There are many features in the Earth’s crust that involve a jump in physical property across a sharp boundary, for example, an ore deposit in host rocks. Such well defined boundaries are often of interest to geophysicists, however traditional minimum-structure inversion methods produce blurred images of the subsurface. In this paper we explore the application of a level set inversion method to recover a sharp boundary between two slowness values, one characterizing an inclusion, e.g. an ore body, the other characterizing a background, e.g. host rock, from first arrival travel time data. The scenario considered is that of cross-borehole tomography in two dimensions.