Recent Developments and Verifications of Multidimensional and Data-Adaptive Inversion of Borehole UDAR Measurements

Ultradeep azimuthal resistivity (UDAR) measurements provide advanced subsurface imaging capabilities by bridging the gap between traditional well logging and seismic interpretation. However, interpreting UDAR measurements in complex, spatially heterogeneous, or anisotropic formations remains challenging. Traditional two-dimensional (2D) and three-dimensional (3D) inversion procedures are computationally intensive and unsuitable for real-time applications. We describe our recent progress in the development of fast modeling and inversion algorithms for the interpretation of UDAR measurements. These algorithms are designed for multi-CPU clusters and tailored for integration with local 3D geological models and arbitrary well trajectories. Modeling employs a finite-volume solution of Maxwell’s equations implemented on an adaptive Lebedev grid, effectively accounting for diverse formation complexities and tool configurations. A new block-based solver computes multi-input multi-output (MIMO) responses efficiently, significantly reducing CPU runtime. Inversion is performed with a gradient-based approach (Occam-type) and incorporates regularization to account for measurement noise and non-uniqueness in the estimation. Furthermore, inversion complexity grows progressively from zero-dimensional (0D) to 3D, based on the localized dimensionality of both measurements and the spatial distribution of electrical conductivity. The method is successfully validated with challenging synthetic and field measurements acquired in the North Sea by various service companies. It is confirmed that the modeling and inversion algorithms are efficient, stable, and reliable for estimating the spatial distributions of anisotropic electrical conductivity around the well trajectory. The Jacobian matrix is efficiently calculated and updated by the modeling algorithm, which is as accurate as the traditional perturbation method but five orders of magnitude faster. In addition, we observe that both data misfit and model uncertainty decrease as inversion dimensionality increases. Our adaptive inversion method also significantly reduces computational costs by triggering expensive 2D and 3D inversions only, when necessary, along the well trajectory. The current modeling algorithm has the potential to be further optimized for hybrid GPU-CPU implementation to enable real-time 2D and 3D inversions.