  Borehole seismic data is obtained by receivers located in a well, with
sources located on the surface or in another well. Using microlocal analysis,
we study possible approximate reconstruction via linearized, filtered
backprojection of an isotropic sound speed in the subsurface for three types of
data sets. The sources may form a dense array on the surface, or be located
along a line on the surface (walkaway geometry) or in another borehole
(crosswell). We show that for the dense array, reconstruction is feasible, with
no artifacts in the absence of caustics in the background ray geometry, and
mild artifacts in the presence of fold caustics in a sense that we define. In
contrast, the walkaway and crosswell data sets both give rise to strong,
nonremovable artifacts.
