This command identifies pairs of parameters that are used to calculate a smoothness regularization term. Weighted differences between the two estimated values are added to the objective function. The pairs are identified by the ordering number in the PARAMETER block. A reagularization weight can be given for the regularization term as a whole (keyword BETA; default: 1.0). Moreover, for each pair, a standard deviation can be provided (default: 1.0); for smoothing, this standard deviation is typically related to the separation distance between the two parameter points. Note, however, that this regularization approach is not restricted to spatial smoothing of a field of estimated parameters of the same type, but can be used to constrain differences between parameters of different types (e.g., the residual saturation for the relative permeability and capillary pressure functions).
The information can be given directly in the iTOUGH2 input file, or on a separate file given after keyword FILE). Two integers are read in free format to indicate the parameter pair. Providing a standard deviation is optional.
This command can be given in the PARAMETER block (as it relates to differences in estimated parameter values), or in the OBSERVATION block (as it adds to the objective function as do other residuals between observed and measured values).
Regularization by means of differences between an estimated value and its preferred value is accomplished through command >>>> PRIOR.
>> REGULARIZATION, BETA: 100.0
1 2 0.1541
1 4 0.2573
2 5 0.2573
4 5 0.1541
5 6 0.1541
5 8 0.2573