Nonlinear Inversion for Multiple Objects in Transient Electromagnetic Induction Sensing of Unexploded Ordnance: Technique and Applications

We develop an inversion technique to process overlapping data that arise from closely spaced targets. In contrast to a usual single-object inversion model, a multiobject problem is more challenging because of the increased number of parameters to be found and because of the additional nonlinearity and nonuniqueness. Our solution strategy is to break down the full problem into a sequence of smaller problems so that optimization is conducted in a lower dimensional model space. In the numerical implementation, a set of nonlinear model parameters, e.g., the locations of the underlying sources, is sought while the set of linear model parameters, i.e., their polarization tensors, are updated accordingly in a nested manner. This is an explicit separable nonlinear optimization technique that we cast. We employ a joint diagonalization to find an average principal direction among multiple magnetic polarizability tensors. Since the principal directions are more sensitive to the inaccuracies in the estimated polarization tensor, we suggest a subsequent procedure to optimize the two sets of parameters: orientation and principal polarizations of objects. For initialization, we propose a selected multistart nonlinear algorithm for source localizations that paves an efficient way to find a good initial guess of model parameters and makes the nonlinear inversion effectively automated. We report the new applications of the technique to the test-stand and field data acquired with next-generation sensor systems of the TEMTADS and MetalMapper and study the issue of the spatial resolution of overlapping anomalies through inversions and using the metric defined as the total uncertainty of the polarizabilities.