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Once we have created an image perturbation , we can invert for the corresponding perturbation in slowness. Mathematically, this amounts to solving an optimization problem like Claerbout (1999)
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(1) |
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where
- is a data-fitting operator, mainly composed of a scattering and a downward continuation operator, but which also incorporates the background wavefield Biondi and Sava (1999),
- is a model-styling operator, either an isotropic Laplacian or an anisotropic steering-filter Clapp and Biondi (1998), which imposes smoothing on the model,
- and are respectively the slowness perturbation (the model) and the image perturbation (the data),
- is a scalar parameter controlling the weight of each of the individual goals.
To speed-up the inversion procedure, we can precondition the model in Equation 1 and solve the system
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(2) |
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where is the preconditioned model variable.
Next: Slowness update and the
Up: Theory
Previous: Residual migration
Stanford Exploration Project
4/27/2000