STOCHASTIC REGULARIZATION - SMOOTHNESS OR SIMILARITY

Inversions of geophysical data often involve solving large-scale under determined systems of equations that require regularization, preferabl y through incorporation of a priori information. Since many natural ph enomena exhibit complex random behavior, statistical properties offer important a priori constraints. Inversion constrained by model covaria nce functions, a form of stochastic regularization, is formally equiva lent 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 uniquel y the relative contributions of smoothing and damping, such that the h igher the fractal dimension the greater the damping contribution. Howe ver, if the model discretization interval exceeds the characteristic s cale length of the parameters to be resolved, stochastic regularizatio n artificially reduces to only damping constraints.