This thesis develops a new technique for estimating quasi-homogeneous and
quasi-stationary sea surface wave frequency-direction spectra using acoustic tomography.
The analysis of acoustic (mode and ray) phase and travel time perturbations
due to a rough sea surface is presented. Two canonical waveguides (ideal shallow
water and linear squared index of refraction) are used as examples for the mode
perturbation. The analysis is used to explain high mode coherence measured in
the FRAM N experiment. The forward problem of computing the acoustic phase
and travel time perturbation spectra given the surface wave spectrum is solved to
first order. An application of the technique to ray phase data taken during the
MIZEX '84 experiment is shown. The inverse problems for the homogeneous and
quasi-homogel1eous frequency-direction spectrum are introduced. The theory is applied
to synthetic data which simulate a fetch-dependent sea. The estimates made
agree well with the "actual" (synthetic data) spectrum. The effect of noise in the
travel time estimates is studied. The sensitivity of the technique. to the number
of rays used in the inversion is investigated and the resolution and variance of the
inverse method are addressed.