Not only the kinematic response of the migration is important, seismic data amplitudes also have the potential to provide information on reservoir properties. However, the most common implementation of shot-profile reverse-time migration uses the zero lag of the cross-correlation of the source and the receiver wavefields as imaging condition. This implementation has the advantage of being robust and honoring the kinematics of Claerbout's imaging principle Claerbout (1971) but does not honor the dynamics of the problem, resulting in the loss of amplitude accuracy.
I find that a damped imaging condition is more appropriate to obtain accurate amplitudes. I define the imaging condition as the zero lag of the cross-correlation of the source and the receiver wavefields divided by the sum of autocorrelation of the source wavefield and a constant damping factor. The division by the autocorrelation of the source wavefield acts as a normalization by the subsurface illumination.
The damping factor is useful because it avoids division by zero. Unfortunately, it introduces an error in the image amplitudes. I used a mask function that is inversely proportional to subsurface illumination to avoid the use of the damping when it is not needed (space and time variable damping).
Using a shot from a 3D marine seismic dataset acquired in a complex area, I compare three different imaging conditions: cross-correlation, division with constant damping, and division with variable damping. I find that the variable damping imaging condition preserves the amplitudes in areas with good subsurface illumination. In areas with poor subsurface illumination, it does the same job as the constant damping imaging condition.