The Interaction of Inhomogeneous Waves and Gaussian Beams with Mud in Between a Hard Solid and an Ideal Liquid

Mud is classified as a Bingham liquid, which, situated in between a hard solid and an ideal liquid, forms a rheological system in which the physical parameters vary continuously. Moreover, inside this liquid, there is often a transition zone (at the nautical bottom) in which the shear wave velocity varies almost exponentially. First we translate this rheological system into a theoretical rheological model that is numerically susceptible to predict its physical influence on impinging sound. Then, we show theoretically how the interaction of sound with this rheological model is solved. Finally, we present some numerical results for impinging inhomogeneous waves and we show how a bounded beam interacts with this continuously layered system. The paper shows that it is theoretically possible to apply the inhomogeneous wave theory for such a system and also that the Fourier description of bounded beams works excellent for describing the propagation of bounded beams through mud. Even though it is widely known that echo sounding cannot reveal the position of the nautical bottom, we show that its position influences the reflected beam pattern for oblique incidence, which is promising for nautical depth determination in harbors and rivers.