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For narrow azimuth data,
conical-wave source migration has been demonstrated as an efficient way to image the subsurface Duquet et al. (2001); Whitmore (1995); Zhang et al. (2005).
The conical-wave source data are generated as follows
| ![\begin{displaymath}
R_c(p_x,s_y;r_x,r_y,z=0,\omega)=\int R(s_x,s_y;r_x,r_y,z=0,\omega)e^{i\omega (s_xp_x)}ds_x.\end{displaymath}](img13.gif) |
(9) |
And the corresponding conical source at the surface is
| ![\begin{displaymath}
S_c(p_x,s_y;r_x,r_y,z=0,\omega)=\int e^{i\omega(s_xp_x)} ds_x.\end{displaymath}](img14.gif) |
(10) |
Similar to the plane-wave source migration, the image of a conical-wave source can be obtained by
cross-correlating the source and receiver wavefields weighted with the frequency
:
| ![\begin{displaymath}
I_{p_x,s_y}(x,y,z)=\int \omega \bar{S_c}(p_x,s_y;x,y,z,\omega)R_c(p_x,s_y;x,y,z,\omega)d\omega,\end{displaymath}](img15.gif) |
(11) |
where
and
are the conical-wave source and receiver
wavefields extrapolated from the surface using equation 1 and 2. The final image is
generated by stacking images of all possible conical-wave sources of all sail lines:
| ![\begin{displaymath}
I_c=\int\int I_{p_x,s_y}(x,y,z) dp_xds_y.\end{displaymath}](img18.gif) |
(12) |
Similar to the 3D plane-wave migration, the image of conical-wave migration is equivalent to the shot-profile migration.
Next: 3D plane-wave migration in
Up: 3D plane-wave migration
Previous: Plane-wave source migration
Stanford Exploration Project
5/6/2007