Although the petroleum industry has imaged reflections from the sides of salt domes, steeply dipping structures have not been imaged as reflectors outside of sedimentary basins; to do so requires appropriate data acquisition, prestack depth migration, and an excellent seismic velocity model. Poststack time migrated seismic images, normal moveout velocity analysis, well logs, and other geologic information are used to build the velocity model. In regions of interest outside of sedimentary basins, such as major strike-slip faults, seismic reflectivity is often sparse and little is known of detailed subsurface geology. Alternate methods of velocity model construction must be used. First arrival (refraction and turning ray) traveltime tomography is proposed to construct the preliminary velocity model for steep-dip prestack depth migration in settings with little a priori subsurface information. A densely spaced synthetic seismic data set with long-offset recording, modeled after a real survey across the San Andreas Fault, was constructed using a finite-difference algorithm. First arrival traveltimes were picked from the data and a velocity model was constructed using tomography. The velocity model was used to perform a Kirchhoff prestack depth migration of the synthetic shot gathers. The subsurface structure was sufficiently reconstructed that the velocity model could be refined through migration velocity analysis. A series of tomography tests was used to determine the spatial resolution limits of the velocity model. Isolated erroneous anomalies with sizes near the resolution limits were added to the velocity model derived from tomography and used as input for migration. This pessimistic test provided an adequate image and identifiable arrivals in migrated common image gathers, allowing the velocity model to be improved through migration moveout analysis. Data acquisition requirements for tomography include long recording offsets and times, larger sources, and dense spacings, very similar to the requirements for steep-dip reflection imaging. / Master of Science