Make Strata Grid Files

For each strata in the drillhole, this routine can generate 3D grid files of the strata thickness, top & bottom elevation, and attributes such as calcium, moisture, sulfur, and BTU. The grid files make up the geologic model in StrataCalc. A 3D grid file is a rectangular mesh of grid cells where each grid cell is the same size rectangle. The elevation or Z value of the four grid corners equals the value at those points. For example, consider a grid cell for a 3D grid mesh of strata thickness. The X and Y coordinates of a grid cell could be (0,0), (10,0), (10,15), and (0,15). The z values, which might be 4.5, 4.7, 4.8, and 4.6, represent the strata thickness at the four X and Y coordinates.

Make Strata Grid Files reads the strata data from the drillholes. The strata data is correlated and processed for beds, pinch out and conformance as specified in the Configure -Mining Module. The strata data points are then used with the selected modeling method to calculate the grid. There are 5 methods for modeling: Triangulation, Inverse Distance, Polynomial, Kriging and Least Squares. There is an option to use a parameter file (made with Define Parameters) to filter the strata data points. For example, when creating a thickness grid for the overburden of 6_COAL, you could have a parameter filter of THICKNESS 6_COAL > 1.0. This filter would make the program use only drillholes with 6_COAL greater than 1.0 when calculating the 6_COAL overburden grid. See the Define Parameter File command for more description on parameters.

The routine starts by prompting for the location of the grid files to create. The location can be specified by picking the lower left and upper right corners or by selecting an existing grid file which sets the new grid location and resolution to match the selected existing grid file. Next there is the Make Strata Grid File dialog for choosing the grid cell resolution, modeling method and other parameters.

• Range of Elevations/Values to Process: Only values that fall within the range specified by the Low and High will be used in the gridding. Values that fall outside this range will be ignored.
• Modeling Method: There are 5 modeling methods available for geologic gridding, with many settings for each method. They are Triangulation, Inverse Distance, Kriging, Polynomial and Linear Least Squares. They are described in more detail below.
• Use Triangulation Subdivision: When modeling with triangulation, this option will divide each triangle into 3 or more smaller triangles for smoother modeling.
• # of cells in X and Y / Total Cells: The Grid Resolution will determine the number of grid cells in the X and Y directions. Most of the time, the user specifies the Dimensions of Cells. This calculates the number of cells in the X and Y direction. Multiplying the two together gives the Total number of Cells. This number determines the processing speed for other commands such as reserves and GFU. A good rule of thumb is to try and keep the Total Cells less than 500,000. Any number larger than this and most processors will use up all the RAM and go to the hard drive and processor, which can slow it down. There is no limit to the grid size though. Every computer is different, so try a few and see which size works for you at a reasonable processing time, and captures the accuracy you need.
• Grid Resolution: This is either the number of cells in the X and Y direction or the Dimensions of a Cell in the X and Y direction. Unless the ore body is long and narrow, the Dimensions of a Cell should match in the X and Y direction creating square cells. In rare instances, rectangles can better model a long, slender ore body.
• Label Values of Data Points: This option will draw a label next to each drillhole indicating what value was used at each drillhole for the gridding. Set a Text Layer and Text Size here. This option is a good way to visualize and check the data points that the program is using.
• Create Data Points Report: The Create Data Points Report option is another way to check the data points that are used in griddling. This option will create a report of the griddling data points. This report is displayed in the Standard Report viewer where it can be saved, printed or put on screen.
• Create Composite Grids: The Create Composite Grids option allows you to select multiple strata or beds to combine instead of griddling the strata individually. With compositing, the program shows the same strata selection dialog with the list of strata but you can now select multiple strata by picking from the strata list while holding down the Shift or Ctrl keys on the keyboard. For composites you can grid the top elevation which is the highest elevation at each drillhole for the composite, the bottom elevation which is the lowest composite elevation, the thickness which is the sum of the thicknesses for all the composite strata, or composited strata attributes.
• Use Parameter File: Turning this option on will use a parameter filter file made in Parameter Compliance.

