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In practice, most signal processing strategies for discrimination of buried objects are clutter limited. This applies even to discrimination of shallow sizable metallic objects, such as unexploded ordnance (UXO), which are to be found predominantly in the top meter of soil. The environment typically features widespread metallic clutter from detonated ordnance or other sources. Such fragments can be numerous and are often shallower than the objects of interest. Currently, the preeminent remote sensing mode for buried UXO is ultrawideband electromagnetic induction (EMI), operating over part or all of the band from some tens of hertz up to perhaps hundreds of kilohertz. Particularly because EMI fields fall off sharply with range, signals from shallow clutter may be relatively strong and can easily obscure essential scatterer signatures. To treat this, a rational theory of EMI scattering from widespread metallic clutter is formulated and tested. For dense, well-distributed clutter, analytical rules are derived for dependence of signal strength on sensor elevation, under various fundamental excitation types. For more erratic, sparse clutter distributions, signal statistics from Monte Carlo simulations show patterns like those from the analytical rules. The dependence of clutter signal magnitude on antenna elevation is determined for both thin surface layers and for volume layers of widespread small items, and for both dense and sparse clutter distributions. These are contrasted with the patterns expected from single, larger, discrete objects of interest, and the contrast is exploited in discrimination exercises for the screening problem. For sparse clutter distributions, results from inversion processing formulations that account for the patterns of clutter statistics are compared to simple least squares treatments.