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We apply the inversion scheme of Zheng and Pšenčík (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 surrounding the borehole receiver array. The inversion scheme is based on linearized equations expressing qP -wave slowness and polarization vectors in terms of weak anisotropy (WA) parameters. It thus represents an alternative approach to Horne and Leaney (2000), who based their procedure on inversion of the Christoffel equation using a global optimization method. The presented inversion scheme is independent of structural complexities in the overburden and of the orientation of the borehole. The inverson formula is local, and has therefore potential to separate effects of anisotropy from effects of inhomogeneity. The data used are components of the slowness vector along the receiver array and polarization vectors. The inversion is performed without any assumptions concerning the remaining components of the slowness vector. 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. Inverted are the raw data as well as data, in which weighting is used to reduce the effect of outliers. It is found that the WA parameters ǫ z , ǫ 15 and ǫ 35 are considerably more stable than the parameters ǫ x and δ x . The latter two parameters are also found to be strongly correlated. Weaker correlation is also found between the mentioned two parameters and ǫ z . 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.