Masking the damping factor

The damping factor is useful because it avoids instability in noisy-signal division but problematic because it biases the image amplitudes. I propose to add a mask function inversely proportional to the subsurface illumination at each point Rickett (2001).  

$$\bf w \quad \alpha \quad \frac{1}{d^2}.$$ (3)

When $\bf d^2$ has enough energy to contribute to the image, the damping factor $\varepsilon$ is set to zero. When factor $\bf d^2$ is small, the damping factor is kept to avoid zero division. Thus, the imaging condition can be set as  

$$\bf r=\sum_{shot}\sum_{t}\frac{ ud}{ d^2+w \varepsilon^2},$$ (4)

where the damping is now variable in space and time.