Modeling and Inversion in the Ocean Waveguide Using Born and Rytov Approximation

The deep ocean has a refractive waveguide velocity structure created by variations in temperature, salinity and pressure. Because the sound speed changes slowly with range and average depth-dependent profiles are known from measurements, an approximate solution to the acoustic field in the waveguide can be formed using perturbation techniques. We then seek to formulate a direct inversion algorithm based on the perturbative solutions. Under certain restrictions, the unknown velocity perturbations about a background profile and the scattered field data can be written as a Fourier transform pair. In this thesis, we investigate two well-known perturbative solutions the Born amplitude expansion and the Rytov phase expansion. The approximations, although closely related, behave quite differently depending on the size of the perturbation, the distance traveled in the perturbed media and the local field gradient. Studying the behavior of the approximations in the forward problem gives an indication of the size and type of perturbations recoverable in the inverse problem. We begin by investigating the perturbative solution behavior for simple velocity structures. In a constant velocity or a layered waveguide, the solutions and the first order errors can be derived explicitly. RRH