Ray theory techniques are used to investigate a time-reversal phenomenon seen during the KIWI-ONE (Phase II) propagation experiment. Shots detonated along a track between New Zealand and South America were received by a deep suspended hydrophone. For ranges less than 3000 km, the standard SOFAR energy crescendo and abrupt termination is apparent, but for longer ranges, more than half of the received energy arrives after the strong axial arrival. This unexpected time reversal is shown to be cause by a broad minimum layer in the sound-speed field beyond 3000 km. Computer ray traces show that this broad minimum layer can produce the 1 sec of time reversal seen at 5300 km, while a more nearly classic SOFAR profile measured at the receiver exhibits negligible reversal. Traces simulating KIWI shot signatures were performed through a range-dependent sound-speed field with a linear segmented bottom. The calculated arrival structure agrees well with the data in both time and level. Fine structure of the arrival-time distribution is shown to correspond to discontinuities in the gradient in the broad minimum layer. [Supported by ONR 412.]