This paper presents and interprets some observations of the limb polarization of Sr  4607 Å obtained with the spectropolarimeter of the French-Italian telescope THEMIS in quiet regions close to the solar North Pole on 2002 December 7-9. The linear polarization was measured for a series of limb distances ranging from 4 to 160 arcsec, corresponding to heights of optical depth unity in the line core ranging from about 330 to 220 km, respectively, above the τ 5000 = 1 level. To increase the

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... etric sensitivity, the data were averaged along the spectrograph slit (one arcmin long) set parallel to the solar limb. Since the data show no rotation of the linear polarization direction with respect to the limb direction, the observed depolarization is ascribed to the Hanle effect of a turbulent weak magnetic field, the zero-field polarization being derived from a model. The interpretation is performed by means of an algorithm which describes the process of line formation in terms of the atomic density matrix formalism, the solar atmosphere being described by an empirical, plane-parallel model. The collisional rates entering the model (inelastic collisions with electrons, elastic depolarizing collisions with neutral hydrogen), have been computed by applying fast semi-classical methods having a typical accuracy of the order of 20% or better (see Derouich 2004), leading to 6% inaccuracy on the magnetic field strength determination. We assume a unimodal distribution for the intensity of the turbulent field. The computed intensity profile has been adjusted to the observed one in both depth and width, by varying both microturbulent and macroturbulent velocities. The best adjustment is obtained for respectively 1.87 km s −1 (micro) and 1.78 km s −1 (macro). The evaluation of the magnetic depolarization leads then to the average value of 46 Gauss for the turbulent magnetic field strength, with a gradient of −0.12 Gauss/km. Our results are in very good agreement with the value of 60 Gauss determined at large µ, in the volume-filling field case, by Trujillo Bueno et al. (2004, Nature, 430, 326), using a 3D magneto-convective simulation. This validates our method.