Oceans are a vast, complex world where underwater sound is the most efficient tool available to understand its detailed characteristics. However the underwater channel has a very complex geometrical and material structure and hence special techniques are required to model it. Analytical solutions are feasible only when one makes gross assumptions and approximations. Several numerical and semi-numerical techniques have been developed for estimating the sound field in the ocean channel. But no single method is capable of handling all possible environmental conditions, frequency, and ranges of interest in remote sensing problems. We explore in this chapter the scope and feasibility of finite element method in underwater remote sensing. The current study is based on a channel model with cylindrical symmetry and a time-harmonic source signal. A variational formulation is used to derive the finite element model for acoustical radiation, scattering and propagation in the ocean. A Bayliss-type radiation boundary condition is used to model the far field behaviour without the need to deal with a large solution domain. Since the ocean geometry can support several propagating, evanescent, and radiation modes, a penalty function approach is employed to impose the far field radiation condition. A distinct feature of the ocean channel is its depth-dependent sound speed. The eigensolution for this channel is required for imposing the radiation condition at the truncation boundary. We have cast this eigenproblem in a variational form and employed a Rayleigh-Ritz method to obtain an approximate eigensolution. This approach has provided a good approximation of the depth eigenmodes in a compact semi-analytic form. We have employed our finite element algorithm to model several range- and depth-dependent ocean problems. Our numerical study has established that our finite element algorithm gives accurate results with reasonable effort. In particular, our finite element approach is most appropriate for shallow water problems where the interaction of wave modes with irregular ocean bottom is quite complex. The penalty function approach employed to implement the radiation boundary condition has been found to be robust over a wide range of penalty scale factors. We have also extended this work for the case of irregular elastic sea bed. We continue to explore and further develop our finite element approach by applying it to several other ocean acoustic problems encountered in the remote sensing of ocean environment.
Part of the book: Environmental Applications of Remote Sensing