Point to point propagation over a phase gradient grooved surface

Previous work on deriving a modal theory for predicting point-to-point propagation over a uniformly grooved surface is extended to predict propagation over a periodic variable depth grooved surface with a low flow resistivity porous material of different thickness in each groove. The form of the surface is intended to create an approximately linear phase gradient for plane waves reflected from the surface. The resulting attenuation due to ground effect is found to be larger and more broadband than predicted over either an acoustically hard grooved surface or an acoustically soft layer with thickness equal to the largest groove depth for the same source-receiver geometry. Various contributions to the excess attenuation spectrum from surface waves associated with the different groove depths, quarter wavelength resonances in the grooves, the phase gradient for plane wave reflections and diffracted modes are investigated. As result the broadband nature of the excess attenuation is explained and important parameters in designing such surfaces are identified