Regularization is usually necessary to guarantee a solution to a given inverse problem. When constructing a model that gives an adequate fit to the data, some suitable method of regularization which provides numerical stability can be used. When investigating the resolution and variance of the computed model parameters, the character of regularization should be specified by the a priori information available. This avoids arbitrary variation of the damping to suit the interpreter.For geophysical inverse problems we determine the appropriate level of regularization (in the form of parameter covariances) from power spectral analysis of well-log measurements. For resistivity data, well logs indicate that the spatial variation with depth can be described adequately by a scaling noise model, that is, one in which the power spectral density is proportional to some power (alpha ) of the frequency. We show that alpha , the scaling exponent, controls the smoothness of the final model. For alpha < 0, the model becomes smoother as alpha becomes more negative.As a specific example, this approach is applied to the magnetotelluric inverse problem. A synthetic example illustrates the smoothing effect of alpha on inversion. Comparison between the scaling noise approach and a previous Backus-Gilbert type inversion on some field data shows that using the appropriate value of alpha (-1.8 for this example) results in a model which is structurally simple and contains only those features well resolved by the data.