Abstract: An algorithm is proposed for local evaluation of weakly anisotropic (WA) parameters from measurements of slowness vector components and particle motions of qP waves at individual receivers in a borehole of walkaway vertical seismic profile (VSP) experiment. Formulae for a special case of a single VSP profile are obtained under the assumption of weak but arbitrary anisotropy of the medium. The knowledge of a single component of the slowness vector and the polarization vector is sufficient for performing an inversion in a medium with an arbitrary overburden. A synthetic test is carried out to verify the correctness of the formulae and the method is applied to the observed data from the Java Sea region to invert for the WA parameters in the borehole.