Analytical 2-D Model for Calibration of Ultradeep Azimuthal Resistivity Measurements

In this work, we develop a novel analytical solution for the electromagnetic (EM) field in a 2-D cylinder-plane model that is utilized to calibrate the measured data from airhang experiments with an ultradeep azimuthal resistivity (UDAR) tool. The tool adopts a set of tilted coil antennas wound around the drill collar and is lifted horizontally above the sea water for signal calibration. The EM fields are first solved in the cylindrical and rectangular coordinate systems to match the boundary conditions of the cylindrical and plane interfaces, respectively. After the mutual transformation relationships between two types of waves, cylindrical waves and plane waves, are derived, the whole-space field is expressed exactly in the spectral domain. The voltage expression for a tilted receiving coil is further obtained via a 1-D integral. These formulations ensure the high accuracy and efficiency of forward modeling for UDAR tools with multiscale measurements and high conductivity contrast. Finally, we propose a preliminary calibration formulation based on data fitting and apply it to simulate airhang experiments to investigate the effects of sea water.