ADCIGs movement with wrong velocity

We use the ray-tracing to predict the localization of the energy in the synthetic dataset migrated with the wrong velocity. The ray-tracing is illustrated by Figure . Starting from the true position of the image point (the diamond on the Figure), we seek the position of the image point (stars on the figure) when an incorrect migration velocity is used. The reflector has a fixed azimuth and dip. We first model the events recorded at the surface at one particular aperture and reflection azimuth. Once the true events are known, the source and the receiver rays are shot in a media with an incorrect velocity this time. If the velocity is too slow, then the rays stop at two distinct end points. Knowing the position of the end points and the ray parameters, the position of the image point in the angle domain for an incorrect migration velocity is determined through a geometric construction similar to the one in . It is also possible to use the normal shift described in the 2-D case since we have shown that the 3-D problem can be recast as 2-D one. We test this procedure on an image point on the 60 dip reflector and whose location is (400,400,1300) in image. We choose a source-receiver pair such as the aperture angle is $32^\circ$. Again, our goal is to find where the true image point has moved because of the use of an incorrect migration velocity. We observe on Figure that the coordinates of the apparent image point in the angle domain computed by ray-tracing do match those of the image point in the model migrated with the wrong velocity.

 

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Figure 10 Dataset migrated with the incorrect velocity.