Inversions of geophysical data often involve solving large-scale underdetermined
systems of equations that require regularization, preferably through
incorporation of a priori information. Since many natural phenomena
exhibit complex random behavior, statistical properties offer important
a priori constraints. Inversion constrained by model covariance functions,
a form of stochastic regularization, is formally equivalent to imposing
simultaneously the auxiliary constraints of (i) model correlation
(smoothness) and (ii) similarity with a preferred model (damping).
We show that a priori stochastic information defines uniquely the
relative contributions of smoothing and damping, such that the higher
the fractal dimension the greater the damping contribution. However,
if the model discretization interval exceeds the characteristic scale
length of the parameters to be resolved, stochastic regularization
artificially reduces to only damping constraints.