Abstract

Surface water-wave scattering over highly-variable bottoms is the theme of this presentation. Interesting phenomena, such as the apparent diffusion and the time-reversed refocusing of these waves, can be understood through a probabilistic modeling of disorder. Namely the bottom topography profile can be interpreted as a random coefficient in the differential equations. Reduced modeling, from the Euler equations, play a fundamental role in the asymptotic theory and computations. The reduced models are Boussinesq-type systems. An overview of these issues will be presented indicating, for example, how a tsunami can be attenuated in the coastal region through its interaction with the bottom. Also how time-reversed refocusing performs the waveform inversion. It will be shown that asymptotically-equivalent Boussinesq systems may lead to different waveform inversion. Hence a recent non-local formulation (Fokas & Nachbin, 2012) has a great potential for studying the full potential-theory scattering problem.