Abstract
The loss of temporal coherence after long range propagation in shallow water is often studied as a consequence of sound speed variability from internal waves. Here we add the complication of small amplitude and very long wavelength random fluctuations of bottom bathymetry. It is shown that the same range dependent sound speed fluctuations result in markedly different coherence times depending on acoustic wavelength and mode number - a first order effect. A range dependent PE code (MMPE) is used to predict temporal coherence for individual surface reflected- bottom-reflected (SRBR) mode arrivals. Here a mode coherence calculation is developed and compared for varying RMS bathymetry. Temporal coherence is inferred from mode coherence. We find first order and /or low frequency modes are insensitive to the bottom but when the (sine of the mode angle approaches 1/10 of an acoustic wavelength) the modes structure in amplitude and phase is randomized and the signal decorrelate rapidly in time from just the slightest temporal variations in sound speed. It doesn't take much; just 1 m in 200m of range will randomize all but the first mode at mid frequencies (.5 to 1 kHz). Predictions are in close agreement with SW06 mode coherence measurements.