We have applied 2D frequency-domain acoustic waveform tomography to two different sections of a marine seismic reflection line from southwest Alaska: one section with a deep igneous basement overlain by a thick pile of sediments and the other section with a shallow basement and a thin sedimentary cover. We have evaluated the appearance of dispersive guided waves on both sections, and we have determined that with appropriate data preconditioning it is possible to invert the data using 2D acoustic waveform tomography. Where the basement is deep, we first reduced the dispersive wave contamination of the seismic field data by trace editing, band-pass filtering, and careful choice of the data window for inversion. We then tested different objective functions and inversion scheduling before selecting an approach based on the logarithmic phase, which could be followed by joint phase and amplitude inversion. Where the basement is shallow, the starting model itself, which was generated by ray-based first-arrival tomography, generated acoustic guided waves, necessitating the use of an absorbing boundary condition at the free surface. Logarithmic phase inversion was used, but the amplitude inversion did not converge. To invert seismic data from both sections, we used a layer stripping strategy in which the gradient was used at each stage of the inversion process to check the corresponding model updates. Our results were validated by comparison between synthetic and observed waveforms, comparison of residual phase error plots for the initial and final velocity models, and comparison of waveform tomography velocity models with migrated images. Waveform tomography permits interpretation of the subsurface close to the seafloor where reflection images are contaminated by water-layer multiples, and we inferred the existence of a fault zone from a low-velocity anomaly within the igneous basement.