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In a previous paper, we argued that the inversion of Stokes profiles appliedto spectropolarimetric observations of the solar internetwork yieldunrealistically large values of the inclination of the magnetic field vector($\gamma$). This is because photon noise in Stokes $Q$ and $U$ are interpretedby the inversion code as valid signals, that leads to an overestimation of thetransverse component $B_\perp$, thus the inclination $\gamma$. However, ourstudy was based on the analysis of linear polarization signals that featuredonly uncorrelated noise. In this paper, we develop this idea further and studythis effect in Stokes $Q$ and $U$ profiles that also show correlated noise. Inaddition, we extend our study to the three components of the magnetic fieldvector, as well as the magnetic filling factor $\alpha$. With this, we confirmthe tendency to overestimate $\gamma$ when inverting linear polarizationprofiles that, although non-zero, are still below the noise level. We alsoestablish that the overestimation occurs mainly for magnetic fields that arenearly vertical $\gamma \lesssim 20\deg$. This indicates that a reliableinference of the inclination of the magnetic field vector cannot be achieved byanalyzing only Stokes $I$ and $V$. In addition, when inverting Stokes $Q$ and$U$ profiles below the noise, the inversion code retrieves a randomly uniformdistribution of the azimuth of the magnetic field vector $\phi$. To avoid theseproblems, we propose only inverting Stokes profiles for which the linearpolarization signals are sufficiently above the noise level. However, thisapproach is also biased because, in spite of allowing for a very accurateretrieval of the magnetic field vector from the selected Stokes profiles, itselects only profiles arising from highly inclined magnetic fields.

Inferring the magnetic field vector in the quiet Sun. II. Interpreting results from the inversion of Stokes profiles