An Empirically Based Ellipsoidal Model for Multiple Frequency Emi Signatures From Uxo

Efforts to model electromagnetic induction (EMI) signatures from unexploded ordnance (UXO)<br>have focused on the magnetic polarizability constants that characterize the dipole response of the UXO<br>along its axes. These polarization factors are a function of time or frequency depending on the EMI data.<br>While these curves can be analytically modeled in terms of size and composition for simple shapes like<br>spheres, an analytic representation for the response from general objects has proven elusive.<br>Functional forms have been found that fit polarization response functions for a wide variety of<br>objects. One such form is presented here in the frequency domain. This matches the analytic cases for<br>both a sphere and an infinite cylinder in the high permeability limit. The parameters for this empirical<br>function can be related to the demagnetization and time constants, as well as the volume, of the object.<br>For the case of an ellipsoid, the demagnetization constants and volume are analytically well-defined,<br>while the time constants are not. Here, we assume the time constants to scale as the ellipsoid dimensions<br>squared. While this assumption is a weak one, data inversions will be presented that return consistent<br>size dimensions for a given UXO item.