5.0 MicroMODEL GRADE MODELING

5.1 Introduction

The Grade Modeling Sub-Menu appears below:

  1. Return To Main Menu
  2. Command Shell
  3. Polygonal Reserve Calculation
  4. Polygonal Reserve Plotting
  5. Variogram Analysis (Menu)
  6. Point Validation Presort
  7. Point Validation
  8. Grade Modeling Presort
  9. Grade Modeling
  10. Model Frequency Analysis and Basic Statistics
  11. Model Cumulative Frequency Analysis
  12. Model Correlation Analysis
  13. Graphical Display of Grade Model (Menu)
  14. Model Manipulation
  15. Clean-Up Directory

The purpose of the Grade Modeling Module is to allow the user to run geostatistical analyses, create three-dimensional grade models, and display these grade models for any label in the MicroMODEL system. It is not necessary to build a grade model for each label. Only labels that are required during Pit Evaluation need to be modeled.

Both Kriging and Inverse Distance to a Power (IDP) are available for point validation (jackknifing) and grade modeling. Point validation allows the user to test presort and modeling parameters before any grade models are constructed.

MicroMODEL also has the facility to assign grade values from the composites to a block grade model using the nearest neighbor (polygonal) modeling method. A program which plots the true polygons for a specified bench is also available.

In the Data Entry and Compositing Modules, the statistical programs always access data from either the current sample or the current composite label. In the Grade Modeling module, each grid is associated with a GRADE MODEL LABEL NUMBER and a MODELING METHOD. Therefore, the user must set the CURRENT GRADE LABEL to whichever grade model label with which the resulting grade grid model is to be associated, before proceeding to any of the grid modeling, or grid statistics programs. In addition, the user must also set the CURRENT SAMPLE DATA LABEL, or the CURRENT COMPOSITE DATA LABEL, to point to the required input data label (either SAMPLE or COMPOSITE data). The current sample data, composite data, and grade model labels can be set with choice buttons located at the top of the Grade Modeling Submenu. MicroMODEL often prompts the user for the Grid Type, which refers to the modeling method used to create a particular grade grid model. For more information on labels, and label types, please refer to Volume II, Section 1.3.

5.2 Command Shell

This menu choice enables the user to invoke commands and run external programs without exiting MicroMODEL. Refer to Section 1.2 for details.

5.3 Polygonal Reserve Calculation

This option allows the user to produce a block grade model using the polygonal (nearest neighbor) modeling method. The resulting polygonal grade model can then be processed by the Reserves Evaluation module to obtain an approximate polygonal reserve. Since this method of modeling uses the block model, it does not result in a "true" polygonal reserve. See Volume I, Section 4.5.1 for further discussion of MicroMODEL's Polygonal Grade Modeling program.

This program uses composites from the current composite label as input. Output is to the Polygon Model Type of the current Grade Label. Since the program assigns grade values to an entire block within the given radius, the drill holes should be composited by bench. The only parameter that this program requires from the user is the MAXIMUM RANGE OF A POLYGON. Block centroids that are not within range of a composite remain at the unestimated flag value of -999.99.

The ANSWERSET NAME identifies this set of answers, and serves no other purpose but to identify each run.

5.4 Polygonal Reserve Plotting

This option allows the user to produce bench plots of the polygons that were used during Polygonal Grade Modeling. The calculated polygons are plotted along with the mid-bench composite grade value and the area of influence of the polygon. The standard MicroMODEL plan view plot controls are also available to structure the plot as required.

The ANSWERSET NAME identifies this set of answers, and serves no other purpose but to identify each run.

The CHARACTER SIZE option for this program is currently fixed at 0.25. The character size determines the character height relative to the row dimension. See Volume I, Section 6.3.8 for further discussion of the character size parameter.

The LOCAL GRID can be displayed according to three LOCAL GRID PLOTTING OPTIONS. Refer to section 1.8 and chapter 11 for details.

The GLOBAL GRID can be displayed on the finished plot. The appearance of the GLOBAL GRID is governed by two GLOBAL GRID PLOTTING OPTIONS. Refer to section 1.8 and chapter 11, plotting.

If the GLOBAL GRID is to be plotted, the user must specify a GLOBAL GRID INTERVAL in the project units (Feet or Meters) and a PEN COLOR for the GLOBAL GRID LINES. The character size is the same as that indicated earlier (0.25). For further explanation on GLOBAL GRID OPTIONS, see chapter 11, Plotting.

The user can structure the output format for the area and grade by specifying the NUMBER OF CHARACTERS BEHIND THE DECIMAL when prompted. If the user does not want to have characters behind the decimal point and also does not wish to display the decimal point, a -1 should be entered. Refer to section 1.8 for details.

The user can control the "smoothness" of the plotted polygons with the POLYGON RESOLUTION. This parameter determines the size of the increments for polygon plotting. Higher resolutions produce better looking plots, but take longer to create than lower resolutions, which produce rougher polygons. It is recommended that the user always use the highest POLYGON RESOLUTION setting, which is 8.

