This study is motivated by the lack of measurements of effective transverse isotropy (TI) at the seismic scale. Then, the purpose is to determine the TI parameters at the receivers locations from three component offset VSPs recordings. The data set consists of both polarization directions and vertical apparent slowness corresponding to different offsets. These velocities are measured from the vertical travel times between at least two receivers in the well. The polarization directions are measured by the angle Y from the vertical direction. In order to estimate the TI parameters, we study P- and SV- waves propagation in transversely isotropic (TI) media. A TI medium is described by live independent elastic moduli but only four of them are needed for describing the propagation of P- and SV- waves and then SH- waves correspond to an uncoupled problem. Velocities and polarization expressions are functions on these four elastic moduli and on the incidence angle O which is not directly approachable from the data set. Then, we define two TI parameters which simplify these expressions and correctly describe velocity variations with O. These two parameters are combinations of the four elastic moduli and are slightly different from classical TI parameters. Hence, we propose an exact expression of 0 as a function of Y which allows us to express velocities as a function of Y without any approximations. A method is proposed to apply this model for solving the inverse problem of estimating TI parameters from the data set. We settle, from the sensitivity of this model to parameters variations, the range of incidence for which the TI parameters are accurately estimated. Furthermore, we show how a priori error on data (due to uncertainties on measurements) is transmitted on parameters values. This method is checked on synthetic data and on two real VSPs. The fist one was recorded recorded on the test site of the Colorado Sehool of Mines (White et al., 1983). The second one is a walkaway recorded in the Paris Basin. In a last part, a model is defined for taking into account, in the inverse problem, the pressure meaured in a fluid-filled borehole embedded in a TI medium as an additional datum. This model is checked on synthetic data.
