Boundary Element Calculation of Eddy Currents in Cylindrical Structures Containing Cracks

Electromagnetic fields due to excitation coils in boreholes containing cracks have been calculated using a boundary element method formulated in terms of a scalar decomposition of the field. By using a Green´s kernel that ensures continuity of the tangential electric and magnetic field at the cylindrical surface, it is only necessary to render the flaw region in a discrete form. The effect of an ideal crack, one with zero opening but acting as a perfect barrier to eddy currents, is here represented by a current dipole layer orientated normal to the crack surface. An integral equation determines the source density on the crack and a numerical solution is found using boundary elements. The coil impedance change due to the crack is then computed using an expression based on a reciprocity principle.