$\rm QFit$ is limited here to its energy range of relevance, $\rm E_{\nu} \leq 2$ TeV.[]{data-label="aefffig"}](./Aeff_12Line_BBFitS_AAFitM_LogScale_ANUNU_New.eps){width="0.8\linewidth"}

Two reconstruction algorithms are used in this paper. The first one is based on the minimisation of a $\rm \chi^{2}$-like quality parameter of the reconstruction, $\rm Q$, which uses the difference between the expected and measured times of the detected photons, taking into account the effect of light absorption in the water [@bbfit]. The second algorithm consists of a multi-step procedure to fit the direction of the muon track by maximising a likelihood ratio, $\rm \Lambda$, which describes the quality of the reconstruction [@ps]. In addition to the $\rm \Lambda$ parameter, the uncertainty of the muon track angle, $\rm \beta$, is used for the track selection. These two algorithms are respectively called here $\rm QFit$ and $\rm \Lambda Fit$. $\rm QFit$ is used for muon events reconstructed in a single detection line (single-line events), and $\rm \Lambda Fit$ for muon events reconstructed on more than one detection line (multi-line events) in order to reach the best efficiency of reconstruction in the entire neutrino energy range. For $\rm QFit$ and $\rm \Lambda Fit$, a selection on the quality parameter $\rm Q < 0.8$ and the 