Robust Inversion of Time-domain Electromagnetic Data: Application to Unexploded Ordnance Discrimination

Abstract

We invert time-domain electromagnetic data for the purpose of discriminating between buried unexploded ordnance (UXO) and non-hazardous metallic clutter. The observed secondary magnetic field radiated by a conductor is forward modeled as a linear combination of decaying, orthogonal dipoles. We show via a perturbation analysis that errors in the measurement of sensor position propagate to non-normal errors on the observed data. A least squares (L2) inversion assumes normal errors on the data, so non-normal errors have the potential to bias dipole parameter estimates. In contrast, robust norms are designed to downweight the effect of outlying (noisy) data and so can provide useful parameter estimates when there is a non-normal component to the noise. When positional errors are modeled as independent Gaussian perturbations, we find that weighted least squares and robust inversions have comparable performance. Both inversion techniques estimate data uncertainties from observed data, and this has the effect of making the least squares inversion robust to outliers. However, when simulated errors are correlated, robust inversion with a bisquare norm provides a marked improvement over L2 inversion. Application of robust inversion to real data sets from Camp Sibert, Alabama produced an incremental improvement to the initial L2 inversion, identifying outlying ordnance items and improving discrimination performance.