The SIM2D Procedure

This example exhibits a more detailed investigation of the variation of simulated Thick variable values. You use the same thick data set from the section Getting Started: SIM2D Procedure, and you are interested in the simulated values statistics at two selected grid points.

Specifically, you perform a simulation asking for 5,000 realizations (iterations) at two points of the region defined in the section Preliminary Spatial Data Analysis. These are the extreme southwest point and a point toward the northeast corner of the region. Since you want to avoid performing the simulation across the whole region, you need to produce a GDATA= data set to specify the coordinates of the selected points. These steps are implemented using the following DATA step and statements:

title 'Investigation of Random Field Variability';

data thick;
   input East North Thick @@;
   label Thick='Coal Seam Thickness';
   datalines;
    0.7  59.6  34.1   2.1  82.7  42.2   4.7  75.1  39.5
    4.8  52.8  34.3   5.9  67.1  37.0   6.0  35.7  35.9
    6.4  33.7  36.4   7.0  46.7  34.6   8.2  40.1  35.4
   13.3   0.6  44.7  13.3  68.2  37.8  13.4  31.3  37.8
   17.8   6.9  43.9  20.1  66.3  37.7  22.7  87.6  42.8
   23.0  93.9  43.6  24.3  73.0  39.3  24.8  15.1  42.3
   24.8  26.3  39.7  26.4  58.0  36.9  26.9  65.0  37.8
   27.7  83.3  41.8  27.9  90.8  43.3  29.1  47.9  36.7
   29.5  89.4  43.0  30.1   6.1  43.6  30.8  12.1  42.8
   32.7  40.2  37.5  34.8   8.1  43.3  35.3  32.0  38.8
   37.0  70.3  39.2  38.2  77.9  40.7  38.9  23.3  40.5
   39.4  82.5  41.4  43.0   4.7  43.3  43.7   7.6  43.1
   46.4  84.1  41.5  46.7  10.6  42.6  49.9  22.1  40.7
   51.0  88.8  42.0  52.8  68.9  39.3  52.9  32.7  39.2
   55.5  92.9  42.2  56.0   1.6  42.7  60.6  75.2  40.1
   62.1  26.6  40.1  63.0  12.7  41.8  69.0  75.6  40.1
   70.5  83.7  40.9  70.9  11.0  41.7  71.5  29.5  39.8
   78.1  45.5  38.7  78.2   9.1  41.7  78.4  20.0  40.8
   80.5  55.9  38.7  81.1  51.0  38.6  83.8   7.9  41.6
   84.5  11.0  41.5  85.2  67.3  39.4  85.5  73.0  39.8
   86.7  70.4  39.6  87.2  55.7  38.8  88.1   0.0  41.6
   88.4  12.1  41.3  88.4  99.6  41.2  88.8  82.9  40.5
   88.9   6.2  41.5  90.6   7.0  41.5  90.7  49.6  38.9
   91.5  55.4  39.0  92.9  46.8  39.1  93.4  70.9  39.7
   55.8  50.5  38.1  96.2  84.3  40.3  98.2  58.2  39.5
   ;

data grid;
   input xc yc;
   datalines;
   0   0
   75  75
   ;

Then, you run PROC SIM2D with the same parameters and characteristics as those shown in the section Preliminary Spatial Data Analysis. This time, however, you ask for simulated values only at the two locations you specified in the previous DATA step. The following statements execute the requested simulation:

proc sim2d data=thick outsim=sim1;
   coordinates xc=East yc=North;
   simulate var=Thick numreal=5000 seed=79931
            scale=7.4599 range=30.1111 form=gauss;
   mean 40.1173;
   grid gdata=grid xc=xc yc=yc;
run;

After the simulation is performed, summary statistics are computed for each of the specified grid points. In particular, you use PROC UNIVARIATE and a BY statement to request the quantiles and the extreme observations at these locations, as the following statements show:

proc sort data=sim1;
   by gxc gyc;
run;

proc univariate data=sim1;
   var svalue;
   by gxc gyc;
   ods select Quantiles ExtremeObs;
   title 'Simulation Statistics at Selected Grid Points';
run;

The summary statistics for the first grid point (East=0, North=0) are presented in Output 85.2.1.

Finally, Output 85.2.2 displays the summary statistics for the second grid point (East=75, North=75).

For each simulation location, a single realization might result in values that differ significantly from the random field mean at that location. However, the averages of progressively larger numbers of realizations tend to shorten this gap and reduce the simulation variability, as exhibited in the results for the two example locations in Output 85.2.1 and Output 85.2.2. At the limit of an infinite number of realizations, the simulation mean recovers the mean and covariance structure of the random field.