  A spectral line inversion code, Very Fast Inversion of the Stokes Vector
(VFISV), has been used since May 2010 to infer the solar atmospheric parameters
from the spectropolarimetric observations taken by the Helioseismic and
Magnetic Imager (HMI) aboard the Solar Dynamics Observatory (SDO). The magnetic
filling factor, the fraction of the surface with a resolution element occupied
by magnetic field, is set to have a constant value of one in the current
version of VFISV. This report describes an improved inversion strategy for the
spectropolarimetric data observed with HMI for magnetic field strengths of
intermediate values in areas spatially not fully resolved. The VFISV inversion
code has been modified to enable inversion of the Stokes profiles with two
different components: one magnetic and one non-magnetic. In this scheme, both
components share the atmospheric components except for the magnetic field
strength, inclination, and azimuth. In order to determine whether the new
strategy is useful, we evaluate the inferred parameters inverted with one
magnetic component (the original version of the HMI inversion) and with two
components (the improved version) using a Bayesian analysis. In pixels with
intermediate magnetic field strengths (e.g. plages), the new version provides
statistically significant values of filling fraction and magnetic field vector.
Not only does the fitting of the Stokes profile improve, but the inference of
the magnetic parameters and line-of-sight velocity are obtained uniquely. The
new strategy is also proven to be effective for mitigating the anomalous
hemispheric bias in the east-west magnetic field component in moderate field
regions.
