The concept is simple: one minimizes or maximises some penalty on the model, m, whilst demanding that the model fit the observed data to within some reasonable level of misfit, X^2. A Lagrange multiplier formulation is usually employed to realise this concept, so that an unconstrained functional U
U = R(m) + µ^{-1}X(m),
is minimized. The first term, R(m) is a functional of the model which returns a property which one wishes to penalise. The term X (m) measures the misfit obtained by the model. The relative importance of the model penalty and the misfit is controlled by the Lagrange multiplier µ^-1: when µ is zero minimising U simply minimizes the misfit at whatever cost to model penalty; when µ is infinite minimizing U minimizes the penalty on the model no matter how badly the penalised model fits the data. µ is chosen so that X (m) = X*, the target misfit.
Constable, S.C., R.L. Parker, and C.G. Constable, 1987: Occam's Inversion: a practical algorithm for generating smooth models from EM sounding data, Geophysics, 52, pp. 289-300.
deGroot-Hedlin, C. and S.C. Constable, 1990: Occam's inversion to generate smooth, two-dimensional models from magnetotelluric data, Geophysics, 55, pp. 1613-1624.
Constable, S.C., 1991: Comment on `Magnetotelluric appraisalusing simulated annealing' by Dosso and Oldenburg, Geophys. J. Int., 106, pp. 387-388.
deGroot-Hedlin, C. and S. Constable, 1993: Occam's inversion and the North American Central Plains electrical anomaly, J. Geomag. Geoelect., 45, pp. 985-1000.