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The sparse solver in the time domain employs a regularization term
that enforces spikyness in the model space Nichols (1994). This approach
is well-suited for time-domain processing and makes use of
iterative solvers as opposed to direct inversion
as described in equations (14) and (15).
For instance, by choosing an approximation of the norm
for the model space regularization, we can focus
the energy of the model vector into its main components.
Ulrych et al. (2000) advocate a regularization by the Cauchy-Gauss
model. In any case, the objective function to minimize becomes
| |
(17) |

where is the norm and where |.|_{sparse}
induces a sparse model. Iteratively reweighted least-squares
algorithms with the proper weighting function produce an artifact-free
model space Bube and Langan (1997).
A more ambitious Huber norm can be used as well
Guitton and Symes (1999) for the case.

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Stanford Exploration Project

4/29/2001