The waveguide invariant β and bottom reflection phase-shift parameter P

It is known that the waveguide invariant β is affected by the shallow-water environment. In this paper the effect due to bottom sediment is investigated. It is found that the effect of sediment bottom can be concentrated on one parameter P – the bottom reflection phase shift parameter. For a Pekeris waveguide, under WKB approximation, a very simple analytic relation is given: β≈1+P/(k0Heff), here Heff is the `effective depth', and Heff =H+P/2k0. It is shown that the value of β related to different high-speed sediments (including layered sediment) is ranged in 1.0 and 1.5. Some numerical examples including the layered sediment case are conducted to verify this result. Good agreement between the results calculated by KRAKEN and by WKB with parameter P has been found. The advantage of using parameter P is that it can cover any type of high-speed sediment even including shear wave effect, moreover, it also works for layered sediment provided using P(o/mega) instead of constant P. Hence, by using parameter P allows us to have a model-free platform to investigate the sound field in shallow-water including the bottom effect on the waveguide invariant β. [This work was supported by NSFC under Grant No.10874201 and No.11074271]