Wave-equation tomography for anisotropic parameters |

Figure 2 shows the model perturbations, with a rectangular slowness anomaly that is 10% lower than the background slowness on the left, and a rectangular anisotropic anomaly on the right. The perturbation in within the rectangular block is constant ( ). Figure 3 shows the perturbed image at the zero lag of the subsurface offset due to the model perturbations after applying the forward WETom operator. Adjoint WETom operator back-projects the perturbed image into the model space, and outputs the gradient for the model perturbation, as shown in Figure 4. Comparing Figure 2 and Figure 4, we can see that the gradients provide the correct direction and shape of the perturbation to conduct a line search in a given inversion scheme.

background
Background isotropic model. Left is the velocity model with one reflector, and right is the
model with constant zero.
Figure 1. |
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perturb
Model perturbations. Left is a rectangular slowness anomaly that is 10% lower than the background slowness , and right is a rectangular anisotropic anomaly with a constant value of
.
Figure 2. |
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Dimage
Perturbed image from the forward anisotropic WETom operator. The image is extracted from the zero lag of the subsurface offset.
Figure 3. | |
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Dmodel
Back-resolved gradient for the model updates. Left is the gradient for slowness, and right is the gradient for
.
Figure 4. |
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Wave-equation tomography for anisotropic parameters |

2010-05-19