strongly lensed type Ia supernovae expected for the three methods with the base choice of free parameters, as outlined in Section 2. Our results demonstrate that the method based on detecting highly magnified supernovae surpasses the image multiplicity technique for relatively shallow surveys with limiting magnitudes $\lesssim 22$. In particular, for a survey with a 21 magnitude depth, the magnification method is expected to find $\sim 20$ times more strongly lensed supernovae than the image multiplicity method. Due to the stronger dependence on the limiting magnitude for the image multiplicity method, this ratio becomes larger for even shallower surveys, with a 3-fold change per magnitude in the $i$ band.

For limiting magnitudes $\gtrsim 23$, increasing survey depth does not improve the performance of the magnification method, but it appreciably increases the rates for the other method. For deep surveys like the LSST, detecting multiple images appears to become a more powerful means for finding lensed type Ia supernovae than gravitational magnification. The image multiplicity method is expected to yield about twice as many detections as the magnification method at a limiting magnitude of $24$. The difference between the two methods becomes even more prominent for deeper surveys: the rates expected 