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In principle, the number of iterations should not be an important
parameter since we should iterate until the solution converges.
However, determining the correct value of is a
long-standing difficulty with large exploration-type geophysical
inverse problems.
Conventional solutions Menke (1989) such as picking the knee of misfit
vs. model norm curves, or examining the singular-values of the
operator matrix are not practical when the model-space is a large
multi-dimensional image.
If the choice of is too small, the solution will begin to
degrade as the number of iterations increases as poorly resolved
eigenvectors leak into the model space.
On the other hand, if the choice of is too large, the
solution will converge to a smooth model that does not satisfy our
first fitting goal [expression (7)].
Despite these difficulties, with preconditioned problems we often
obtain good results after only a few iterations without the solution
fully converging, and with little or no dependence on the the choice
of . Well-resolved low-frequency eigenvectors
propagate into the solution quickly after only a few iterations.

Therefore, to reduce the dimensionality of the parameter space, we
set , and keep the filters smooth by restricting the
number of conjugate-gradient iterations Crawley (1999).
After solving the problem only once, we can plot misfit vs. model norm
curves for intermediate solutions with varying number of iterations,
and choose the best result.

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Stanford Exploration Project

4/29/2001