An alternative to using standard perturbation theory to compute the mode attenuation coefficients is to use a reflection coefficient argument. For an iso velocity waveguide, assume the magnitude of the bottom reflection coefficient to be close to unity, i.e., approximately Professional Australia Essay Writers | AustraliaEssayWriting.com

a. Derive an expression for the cycle distance associated with a mode. Using this cycle distance, express the change in the acoustic field as a function of the acoustic field itself, the cycle distance and the loss per bounce. This simple differential equation gives the modal attenuation coefficient.

b. What happens for the non-isovelocity case? Compute a skip distance by taking advantage of the fact that the horizontal wavenumber of a mode is constant whereas the vertical wavenumber varies with depth.