A hybrid finite element/method of moment formulation for single frequency eddy current inversion

Eddy-current inverse techniques using single-frequency currents have been applied with limited success to the reconstruction of crack width and thickness profiles primarily for one-dimensional and axisymmetric geometries. Because of the diffusive nature of the induced low-frequency eddy currents, the reconstruction process differs from high-frequency wave propagation methods. On the physical basis that both diffusive and wave phenomena can be described by the same Green´s function with either a complex or real wave number, an integral formulation for the low-frequency magnetic vector potential is presented. By employing an iterative Born approximation algorithm and the method of moments, a reconstruction method for the conductivity profile in a metallic specimen is developed. To make this formulation amenable to complex geometries, finite-element analysis techniques are utilized to compute the integral kernel. The inversion process is tested with synthetic data generated by the numerical solution of a generic embedded flaw in a full-space and a surface-breaking defect