Dip and offset together

DMO IN THE PROCESSING FLOW

Instead of implementing equation (8.28) in one step we can split it into two steps. The first step converts raw data at time $t_h$ to NMOed data at time $t_n$.

$$t_n^2 \eq t_h^2 - {h^2 \over{v_{\rm half}^2}}$$ (29)

The second step is the DMO step which like Kirchhoff migration itself is a convolution over the $x$-axis (or $b$-axis) with

$$t_0^2 \eq t_n^2 \left( 1 - {b^2 \over h^2} \right)$$ (30)

and it converts time $t_n$ to time $t_0$. Substituting (8.29) into (8.30) leads back to (8.28). As equation (8.30) clearly states, the DMO step itself is essentially velocity independent, but the NMO step naturally is not.

Now the program. Backsolving equation (8.30) for $t_n$ gives

$$t_n^2 \eq {t_0^2 \over 1-b^2/h^2 } .$$ (31)

In figures 8.24 and 8.25, notice the big noise reduction over Figure 8.18.

dmatt Figure 24. Impulse response of DMO and NMO

coffs Figure 25. Synthetic Cheop's pyramid

Dip and offset together