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Regularized Inversion with model Preconditioning (RIP)

To speed the convergence of the inversion, we can reformulate the inversion problem as a Regularized Inversion with model Preconditioning (RIP) through the use of a preconditioning operator 43#43. This operator should be as close to the inverse of the regularization operator as possible so that 44#44.By mapping the multi-dimensional regularization operator 39#39 to helical space and applying polynomial division, we can apply the exact inverse so that 45#45 (). We also use the preconditioning transformation 46#46 (). My objective function then becomes:

 
 47#47 (22)

In fitting goals this is:

   48#48 (23)
(24)

Now the model styling goal contains the identity operator 49#49, which is very well conditioned. This will allow the iterative inversion to converge faster.


next up previous print clean
Next: Regularization schemes and operators Up: Regularized least-squares inversion Previous: Regularized inversion
Stanford Exploration Project
10/31/2005