A convolutional sequence of matrix operators is offered as a convenient deterministic scheme for processing a multicomponent vertical seismic profile (VSP). This sequence is applied to a nine-component near-offset VSP recorded at the Conoco borehole test facility, Kay County, Oklahoma. These data are corrected for tool spin and near-surface anisotropy together with source coupling or imbalance. After wave-field separation using a standard f -k filter, each source and receiver pair for the upgoing waves is adjusted to a common reference depth using a matrix operator based on the downgoing wavefield. The up-and downgoing waves are then processed for anisotropy by a similarity transformation, to separate the qS1 and qS2 waves, from which the anisotropic properties are estimated. These estimates reveal a strong (apparent) vertical birefringence in the near-surface, but weak or moderate values for the majority of the subsurface. The target zone consists of a thin sandstone and deeper shale layer, both of which possess a strong vertical birefringence. The sandstone corresponds to a zone of known fluid flow. An observed qS2 attenuation and polarization change in the shale suggest it contains large fractures.