A comparison of automatic techniques for estimating the regularization
parameter in nonlinear inverse problems
Colin G. Farquharson & Douglas W. Oldenburg.
[2004, Geophysical Journal International, 156, 411-425.]
SUMMARY
Two automatic ways of estimating the regularization parameter in under-determined,
minimum-structure-type solutions to nonlinear inverse problems are compared: the
generalized cross-validation (GCV) and L-curve criteria.
Both criteria provide a means of estimating the regularization parameter when only
the relative sizes of the measurement uncertainties in a set of observations are
known.
The criteria, which are established components of linear inverse theory, are
applied to the linearized inverse problem at each iteration in a typical iterative,
linearized solution to the nonlinear problem.
The particular inverse problem considered here is the simultaneous inversion of
electromagnetic loop-loop data for one-dimensional models of both electrical
conductivity and magnetic susceptibility.
The performance of each criteria is illustrated with inversions of a variety of
synthetic and field data-sets.
In the great majority of examples tested, both criteria successfully determined
suitable values of the regularization parameter, and hence credible models of the
subsurface.
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Last update: 23 June 2005.
Colin Farquharson