Application of the method of auxiliary sources to the wide-band electromagnetic induction problem

The Method of Auxiliary Sources (MAS) is formulated and applied to solution of wide-band electromagnetic induction problems involving highly conducting and possibly permeable metallic objects. Improved remote sensing discrimination of buried unexploded ordnance (UXO) motivates the study. The method uses elementary auxiliary magnetic charges and magnetic current elements to produce the unknown field. Auxiliary sources are located on virtual surfaces that usually conform to but do not coincide with the real surface of the object. Once the source coefficients are determined, the secondary field can easily be found. The method involves no confrontations with source or Green's function singularities. It is capable of treating penetrable as well as nonpenetrable objects. Because the solution is composed of fields that automatically satisfy the governing equations, by construction, all approximation resides only in the enforcement of boundary conditions at matching (collocation) points. Accuracy in satisfying the boundary conditions can be evaluated explicitly using noncollocation points over the surface. This in turn allows one to identify problem areas on the surface and make intelligent adjustments of the source distributions, to improve solutions at minimal cost. A general 3-D formulation is presented, and a version specialized to treat bodies of revolution is applied in the specific test cases discussed. Good performance of the method is observed, based on a modest number of degrees of freedom. Results are given and compare very well with available analytical and experimental data. Finally, we illustrate the utility of the method for investigating shape and orientation sensitivities for fundamental geometries as well as such targets as UXO.