in computational time.

Reduced memory requirements for large-area modelling.

Effective acceleration using Krylov subspace methods.

Abstract

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