Propagation in a waveguide with range-dependent seabed properties

The ocean environment contains features affecting acoustic propagation that vary on a wide range of time and space scales. A significant body of work over recent decades has aimed at understanding the effects of water column spatial and temporal variability on acoustic propagation. Much less is understood about the impact of spatial variability of seabed properties on propagation, which is the focus of this study. Here, a simple, intuitive expression for propagation with range-dependent boundary properties and uniform water depth is derived. It is shown that incoherent range-dependent propagation depends upon the geometric mean of the seabed plane-wave reflection coefficient and the arithmetic mean of the cycle distance. Thus, only the spatial probability distributions (pdfs) of the sediment properties are required. Also, it is shown that the propagation over a range-dependent seabed tends to be controlled by the lossiest, not the hardest, sediments. Thus, range-dependence generally leads to higher propagation loss than would be expected, due for example to lossy sediment patches and/or nulls in the reflection coefficient. In a few instances, propagation over a range-dependent seabed can be calculated using range-independent sediment properties. The theory may be useful for other (non-oceanic) waveguides.