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The condition number of the targetoriented Hessian matrix can be high, making the solution of the nonstationary leastsquares filtering problem in equation (3) unstable.
One solution is adding a smoothing regularization operator to equation (3):
 

 (4) 
where the choice of the identity operator () as regularization operator is customary. A more sophisticated regularization scheme could involve applying a smoothing operator in the reflection angle (or offset rayparameter) dimension Kuehl and Sacchi (2001); Prucha et al. (2000) or, more generally, in the reflection and azimuth angles.
Next: Regularization in the prestack
Up: Linear leastsquares inversion
Previous: Linear leastsquares inversion
Stanford Exploration Project
5/6/2007