An original method is presented that allows us to measure the local shear-wave birefringence properties over any depth interval. It requires the acquisition of two shear-wave vertical seismic profiles (VSPs), each with different initial polarizations of the shear wave. The method is based on the estimation of a two by two matrix (called the propagator matrix) that represents a linear operator between two states of polarization. No information is required about layering above the zone of interest (in particular, about the weathering zone). If these two states of polarization correspond to the direct downgoing shear wave at two different depths z 1 and z 2 , the operator represents the transmission properties between the two depths. Under the previous hypothesis, this operator is independent of the source polarization and can be accurately estimated by a least-squares method in the frequency domain. Physically, this operator is a multicomponent deconvolution, whose column vectors represent the state of polarizations at a depth z 2 for two linear and mutually perpendicular polarizations at depth z 1 . This allows for the measurement of the birefringence properties in all azimuthal directions to determine the directions for which a linearly polarized shear-wave propagates.In addition, the method can be applied to perform the deconvolution of the upgoing wavefield by the downgoing wavefield to obtain a reflection matrix. Then the matrix can be interpreted in terms of anisotropy below the receiver depths (particularly below the well bottom) and in terms of anisotropy of the reflector itself.The proposed method is validated on synthetic data and is applied to real data from the Paris basin. For this particular data set, the birefringence is located in two layers; the first layer consists of unproductive sands and clays while the second one corresponds to a carbonate oil reservoir from the Dogger formation. The natural directions in both layers are very close to the main directions known for the regional stress field. The presence of fractures in the reservoir layer can explain the strong birefringence ratio (>6 percent).