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Prior to 1990, UXO were generally modeled or approximated as compact, ferrous objects; the model was effectively a uniformly magnetized sphere of iron at a specified or an unknown distance from the magnetic sensor. Correlations were developed between various UXO, represented as compact masses of iron, and magnetic anomaly signature features such as maximum positive value, peak-to-peak value, and wavelength. The uniformly magnetized sphere, equivalent to a point dipole model external to the sphere, cannot account for magnetic phenomenology of actual UXO, which exist in forms ranging from approximately spherical to highly elongated, with elongations as large as 5 (ratio of length to diameter). UXO are generally ferrous, with large magnetic permeability, although some can contain aluminum or other non-magnetic metals. This paper reviews the phenomenology of models applied to simulation of UXO magnetic anomalies. The multipole expansion solution of the prolate spheroid model in earth's magnetic field is highlighted, as it replicates most of the phenomenology of UXO magnetic anomalies, and is about the most complicated model for which practical geophysical inversion can be achieved (8-parameter model vector, plus magnitude and orientation of the earth's magnetic field). While the prolate spheroid model works well for the larger UXO (e.g., 60-mm mortars and larger) at distances (burial depth plus sensor height) greater than the length of the target or model, it has not been tested for close distances (less than the target length) and for the smaller UXO (e.g., 20-mm to 40-mm projectiles). Test stand magnetic anomaly measurements for these small UXO at distances equal to the length or less from the sensor are compared to model calculations. The importance of including the octupole component is demonstrated for small ordnance at close distances, and the differences in modeling and inversion results for UXO physical dimension versus UXO ferrous component dimension are presented.