Manual Page for Command >>>> DEVIATION


Syntax
>>>> DEVIATION: sigma

Parent Command
all third-level commands in block > PARAMETER

Subcommand
-

Description
This command specifies the standard deviation sigma of the initial parameter guess. Prior information about model parameter will be weighted by 1/sigma, i.e., the difference between the prior information value p* and the estimate p contributes to the objective function. Commands for specifying the standard deviation are:

>>>> DEVIATION: sigma
>>>> VARIANCE: sigma2
>>>> WEIGHT: 1/sigma

By default, prior information is not weighted, i.e. sigma=infinity. The standard deviation reflects the uncertainty associated with the initial guess. If the initial guess is to be weighted, prior information should originate from an independent source. For example, if porosity will be estimated based on transient pressure data, the prior information value should be taken from a "direct" porosity measurement, e.g. using mercury-porosimetry or oven-drying methods. In these cases, the measured parameter values p* are considered to be additional data points which serve as a physical plausibility criterion for the estimate p. The p* values, along with the observations of the system state z*, are then weighted according to their uncertainties (see >>>> DEVIATION (o)). Note that the relative weighting between prior information and the observations z* depends on the number of calibration points selected. If many transient data points are available, a smaller standard deviation sigma may be specified to increase the relative weight of prior information. In many cases, appropriately weighting the initial guess makes an ill-posed inverse problem unique. Furthermore, the solution becomes more stable if a parameter is not very sensitive. However, using 1/sigma as a regularization parameter to improve the ability to obtain a unique solution with a poorly conceptualized inverse problem inverse problem is not recommended. Erratic behavior of a parameter during the inversion should be taken as an indication that the data do not contain sufficient information for the determination of the parameter. Differences between parameter values that are independently determined from laboratory experiments and inverse modeling suggest the presence of a systematic error or scaling problem. These inconsistencies should be resolved rather than averaged out. The standard deviation sigma is also used to scale the columns of the Jacobian matrix. While the solution of the inverse problem is not affected by the choice of the scaling factor, all the qualitative sensitivity measures are directly proportional to sigma. If prior information is not weighted, the scaling factor is taken to be 10 % of the respective parameter value. Command >>>> VARIATION should be used to change the default scaling factor without concurrently assigning a weight to prior information. When performing uncertainty propagation analyses, sigma designates the parameter uncertainty affecting the model prediction. It is used to generate a set of random parameter values for Monte Carlo simulations, and it represents the standard deviation of a normal distribution if performing linear uncertainty propagation analysis (for more details see commands >>> MONTE CARLO and >>> FOSM, respectively).

Example
> PARAMETER
>> POROSITY
>>> MATERIAL: TUFFn
>>>> PRIOR information : 0.38 (laboratory measurement)
>>>> standard DEVIATION: 0.04 (measurement error)
<<<<
>>> MATERIAL: ALLUV
>>>> PRIOR information : 0.30 (from experience)
>>>> VARIANCE : 0.01 (uncertainty of guess)
<<<<
>>> MATERIAL: FAULT
>>>> initial GUESS : 0.25 (no measurements available)
>>>> WEIGHT : 0.00 (default)
>>>> VARIATION : 0.10 (for scaling of Jacobian)
<<<<
<<<
<<


See Also
>> GUESS | >>> FOSM | >>> MONTE CARLO | >>>> DEVIATION (o) | >>>> PRIOR | >>>> VARIANCE | >>>> VARIATION | >>>> WEIGHT


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Page updated: July 29, 1997