Application of TSA formulation for inversion of a metallic object´s electromagnetic properties from EMI data

Estimating electric conductivity σ (S/m) and magnetic permeability μ (F/m) is of great interest both for industry, mineral exploration, and for geophysical discrimination of buried objects such as unexploded ordnance (UXO). We present here a technique for inferring physical parameters of a metallic object in the EMI frequency range (from tens of Hz to several hundred kHz). Electric conductivity and magnetic permeability are inferred by an inversion algorithm operating on inphase and quadrature received components. The forward model is based on the BIE-TSA formulation, which works well over the majority of the EMI frequency range, especially for magnetic material. The formulation is organized so that most matrices related to object geometry need only be calculated once and the Jacobian matrix can be constructed easily from these matrices. Therefore, both forward solution and Jacobian matrix can be calculated quickly. For material with high magnetic permeability, forward solutions indicate that the scattered field is mostly only sensitive to the ratio of σ and μ. In this case the inversion algorithm becomes ill conditioned and some kind of regularization is needed. The performance of the inversion algorithm was studied under different kinds of regularization, via both theoretical analysis and numerical experiments. An optimized method for choosing regularization is suggested which may also benefit more general inverse problems.