Simultaneous identification of velocity and water depth of linear water waves

In this paper, we propose an algorithm of identification in order to simultaneously estimate the velocity of water waves and the water depth in coastal region. We assume that the motion of water waves is described by linearized water wave equation (LWWE) and the surface wave elevation is measurable. Based on the gradient descent method, we design an algorithm of identification to recover simultaneously both the velocity of water waves and the water depth. Numerical simulations are carried out to show the effectiveness of the algorithm.