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 The VARIOGRAM Procedure

## Sample Variogram Computation and Plots

Using the values of LAGDISTANCE=7.0 and MAXLAGS=10 computed previously, rerun PROC VARIOGRAM without the NOVARIOGRAM option. Also, request a robust version of the semivariogram; then, plot both results against the pairwise distance of each class.

   proc variogram data=thick outv=outv;
compute lagd=7 maxlag=10 robust;
coordinates xc=east yc=north;
var thick;
run;

title 'OUTVAR= Data Set Showing Sample Variogram Results';
proc print data=outv label;
var lag count distance variog rvario;
run;

data outv2; set outv;
vari=variog; type = 'regular'; output;
vari=rvario; type = 'robust'; output;
run;

title 'Standard and Robust Semivariogram for Coal Seam
Thickness Data';
proc gplot data=outv2;
plot vari*distance=type / frame cframe=ligr vaxis=axis2
haxis=axis1;
symbol1 i=join l=1 c=blue   /* v=star   */;
symbol2 i=join l=1 c=yellow /* v=square */;
axis1 minor=none
label=(c=black 'Lag Distance') /* offset=(3,3) */;
axis2 order=(0 to 9 by 1) minor=none
label=(angle=90 rotate=0 c=black 'Variogram')
/* offset=(3,3) */;
run;


 OUTVAR= Data Set Showing Sample Variogram Results

 Obs Lag ClassValue (inLAGDIST=units) Number ofPairs inClass Average LagDistance forClass Variogram Robust Variogram 1 -1 75 . . . 2 0 8 2.5045 0.02937 0.01694 3 1 85 7.3625 0.38047 0.19807 4 2 142 14.1547 1.15158 0.98029 5 3 169 21.0913 2.79719 3.01412 6 4 199 27.9691 4.68769 4.86998 7 5 199 35.1591 6.16018 6.15639 8 6 205 42.2547 7.58912 8.05072 9 7 232 48.7775 7.12506 7.07155 10 8 244 56.1824 7.04832 7.62851 11 9 285 62.9121 6.66298 8.02993 12 10 262 69.8925 6.18775 7.92206

Figure 70.7: OUTVAR= Data Set Showing Sample Variogram Results

Figure 70.8: Standard and Robust Semivariogram for Coal Seam Thickness Data

Figure 70.8 shows first a slow, then a rapid rise from the origin, suggesting a Gaussian type form:

See the section "Theoretical and Computational Details of the Semivariogram" for graphs of the standard semivariogram forms.

By experimentation, you find that a scale of c0=7.5 and a range of a0=30 fits reasonably well for both the robust and standard semivariogram

The following statements plot the sample and theoretical variograms:

   data outv3; set outv;
c0=7.5; a0=30;
vari = c0*(1-exp(-distance*distance/(a0*a0)));
type = 'Gaussian'; output;
vari = variog; type = 'regular'; output;
vari = rvario; type = 'robust'; output;
run;

title 'Theoretical and Sample Semivariogram for Coal Seam
Thickness Data';
proc gplot data=outv3;
plot vari*distance=type / frame cframe=ligr vaxis=axis2
haxis=axis1;
symbol1 i=join l=1 c=blue    /* v=star    */;
symbol2 i=join l=1 c=yellow  /* v=square  */;
symbol3 i=join l=1 c=cyan    /* v=diamond */;
axis1 minor=none
label=(c=black 'Lag Distance') /* offset=(3,3) */;
axis2 order=(0 to 9 by 1) minor=none
label=(angle=90 rotate=0 c=black 'Variogram')
/* offset=(3,3) */;
run;


Figure 70.9: Theoretical and Sample Semivariogram for Coal Seam Thickness Data

Figure 70.9 shows that the choice of a semivariogram model is adequate. You can use this Gaussian form and these particular parameters in PROC KRIGE2D to produce a contour plot of the kriging estimates and the associated standard errors.

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