visual and manual inspections are required.

![ Complex cases treated by [trunk-1]{} for the ID of lines. Panel (a) the simplest case. Panel (b) two candidate lines case. Panel (c) two observed lines have one theoretical line as candidate. Panel (d) two- features, two- candidates (duplets). Panel (e) two velocity-component case. Panel (f) two velocity-component duplets case. See text for details. []{data-label="cases1"}](fig3_Cases.eps){width="8.5cm"}

Line Profile and EWs {#line-profile-and-ews .unnumbered}
--------------------

Our procedure receive a list of lines (previously produced in the ID step) and applies the following treads: Each transition produces an absorption optical depth computed with: $$\tau_{\lambda}=\tau_{0}\phi_{\lambda},$$ the optical depth at the core of the line is $\tau_{0}=\int^{\Delta R}_{0}\tau_0(r) dr = 
N_{\rm ion}^0\frac{\pi e^2}{mc}f_{\rm lu}$, where $\Delta R=N_H/n_H$ is the thickness of the slab, $N_{\rm ion}^0$ is the column density of the ion at the line core (i.e., $\lambda=\lambda_0$), $m$ is the electron mass, $e$ is the electron charge, $c$ is the speed of light, and $f_{\rm lu}$ is the oscillator strength of the transition. The line profile $\phi_{\lambda}$, is assumed to be a Voigt profile ([@rybicki1979a]). The Doppler broadening parameter $v_{\rm Dop}^2=v_{\rm turb}^2+v_{\rm therm}^2$, is the combination of microturbulent ($v_{\rm turb}$) and thermal broadening ($v_{\rm therm}$). The last one 