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Image mispositioning in ADCIGs migrated with wrong velocity

In a previous section, we demonstrated that in an ADCIG cube the imaging point ${I}_{\gamma}$ lies on the line normal to the apparent geological dip and passing through the point where the source and receiver rays cross (Figure [*]). This geometric property enabled us to define the analytical relationship between reflector movement and traveltime perturbation expressed in equation (15). This important result is verified by the numerical experiment shown in Figure [*]. This figure compares the images of the spherical reflector obtained using the low velocity (slowness scaled by $\rho=1.04$)with the reflector position computed analytically under the assumption that ${I}_{\gamma}$ is indeed the image point in an ADCIG. Because both the true and the migration velocity functions are constant, the migrated reflector location can be computed exactly by a simple ``kinematic migration'' of the recorded events. This process takes into account the difference in propagation directions between the ``true'' events and the ``migrated'' events caused by the scaling of the velocity function. Appendix C derives the equations used to compute the migrated reflector location as a function of $\rho$, $\alpha_{\rho}$,and $\gamma_{\rho}$.

The images shown in the six panels in Figure [*] correspond to six different apparent aperture angles: a) $\gamma_{\rho}=0$,b) $\gamma_{\rho}=10$,c) $\gamma_{\rho}=20$,d) $\gamma_{\rho}=30$,e) $\gamma_{\rho}=40$,f) $\gamma_{\rho}=50$.The black lines superimposed onto the images are the corresponding reflector locations predicted by the relationships derived in Appendix C. The analytical lines perfectly track the migrated images for all values of $\gamma_{\rho}$.The lines terminate when the corresponding event was not recorded by the data acquisition geometry (described above). The images extend beyond the termination of the analytical lines because the truncation artifacts are affected by the finite-frequency nature of the seismic signal, and thus they are not predicted by the simple kinematic modeling described in Appendix C.

 
Tomo-slow-4p-overn
Tomo-slow-4p-overn
Figure 13
Comparison of the actual images obtained using the low velocity, with the reflector position computed analytically under the assumption that the image point lies on the normal to the apparent geological dip (${I}_{\gamma}$ in Figure [*]). The black lines superimposed onto the images are the reflector locations predicted by the relationships presented in Appendix C. The six panels correspond to six different apparent aperture angles: a) $\gamma_{\rho}=0$b) $\gamma_{\rho}=10$c) $\gamma_{\rho}=20$d) $\gamma_{\rho}=30$e) $\gamma_{\rho}=40$f) $\gamma_{\rho}=50$.


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next up previous print clean
Next: Residual moveout in ADCIGs Up: Illustration of CIGs kinematic Previous: Transformation of HOCIGs and
Stanford Exploration Project
7/8/2003