Ocean Bathymetry Detection from Surface Wave Measurement

In reality, directly measuring the unknown ocean bathymetry can be a challenging or prohibitive task. In this research, we developed a novel method to deduce the unknown bathymetry from the wave surface information based on a variational data assimilation method. Specifically, the high-order spectral method is utilized to simulate the evolution of nonlinear waves interacting with the bottom. An iterative scheme with a gradient-based optimizer is used to obtain the deduced bathymetry. The method only requires limited information, i.e., the surface elevation at two time instants and free surface velocity potential at one time instant, to deduce the unknown bathymetry. Good agreement between the recovered bathymetry and the real one was obtained in the study.