We apply the inversion scheme of Zheng and Psencik (2002) to the walkaway VSP data of Horne and Leaney (2000) collected in the Java Sea region. The goal is a local determination of parameters of the medium in a vicinity of a receiver situated in a borehole. The inversion scheme is based on linearized equations expressing qPwave slowness and polarization vectors in terms of weak anisotropy (WA) parameters. The presented inversion scheme is independent of structural complexities in the overburden and of the orientation of the borehole. No assumption of local homogeneity around the receiver is necessary. The data used are vertical components of the slowness and polarization vectors. The inversion is performed without any assumptions concerning the orientation of these vectors. The inversion is made (a) assuming arbitrary anisotropy, i.e., without any assumptions about symmetry of the medium, (b) assuming transverse isotropy with a vertical axis of symmetry and (c) assuming isotropy of the medium. The results of inversion show clearly that the studied medium is not isotropic. They also seem to indicate that the studied medium does not possess the VTI symmetry.