Adaptive Multidimensional and Multiresolution Inversion of Borehole Ultra-Deep Azimuthal Resistivity Measurements for 3D Imaging and Geosteering

Summary Real-time well placement through well geosteering relies on accurate imaging of electrical resistivity distribution across the formation to understand spatial heterogeneity of subsurface formations and make informed drilling decisions. Ultra-Deep Azimuthal Resistivity (UDAR) measurements are widely used for this purpose, providing spatial resistivity images essential for geomapping and geosteering. However, well geosteering in complex and heterogeneous formations remains challenging due to the high computational cost of 2D and 3D inversions, and the difficulty of quantifying uncertainty under real-time constraints. This work addresses these challenges by developing CPU-time-efficient multi-dimensional UDAR inversion algorithms capable of both fast imaging and real-time uncertainty estimation. Two complementary inversion approaches are introduced: a gradient-based method that uses adjoint-state techniques for rapid Jacobian computation, and a stochastic method that applies a multi-resolution, multi-fidelity framework to manage computational load. Both methods have been validated through synthetic tests and real field data from the North Sea, verifying their potential to enhance decision-making and well placement during well geosteering operations