KNA: Block Size Optimization

To access this screen:

Using the Advanced Estimation console, select Optimize from the left-hand menu system and then select the Optimize Block Sizes sub-panel.

This panel is used to help determine the optimum block size. A range of statistical parameters are calculated and a Block Size chart is displayed to show the relationship between each parameter and one of the block dimensions.

This panel is only visible if Supervisor data is not being imported. You decide this using the Scenario Setup screen.

Define the size of a model cell in each of the X, Y and Z directions by entering the minimum size, the number of intervals and the increment between successive values for each of the three directions as described in the Optimize section.

The calculation of statistics also needs the number of discretization points in each direction to be defined; these are defined by the Base values selected in the Optimize Discretization sub-panel. In addition a set of search volume parameters, defined by the Base values in the Optimize Search Volume sub-panel, must exist.

Tip: check the Base values in both Optimize Discretization and Optimize Search Volume sub-panels before running a test.

Example

In the following example, only the X block size changes while the block size in Y and Z is fixed at 10m.

Inputs- Variogram Model

The variogram model has been selected by double clicking the required model in the Variogram Model area of the Optimize panel:

This example is based on a single structure spherical anisotropic model with the following parameters:

Nugget: 0.35
Sill: 3.87
Rotation: 22.5 degrees around Z|
Ranges: X - 82.8, Y - 93.2, Z - 25.6

Inputs- Discretization

These parameters are defined by their Base values in the Optimize Discretization sub-panel:

Number of discretization points:
- X: 5
- Y: 5
- Z: 3

The Optimize Discretization panel looks like this:

Inputs- Search Parameters

These parameters are defined by their Base values in the Optimize Search Parameters sub-panel:

The lengths of the search volume axes:
- X: 82.9
- Y: 93.2
- Z: 25.6
  Note: the initial default values are set equal to the maximum variogram ranges in each direction.
Minimum number of samples: 5
Optimum number of samples: 10
Segment method: not applied

In the image below only the Base values are used for optimizing the block size.

The following parameters are defined using the Optimize Block Sizes sub-panel:

Note: Increment values are rounded up to the nearest integer.

Inputs - Combinations

The Test reduced combinations option is checked:

This ensures a total of 8 KNA runs. The combinations of values to be tested are:

Run Tests starts the KNA runs.

Outputs – Slope of Regression

The chart display option Group on separate tabs by has been selected as Test block group so the results for each location are shown on different tabs.

The results for the Well informed location are shown below. The mean slope of regression(green line) has a value of 1 for a block size in X of 10m but reduces as the block size increases:

The corresponding charts for the Moderately informed and Sparse locations are shown below. The mean regression slope for Moderately informed is similar to Well informed, but the mean slope for Sparse is considerably lower reflecting the lower sampling density:

Statistical Parameters

The table below shows the statistical parameters that are reported for each run. These parameters appear in the Measured value (y-axis) list:

Name	Field	Description
Average time per block (ms)	TIME_MS	Processing time for each model block.
Corr(Z, Z*)	CORZZSTR	Correlation between actual value and estimate.
Cov(Z, Z*)	COVZZSTR	Covariance between actual value and estimate.
Cov(Z1, Z)	COVZ1SZS	Covariance between two estimates – multivariate case only.
Kriged estimate	EST	Kriged block estimate.
Kriging efficiency	KRIGEFF	Comparative measure of confidence in block estimate.
Lagrange parameter	LAGRANGE	Lagrange parameter when solving kriging matrix.
Number of samples	NUMSAMP	Number of samples used for block estimate.
Search volume index	SINDEX	Search volume index used for block estimate.
Slope of regression Z/Z*	SLPZZSTR	Slope of regression of actual value on estimate.
Sum of pos. weights	SUMPOSWT	Sum of positive weights.
Variance	VAR	Kriging variance.
Variance of Z*	VARZSTR	Variance of the estimator (Z*)
Weight of mean	WTOFMEAN	Weight assigned to mean of simple kriging.