MIGRATION EQUATION FOR COMMON MIDPOINT SLANT STACK

According to Ottolini 1982, the DSR equation for the downward continuation of common midpoint slant stack is  

$${\partial u \over \partial z } = {{-i\omega \over v} \left[\sqrt{1-(Y+pv)^{2}}+\sqrt{1-(Y-pv)^{2}}\right ]U}$$ (2)

where

$$Y = {{vk_{y} \over 2\omega}}$$

The solution of equation (2) is  

$$U(\omega,z+\Delta z,k)=U(\omega,z,k){\exp \left\{{ {-i\omega... ...1-({vk_{y} \over 2\omega}-pv)^{2}}\right ]\Delta z} \right \} }$$ (3)

We can use this equation to obtain the wave extrapolation for constant velocity. Velocity variations in depth are easily accommodated by varying the velocity v with depth z in equation (3).

*2cm

 

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Figure 1 Computational flow chart of prestack slant stack migration with one-pass PSPI.