An acoustic propagation experiment conducted west of Bermuda during the fall of 1978 demonstrated that individual acoustic arrivals at 900-km range were stable and identifiable over a 48-day period. The observed arrival pattern is interpreted by geometry ray theory and by comparison with a 'synthetic sofargram' (equivalent to a synthetic seismogram) constructed from WKBJ theory. Using geometric ray theory, we examine the expected generation and annihilation of ray paths as a result of the seasonal erosion of the autumnal thermocline. Many rays are converted from purely refracted to surface reflected/refracted rays. The ultimate goal of this work is to interpret variability in acoustic transmission in terms of ocean variabiltiy.