Reconstruction of the simulated 3D magnetic field with the use of local data that lack LOS field component information. The blue sphere represents the celestial sphere. Panel a: ground truth; the GMF obtained as described in Appendix A. The field is rescaled so that it has an RMS norm of 5 μG. Panel b: synthetic data based on the ground truth of Fig. 2a. The radial component of the magnetic field is not measured. Panel c: the mean of the approximating posterior distribution attained via the geoVI algorithm based on the data provided in Fig. 2b. Panel d: mean of the approximating posterior distribution attained for the local data of Fig. 2b as well as integrated measurements of the radial component (Fig. 6b). The side of the box is about 1.6 kpc, or approximately 20 times the GMF correlation length.