Migration velocity analysis for anisotropic models |

On the other hand, the update [Figure 2(d)] is in general larger than the true model [Figure 2(c)]. A trade-off is observed below 1,600 m, where the inverted velocity is smaller but is much larger than the true values. This result illustrates the null space of our inversion problem, since the reflector around 2,200 m is well-focused (although not perfectly focused) in the final image obtained with the inverted model [Figure 3(b)]. This problem can presumably be resolved by increasing the angle coverage at depth and allowing more iterations in the inversion.

Figure 3 compares the subsurface-offset images using the initial model (a), the updated model (b), and the true model (c). After the inversion, the reflectors are focused at zero subsurface-offset, and the depths of the reflectors are closer to the true depths. The focused image shows that we are dealing with a non-linear problem with a large null space. To reduce the size of the null space, and hence the uncertainty in the inverted model, other information such as checkshots or rock-physics prior knowledge is needed (Li et al., 2011b,a).

init-over-true,inv-over-true,true-eta,inv-eta
(a) Ratio of initial velocity over true velocity; (b) ratio of
inverted velocity over true velocity; (c) true
model; (d)
inverted
model.
Figure 2. |
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init-image,final-image,true-image
Subsurface offset
images using the initial model (a), the updated model (b), and the
true model (c).
Figure 3. |
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Migration velocity analysis for anisotropic models |

2011-05-24