  We present a comparison of the Solar Dynamics Observatory (SDO) analysis of
NOAA Active Region (AR) 11158 and numerical simulations of flux-tube emergence,
aiming to investigate the formation process of this flare-productive AR. First,
we use SDO/Helioseismic and Magnetic Imager (HMI) magnetograms to investigate
the photospheric evolution and Atmospheric Imaging Assembly (AIA) data to
analyze the relevant coronal structures. Key features of this quadrupolar
region are a long sheared polarity inversion line (PIL) in the central
delta-sunspots and a coronal arcade above the PIL. We find that these features
are responsible for the production of intense flares, including an X2.2-class
event. Based on the observations, we then propose two possible models for the
creation of AR 11158 and conduct flux-emergence simulations of the two cases to
reproduce this AR. Case 1 is the emergence of a single flux tube, which is
split into two in the convection zone and emerges at two locations, while Case
2 is the emergence of two isolated but neighboring tubes. We find that, in Case
1, a sheared PIL and a coronal arcade are created in the middle of the region,
which agrees with the AR 11158 observation. However, Case 2 never builds a
clear PIL, which deviates from the observation. Therefore, we conclude that the
flare-productive AR 11158 is, between the two cases, more likely to be created
from a single split emerging flux than from two independent flux bundles.
