Identification of water depth and velocity potential for water waves.

Summary The purpose of this paper is to investigate the identification of the water depth and the water velocity potential in a coastal region by using the linearized water wave equation (LWWE). Existence and uniqueness of the solutions to the partial differential equation LWWE are shown by using the semigroup theory. Moreover the analytical solution is found by the separation of variables method. We assume that the surface wave elevation is measurable. We like to recover the water depth and the water velocity potential from the measurement. This identification problem is shown to be well-posed by proving the parameters' identifiability by the surface elevation. Based on the classical gradient descent method we elaborate an identification algorithm to recover simultaneously both the water depth and the velocity potential. Numerical simulations are carried out to illustrate effectiveness of the algorithm.