  In order to bridge the gap between heliospheric and solar observations of
coronal mass ejections (CMEs), one of the key steps is to improve the
understanding of their corresponding magnetic structures like the magnetic flux
ropes (MFRs). But it remains a challenge to confirm the existence of a coherent
MFR before or upon the CME eruption on the Sun and to quantitatively
characterize the CME-MFR due to the lack of direct magnetic field measurement
in the corona. In this study, we investigate the MFR structures, originating
from two active regions (ARs), AR 11719 and AR 12158, and estimate their
magnetic properties quantitatively. We perform the nonlinear force-free field
extrapolations with preprocessed photospheric vector magnetograms. In addition,
remote-sensing observations are employed to find indirect evidence of MFRs on
the Sun and to analyze the time evolution of magnetic reconnection flux
associated with the flare ribbons during the eruption. A coherent
"pre-existing" MFR structure prior to the flare eruption is identified
quantitatively for one event from the combined analysis of the extrapolation
and observation. Then the characteristics of MFRs for two events on the Sun
before and during the eruption, forming the CME-MFR, including the axial
magnetic flux, field-line twist, and reconnection flux, are estimated and
compared with the corresponding in situ modeling results. We find that the
magnetic reconnection associated with the accompanying flares for both events
injects significant amount of flux into the erupted CME-MFRs.
