Inversion of azimuthal electromagnetic logging while drilling based on adaptive damping quasi-Newton method

In azimuthal electromagnetic logging-while-drilling (LWD) resistivity measurements, accurately determining formation resistivities and boundary positions using tool data is crucial for geosteering guidance and critically relies on efficient, robust inversion algorithms. Traditional iterative inversion methods suffer from high computational costs and slow convergence due to requiring full Jacobian matrix calculations in each iteration. Addressing this limitation, this study employs the Quasi-Newton Method for inversion, which utilizes the Broyden condition to update the Jacobian matrix, significantly reducing computational burden and enhancing inversion speed. However, conventional quasi-Newton methods typically use a fixed damping factor, failing to accommodate the diverse update step size requirements across parameters in multi-parameter inversion. To overcome this inherent constraint of conventional quasi-Newton methods— specifically their inability to apply parameter-specific damping based on distinct update needs—we introduce a diagonal adaptive damping matrix to replace the fixed damping factor, enabling dynamic, localized adjustment of incremental step sizes for different parameters. Validation via theoretical three-layer formation models (including anisotropic formations) demonstrates that the proposed method not only effectively improves inversion speed but also enhances inversion accuracy, providing a reliable approach for real-time inversion in azimuthal LWD resistivity applications.