Regularization 2: Differencing across offset  

After imaging with the correct velocity, signal events on all $\bold m_{i,k,m}$ are flat, while crosstalk events have at least some residual curvature, especially at far offsets and in regions with a strong velocity gradient. Provided that the AVO response of the signal changes slowly with offset, the difference (in offset) between adjacent samples of any $\bold m_{i,k,m}$ will be relatively small where there is signal, but large where there is crosstalk noise. We again cast this difference as a model residual:  

$$\bold r_m^{[2]}[i,k,m](\tau,x) = \bold m_{i,k,m}(\tau,x) - \bold m_{i,k,m}(\tau,x+\Delta x).$$ (8)