After the grid options dialog, the program prompts you to select the drillholes and fault lines. After reading in the selected drillholes, there is a Choose a Strata to Process dialog to choose the strata to process from the list. If  Create Composite Grids was turned on, then multiple strata may be selected here. The All, Key Only and Non-Key Only are just viewing options to reduce the number of strata in the window if there are a lot, for ease of selection.

Then the program will prompt for the grid file name to create (.GRD). Next the program will process the strata data points to create the grid and the results are stored in a user-specified file name. The grids created by Make Strata Grid File can be used as the geologic model for the Geologic or Mining Model file. Also the grids can be used in the grid application routines, in the Civil Design module, such as Plot 3D Grid File, Grid File Utilities and Elevation Difference.

Making Strata Grids with Fault Lines
There is an option to select fault lines in addition to the drillholes. The fault lines should be drawn as 3D polylines with elevations that equal the fault differential. The program will grid with all modeling methods using the fault lines for making strata elevation grids.  The 3D fault polylines should be drawn such that the left side of the polyline, relative to the direction of the polyline, is the low side of the fault and the right side is the high side. As each grid corner elevation is calculated, the program checks each drillhole. If the drillhole is on the same side of the fault polyline as the grid corner, then no adjustment is made to the drillhole elevation data. Otherwise the drillhole is projected onto the fault polyline and the polyline value at this point on the polyline is used to adjust the drillhole elevation. For example, if the fault polyline value was 5.0 and the grid corner was on the high side of fault while the drillhole was on the low side, then 5.0 would be added to the drillhole elevation for modeling at that grid corner. If the grid corner was on the low side and the drillhole was on the high side, then 5.0 would be subtracted from the drillhole elevation. Reverse Polyline is a good way to reverse the fault line if it is drawn in the wrong direction.

Triangulation Modeling Method
This method is straight triangulation between the drillholes. Triangulation calculates these values by interpolating on the plane defined by the three points in the triangle that encloses the point. Since triangulation only interpolates, it can only calculate values within the area of the data. Afterwards, an extrapolation routine can then fill in the rest of the grid. This extrapolation uses a safe method that tends to average out the data. There is an option to extrapolation to apply the global trend. This option finds the average slope and direction of the existing data and applies this slope to extrapolating.

Inverse Distance Modeling Method
Inverse distance calculates the grid values by assigning weights to the existing data. The grid values calculated by inverse distance are a weighted average of the existing data. Inverse distance will not carry trends and the calculated grid values will never be higher than the highest existing data point. Likewise the calculated grid values will never be lower than the lowest existing data point. The weights are proportional to the inverse of the distance between the point to be estimated and the existing data point. Closer points are weighted more than points farther away. The inverse distance can be calculated to first, second, or third power which are (1/d), (1/d^2), and (1/d^3) respectively. The power can also be any user-specified number such as 2.5. The inverse distance estimate is a weighted average with the individual weights computed as an inverse power of distance as follows:

where Wi is the weight computed for each sample i, each di is the distance between the location being estimated and sample I , and –power is the inverse distance weighting power.
In Configure under Mining there are several options for controlling inverse distance. The Inverse Distance Search Radius is used for calculating a value at a point such that only drillholes that are within this Search Radius will be used in the calculations. The Inverse Distance Max Samples value limits calculations to the nearest specified number of drillholes to the point. For example, the program will use the nearest 10 drillholes. Inverse distance can also be controlled by quadrants which are divided into northeast, southeast, southwest and northwest. The Min Quadrants setting will use at least this specified number of drillholes from each quadrant as long as there are drillholes in the quadrant within the Search Radius. For instance, a setting of Min Quadrants of one would make the program look for at least one drillhole from each quadrant. The Max Quadrants value limits the number of drillholes used from each quadrant. For example if Max Samples was set to 25 and Max Quadrants was 10, then the total samples would be 25 with no more than 10 of the closest ones from each quadrant.

Elliptical inverse distance modeling method is an option that appears any time the Inverse distance modeling method is chosen. The prompt will appear:

Use inverse distance to which power [First/<Second>/Third/Other]? Second
Use elliptical inverse distance [Yes/<No>]? Yes
Enter azimuth of anisotrophy: 45
Enter anisotropic factor: 1
Calculating grid by inverse distances 33880...

