  The distribution of magnetic field strength at different levels in the solar
photosphere outside active regions was obtained on the basis of the 2D MHD
simulation of magnetogranulation and the synthesis of the V profiles of the Fe
I 1564.8 nm line. The shape of the distribution varies essentially with depth
in the photosphere. The distribution maximum lies about at 25 mT, but it is
found near 35 mT when the spatial averaging of profiles (about 0.5") is taken
into account. Our analysis reveals that the use of the Fe I 1564.8 nm line for
determination of field strength from V profile splitting is the most efficient
and reliable means of measuring fields above 50 mT. The field strength
distribution obtained with the 1564.8 nm line in the fields above 50 mT can
serve as a standard for testing other techniques and spectral lines. The
analysis of the synthesized Fe I 630.2 nm line profiles supports the conclusion
that this line is less suitable for studying field strength distributions
because of its weak magnetic sensitivity to fields below 120 mT. The derived
magnetic field distributions as well as the distributions of asymmetry
parameters and V profile zero-crossings are in good agreement with IR
polarimetry data. They convincingly confirm the assumption that the structure
and strength of photospheric magnetic fields of mixed polarity have continuous
spectra down to scales considerably smaller than the resolution threshold. They
also suggest that the structure and the scales of magnetic fields are closely
related to the granulation structure.
