this approach.

The effective depth of a transient survey in the context of detecting strongly lensed supernovae via magnification is modulated by the extent to which all lensing images contribute to the measured flux. It is natural to consider here two scenarios in which the total observed flux either comes from all images or is simply approximated by the flux of the brightest image. The former, which we adopt as our base model, sets an upper limit on the effective depth and discovery rates with respect to how efficiently the measured flux is integrated over all images. The latter determines the corresponding lower limits. We expect that most realistic detections in typical transient surveys will be intermediate between the two extremes.

Compared to the strategy based on detection of multiple images, the competitiveness of this method heavily relies on follow-up observations. Higher resolution and deeper observations are necessary to both confirm the lensing nature of the candidates (by means of detecting multiple images) and determining the lensing configuration.

Although initially envisaged for finding strongly lensed type Ia supernovae, the method can be also applied to detecting gravitationally lensed core-collapse supernovae [@Gold2018]. Here, using type Ia supernovae as the reference class 