Electromagnetic induction (EMI) has been shown to be a promising technique for unexploded ordnance (UXO) detection and discrimination. The excitation and response of a UXO or any other object to EMI sensors can be described in terms of scalar spheroidal modes consisting of associated Legendre functions. The spheroidal response coefficients B<sup>j</sup><sub>k</sub> correspond to the k<sup>th</sup> spheroidal response to the j<sup>th</sup> spheroidal excitation. The B<sup>j</sup><sub>k</sub> have been shown to be
unique properties of an object, in that objects producing different scattered fields must be characterized by different B<sup>j</sup><sub>k</sub>. Therefore, the B<sup>j</sup><sub>k</sub> coefficients may be useful in discrimination. We use these coefficients rather than dipole moments because they are part of a physically complete, rigorous model of the object's response. Prolate spheroidal coordinate systems recommend themselves because they conform most readily to the proportions of objects of interest.
In clearing terrain contaminated by UXO, the ability to distinguish larger buried metallic objects from smaller ones is essential. Here, a Support Vector Machine (SVM) is trained to sort objects into different size classes, based on the B<sup>j</sup><sub>k</sub>. The classified objects include homogeneous spheroids and composite metallic assemblages. Training a SVM requires many cases. Therefore, an analytical model is used to generate the necessary data. In simulation studies, the SVM is very successful in classifying independent sets of objects of the same type as the training set. Furthermore, we see that the B<sup>j</sup><sub>k</sub> are not related to size or signal strength of the object in any simple or visually discernible way. However, SVM is still able to sort the objects correctly. Ultimately, the success of the SVM trained with synthetic (model derived) data will be evaluated in application to data from a limited population of real objects, including UXO.