Solution to the eddy-current induction problem in a conducting half-space with a vertical cylindrical borehole

The eddy-current induction problem in a conducting half-space with a vertical borehole is studied and a solution based on modal techniques is presented. Owing to the particular characteristics of the specific geometry, the straightforward application of the truncated region eigenfunction expansion method (a well-established tool for the analytical solution of such problems) presents significant difficulties. Therefore, a modified truncation approach has been adopted that treats the problem in two steps, each one based on the superposition principle. The approach proves to be very efficient and numerically robust. Results for the coil impedance are in excellent agreement with those obtained with the finite-element method. From the engineering point of view, the geometry simulates the eddy-current inspection of fastener holes in aircraft structures when coil scanning is performed from the surface. The presented solution constitutes an important step towards the development of a complete model for fastener hole crack inspections.