The data collected in a cross-borehole tomography problem is inherently incomplete, since the boreholes do not completely surround the media under study. The ability of the experiment to resolve structure is therefore limited by poor experimental geometry. We use the method of Backus an Gilbert to investigate the ability of this technique to resolve variations in acoustic velocity and attenuation between the two boreholes. Both integrals that appear in the Backus-Gilbert formulation can be performed analytically, thus expediting the calculations. The resolving kernels have significant horizontal width, demonstrating that the horizontal position of structures can be only poorly resolved.