Evaluating the adjustment

 

The network adjustment summary and statistics are shown in the bottom right of the Network adjustment tab. If using Gravnet for adjustment, the adjustment results are taken from the *.gra file written by Gravnet. If using Numpy for adjustment, similar output is shown.

 

In either case, the primary metrics for evaluating the adjustment is the Chi-square goodness of fit test, the reference factor, and the observation residuals.

 

 

The Chi-square test is a standard metric when adjusting survey observations of all types. The test involves calculating the Chi-square statistic:

 

 

from the residuals (v_i, the difference between observed and adjusted delta-g's and datum values) and their respective weights (p_i). The statistic is compared to a critical value, calculated for the network degrees of freedom (number of observations) and the significance level. The default significance level is 0.05 (5 percent) but can be changed in the Network adjustment options dialog.

 

The result of the Chi-square test ('accept' or 'reject') is shown in the bottom right of the Network adjustment tab.

 

 

For network adjustment statistics to be accurate, the estimated standard deviations of the input data must be accurate. This can be evaluated with the standard deviation a posteriori statistic ("SD a posteriori") in the least-squares statistics in the bottom right of the Network Adjustment tab. A value less than 1 indicates input standard deviation is too high; greater than one indicates input standard deviation is too low. Using the Adjustment menu > Scale standard deviation from results command (or the button on the Tree View toolbar), the standard deviation of the delta-g's is scaled automatically so that the standard deviation a posteriori statistic approaches one. See adjustment options for more information on how the scaling is applied.

 

Only the gravity-difference standard deviations are scaled; the datum observation standard deviations are not.

 

 

Two plots are useful for evaluating the adjustment. The first, shown when the "Adjustment > Plot residual histogram" menu item is selected, is a histogram of the delta-g residuals (i.e., the difference between each observed delta-g and the adjusted delta-g). This plot should approximately follow a normal distribution, with no large outliers. The second plot, "Adjustment > Plot adjusted datum vs. measured", shows a bar plot of the difference between the datum observations (e.g., absolute-gravity measurements) and the adjusted values. The closer these residuals are to zero, the better the adjustment.

 

For campaigns with several surveys, a time series version of the "adjusted datum vs. measured" plot is available. Rather than columns, this plot shows the adjusted value and measured values as separate time-series for each station.