Transient electromagnetic inversion for multiple targets

In UXO contaminated sites, there are often cases in which two or more targets are likely close together and the electromagnetic induction sensors record overlapping signals contributed from each individual target. It is important to develop inversion techniques that have the ability to recover parameters for each object so that effective discrimination can be performed. The multi-object inversion problem is numerically challenging because of the increased number of parameters to be found and because of the additional nonlinearity and non-uniqueness. An inversion algorithm is easily trapped in a local minimum of the objective function that is being minimized. To tackle these problems we exploit the fact that, based on an equivalent magnetic dipole model, the measured electromagnetic induction signals are nonlinear functions of locations and orientations of equivalent dipoles and linear functions of their polarizations. Based on these conditions, we separate model parameters into nonlinear parts (source locations and orientations) and linear parts (source polarizations) and proceed sequentially. We propose a selected multi-start nonlinear procedure to first localize multiple sources and then get the estimated polarization tensor matrix for each item through a subsequent or a nested linear inverse problem. It follows that the orientations of the objects are estimated from the computed tensor matrix. The resultant parameter set is input to a complete nonlinear inversion where all of the dipole parameters are estimated. The overall process can be automated and thus efficiently carried out both in terms of human interaction and numerical computation time. We validate the technique using synthetic and field data.