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# Synthetic data example

In this section, We present a 2-D synthetic example to verify the theory. The reflector of the synthetic model has a spherical shape with a radius of 500 m. Modeling and migration have been done in Biondi and Symes (2003). Figure shows the images obtained with the true (left panel) and a too low () (right panel) velocity models. Figure shows the conventional residual moveout and dip-dependent residual moveout with a same velocity scale parameter. The vertical axes of these three panels are the direction normal to the reflector and the horizontal axes are the opening angle. The ADCIG is at x=3100m, z=720m, where the dip angle is about 45 degree. Panel (a) is the ADCIG without residual moveout. Panel (b) is the ADCIG after conventional residual moveout. Panel (c) is the ADCIG after dip-dependent residual moveout. In Figure , the energy out of 40 degree is the noise due to the illumination. Figure shows the ADCIGs at x=2900m, z=1000m, where the dip angle is about 60 degree. The energy out of 20 degree is the noise due to the illumination. Comparing to 45 degree case, we find that the 60 degree case has a smaller aperture and is more affected by the noise. Since the dip-dependent residual residual moveout moves image points in the direction normal to the reflector (vertical axes in Figure and Figure ), rather than the vertical direction (z direction) as in the conventional residual moveout processing, the former method flattens the ADCIGs better.

migration
Figure 3
Migration results: Left panel is the image migrated with the correct velocity. Right panel is the image migrated with a too slow velocity.

rmo45
Figure 4
Compares between conventional and dip-dependent residual moveout: (a) ADCIG at x=3100m, z=720m without residual moveout; (b) ADCIG at x=3100m, z=720m after conventional residual moveout; (c) ADCIG at x=3100m, z=720m after dip-dependent residual moveout. The vertical axes n is the direction normal to the reflector. The dip angle at x=3100m, z=720m is about 45 degree.

rmo60
Figure 5
Compares between conventional and dip-dependent residual moveout: (a) ADCIG at x=2900m, z=1000m without residual moveout; (b) ADCIG at x=2900m, z=1000 m after conventional residual moveout; (c) ADCIG at x=2900m, z=1000 m after dip-dependent residual moveout. The vertical axes n is the direction normal to the reflector. The dip angle at x=2900m, z=1000m is about 60 degree.

Next: Conclusion Up: Shan and Biondi: Residual Previous: Residual moveout in the
Stanford Exploration Project
10/14/2003