Both atmospheric and hlgh-altitude nuclear explosions will produce magnetic signals that are detectable over very large distance. An underground explosion will also produce a magnetic signal, but it is detectable at much smaller distance. This is because the underground fireball is inertially tamped by the more dense earth, and because the low frequency electromagnetic wave is strongly attenuated by the earth . This proposal describes: a) a classical electromagnetic formalism for quantitative understanding the nature of the underground magnetic effect; and b) a means of absolute time-dependent underground fireball volume measurement. Just as with atmospheric fireball measurements, underground fireball volume is directly proportional to explosive yield. This project addresses the need to develop a better yield determination technique for contained underground nuclear explosions. It will be employed by on-site teams of U.S. and cooperating treaty signatories to monitor treaty limits. It has no major commercial potential as ylet, but conceivably could be applied to earthquake research.