Damping in conventional imaging condition

Conventional shot-profile migration determines the reflection strength at each subsurface point by taking into account only the source and receiver wavefield at that location. Jacobs (1982) compares two different imaging conditions  

$$\bf r=\sum_{shot}\sum_{t} ud,$$ (1)

and  

$$\bf r=\sum_{shot}\sum_{t}\frac{ ud}{ d^2+\varepsilon^2}.$$ (2)

The first is the most commonly used in the industry. It has the advantage of being robust, but has the disadvantage of not computing the correct amplitudes. The second computes the correct amplitudes (except for a damping factor $\varepsilon^2$), but has the disadvantage of relying on a damping factor that cannot be automatically estimated Claerbout (1992).