  Measurements of magnetic fields and electric currents in the pre-eruptive
corona are crucial to study solar eruptive phenomena, like flare and coronal
mass ejections(CMEs). However, spectro-polarimetric measurements of certain
photospheric lines permit a determination of the vector magnetic field at the
photosphere. Thus, substantial collection of magnetograms relate to the
photospheric surface field only. Numerical modeling is carried out by applying
state-of-the-art nonlinear force-free field (NLFFF) reconstruction. Cartesian
nonlinear force-free field (NLFFF) codes are not well suited for larger
domains, since the spherical nature of the solar surface cannot be neglected
when the field of view is large. One of the most significant results of Solar
Dynamic Observatory (SDO) mission to date has been repeated observations of
large, almost global scale events in which large scale connection between
active regions may play fundamental role. Therefore, it appears prudent to
implement a NLFFF procedure in spherical geometry for use when large scale
boundary data are available, such as from the Helioseismic and Magnetic Imager
(HMI) on board SDO. In this work, we model the coronal magnetic field above
multiple active regions with the help of a potential field and a NLFFF
extrapolation codes in a full-disk using HMI data as a boundary conditions. We
compare projections of the resulting magnetic field lines solutions with
full-disk coronal images from the Atmospheric Imaging Assembly (SDO/AIA) for
both models. This study has found that the NLFFF model reconstructs the
magnetic configuration better than the potential field model. We have concluded
that much of trans-equatorial loops connecting the two solar hemispheres are
current-free.
