In the converted-wave method of seismic refraction interpretation, travel times for compressional, converted, and transverse head waves are used in combination to obtain velocities and layer thicknesses. The applicability of the method over interfaces with high dip and curvature is investigated, treating the two- and three-layer cases for layers of uniform velocity, with upper-layer velocity known, where the problem is to calculate velocities at depth and delineate the interfaces. It is shown that although dip and curvature affect the calculation, procedures can be devised to obtain solutions in the presence of these factors. Examples of application of the method in the two-layer case to a plane interface dipping at 30°, and to a curved interface with dip changing linearly from 0° to 27° are given.Depth calculation using intervals between the travel times of converted waves are shown to be independent of dip for a plane interface, but sensitive to curvature for a curved interface. It is shown that in these cases, a satisfactory depth calculation is possible.Ratios of these time intervals are shown to produce depth ratios that are either independent of velocity or with low dependence upon this parameter.A number of capabilities peculiar to the converted-wave method are noted.