This will produce oval shaped inverse distance "bulls eyes" that will use the 2nd weighting power, with the 1st weighting power applied to an azimuth of 45. This option will appear anywhere the Inverse Distance modeling method is selected, such as isopaching.

Kriging Modeling Method
Kriging estimates the grid values by figuring the relationship between all the existing data points and then assigning weights to this data. Kriging finds the best fit linear unbiased estimates for the given data and model. Kriging can carry trends within and beyond the limits of the data and can find new high and low values. You must supply a model that defines the spatial relationship of the data which can be difficult. In fact, Kriging is a very complicated subject and you will need to reference an outside source for a detailed description such as An Introduction to Applied Geostatistics by Isaaks and Srivastava. Carlson uses Ordinary Kriging. All the parameters for this Kriging are specified in the dialog shown.

Polynomial Modeling Method
The polynomial method is based off of triangulation. The difference is that instead of directly interpolating within each triangle, the polynomial method creates smooth transitions by using a fifth degree polynomial function that accounts for neighboring triangles. Since polynomial needs adjoining triangles, when there are fewer than five data points, there will be fewer than four triangles and the polynomial method will revert to straight triangulation. The same extrapolation logic for triangulation applies to the polynomial method.

Linear Least Squares Modeling Method
The linear least squares method finds the least squares best fit plane at each grid corner. The least squares routine weights each data point by inverse distance so that closer points are weighted more than points farther away. So the best fit plane varies at different points on the surface. The linear least squares method extrapolates trends very well. A lower inverse distance factor (i.e. 1.0) will weigh the data points more equally which models the trends more globally (sometimes called "global dip"). Likewise a higher inverse distance factor (i.e. 3.0) will weigh the closer data points more heavily which models local trends strongly (sometimes called "local dip"). Least squares will trend and allows for data points that are new highs and lows, that don’t appear in the original drillhole/point data. It does produce very nice, smooth contours that honor the data points.

Differential Smoothing Factor:

This parameter enables to control smoothness of generated surface. The larger value, the sharper interpolation is obtained. Typical values are:
0.00 - 0.30 ... for smooth interpolation
0.40 - 0.60 ... for normal interpolation (default value is 0.50)
0.70 - 1000.0 ... for sharp interpolation

Sharp / smooth model at local extremes can be improved by increasing the differential smoothing factor. The accuracy of generated surface decreases with increase in this factor. The zero value produces most smooth surface.

Target Accuracy:
This parameter specifies how accurate the generated surface has to be. It represents the percentage value of average difference between z – coordinates of input points and generated surface from (Zmax – Zmin), where Zmin is the minimum value and Zmax is the maximum value of the z – coordinates of the input points. If the calculated accuracy ((Average DZ / Zmax – Zmin) * 100) is less than the Target Accuracy, the process of interpolation stops and outputs the target grid.

Degree of Linear Tensioning:
This parameter enables to set the degree of linear tensioning. It can have four values:
1.    None – for no linear tensioning
2.    Medium – for medium linear tensioning
3.    Strong – for strong linear tensioning
4.    Full – for full linear tensioning

It is clear from the following figure of cross-section of a grid surface that the surface is more linear for higher degree of linear tensioning.

Prompts

Use position from another file or pick grid position (File/<Pick)? press Enter Using the position of an existing file copies the grid resolution and corner point locations to the new grid files. This is useful if you need to have grid files match exactly. Most of the time, grids should match position in the geologic model.
Pick Lower Left grid corner: enter or pick a point
Pick Upper Right grid corner: enter or pick the second point to define the grid position
Make Strata Grid File dialog box
Set the grid resolution and other options. A higher grid resolution increases the processing time. Also choose the Modeling Method in this dialog.
Select drillholes, channel samples and strata polylines.
Select objects: select the drillhole symbols
Select fault lines or Enter for none.
Select objects: press Enter for none, or select the fault lines
Choose Strata to Process dialog
Choose Attribute to Process dialog

Pulldown Menu Location: StrataCalc
Keyboard Command: chgrid