2-D reconstruction of boundaries with level set inversion of traveltimes

There are many features in the Earth's crust that involve a jump in physical properties across a sharp boundary. One example is the boundary of an ore body embedded in host rocks. Such well-defined boundaries are often of interest to geophysicists, however traditional minimum-structure inversion methods tend to produce blurred images of the subsurface, where sharp boundaries are not well defined. In this paper, we explore the application of a level set inversion method to recovering a sharp boundary between two slowness values, one characterizing an inclusion, for example, an ore body, the other characterizing a background, for example, host rocks, from first arrival traveltime data. The slowness values are assumed to be known, for example, from sonic logs. We consider the scenario of cross-borehole tomography in two dimensions, however the method is extendible to the 3-D tomography. We test the method on a series of synthetic examples including both fast and slow inclusions. We also investigate numerically the use of straight ray and bent ray forward modelling in the inversion for media with different velocity contrasts.