Formation Heights of Extreme Ultraviolet Lines in an Active Region Derived by Correlation of Doppler Velocity and Magnetic Field

We study the correlation heights, which indicate the formation height of Extreme Ultraviolet (EUV) lines in an active region using observations from the EUV Imaging Spectrometer (EIS) and Solar Optical Telescope (SOT) on board \emph{Hinode}. The nonlinear force-free field (NLFFF) optimization method is adopted to extrapolate the 3D magnetic fields to higher layers. Three subregions with different characteristics are selected in the active region for this study. The results show that the formation heights in different subregions vary with their different magnetic fields or velocity patterns. After solving the line blending problem between the He {\sc \romannumeral 2} 256.32 \AA and Si {\sc \romannumeral 10} 256.37 \AA lines by the double Gaussian curve fitting, we find that the transition region lies higher in a strong magnetic area. In a pre-flare heating area there possibly exist multithermal loops as implied by comparing the Doppler velocity and the magnetic field on the solar disk.