Row and Column Clipping allows the user to plot a partial section (window) of the model area. The user defines this window with STARTING and STOPPING COLUMNS and ROWS as prompted by MicroMODEL. For further explanation on ROW and COLUMN CLIPPING see chapter 8, Plotting.

Polygon plots can be generated for several sequential benches. The benches are specified by the STARTING AND ENDING LEVEL NUMBERS.

In the second input screen, the user specifies PEN COLORS for various items that will be displayed.

The user can specify the pen color for GLOBAL GRID LINES, LOCAL GRID INTERNAL LINES, LOCAL GRID PERIMETER LINES, LOCAL GRID NUMBERS, AND LOCAL GRID TICS.

The TITLE BLOCK COLUMN questions are for modifying the PLOT FRAME, TITLE BLOCK or SCALE. PLOT FRAME questions deal with the PLOT FRAME EXTENT SPACE and PEN COLOR of the PLOT FRAME EXTENT LINE. The TITLE BLOCK questions concern the dimensions of the SIDE BOX, the TITLE BOX, and the COMPANY NAME BOX. The user specifies widths and heights, the title names, character heights, project number, figure number and the pen color of the internal lines. The SCALE questions control the number of intervals, the length of the intervals, the pen color and the maximum expected plot scale. For a complete discussion of the TITLE BLOCK QUESTIONS, see chapter 11, Plotting.

The Polygon Plotting program produces a scaled plot that can be output at any user specified map scale (see Section 6.3.7). For further explanation on SCALE OF PLOTS, see chapter 11, Plotting.

5.5 Variogram Analysis

5.5.1 Introduction

The programs in the Variogram Analysis Submenu allow the user to calculate and plot the variogram for the current sampled or composited drill hole data label. If the user is anticipating the use of kriged grade modeling for a given sample or composite label, calculation of the variogram and obtaining a variogram model is mandatory.

The analysis of the variogram is also useful in selecting appropriate search distances and other modeling parameters for both the Inverse Distance to a Power (IDP) and kriging methods. The programs in this submenu enable the user to perform variogram analysis on the current sampled or composited drill hole data label. This submenu consists of the following options:

    VARIOGRAM ANALYSIS
  1. 1 Return To Submenu
  2. 2 Command Shell
  3. 3 Calculate and Print Variogram
  4. 4 Print Variogram/Model
  5. 5 Plot Variogram/Model

The first option performs as in all other menus throughout the system. The third option calculates the experimental variogram. The fourth and fifth options print and plot this experimental variogram and/or a fitted theoretical variogram model.

Some of the terminology used in the variogram and grade modeling programs may be new to users unfamiliar with geostatistical methods. Although MicroMODEL was designed for users with little or no prior modeling experience, an introductory understanding of geostatistics is recommended before proceeding with variogram analysis and kriged modeling.

5.5.2 Command Shell

This menu choice enables the user to invoke commands and run external programs without exiting MicroMODEL. Refer to section 1.2 for details.

5.5.3 Calculate and Print Variogram

This option allows the user to calculate experimental variograms, in up to nine directions per run, with user specified directions, tolerances, and lag distances. The resulting variogram data can be printed on the line printer. This experimental variogram data is saved for analysis in the next two options, Print and Plot the Variogram/Model.

The ANSWERSET NAME identifies this set of responses. It also appears as a runtime title along with the project title on the output. The ANSWERSET NAME should contain information that is specific to this run, such as date, operator, important input parameters, etc.

The user is next given the option to choose LOG TRANSFORMATIONS. If this option is selected, then the variogram is calculated based on the natural logarithms of the input data. A THIRD PARAMETER can be included in the log transformation.

The user can also control the data used by the variogram program by requesting to use RANGE LIMITS on the input data. If limits are used, data outside the range specified by the MINIMUM and MAXIMUM values ignored. Classification of data relative to the cutoff grades is made before the data is logarithmically transformed.

The user may also limit the data used in variogram calculations by specifying that only certain rock types are used, or that a rock matching matrix is used. If ALL data values are used, then no further input is requested regarding rock type. If SPECIFIED ROCK CODES are used, then the user must enter the number of different codes, along with the individual rock numbers.

If SPECIFIED ROCK CODES BASED ON A MATCHING MATRIX is selected, then the user must enter the number of different codes, along with the individual rock numbers. Following this, the user must choose whether to include or exclude each and every possible combination of rock codes. For example, should the variogram include a data pairing of rock code number 3 to rock code number 5.

The TYPE OF DATA determines if the input data is to come from the current data label in either the SAMPLED or COMPOSITED drill hole databases.

The user may calculate up to nine variograms for each run, as specified by the NUMBER OF VARIOGRAMS.

For each variogram direction, the user is prompted to enter a TITLE. This title is used to help identify the printouts from the variogram calculations for each direction selected.

The user must enter an AZIMUTH, PLUNGE, and TILT (or RAKE) for each VARIOGRAM. The azimuth is measured in degrees clockwise from North, and the plunge is measured by the angle in degrees downward from horizontal (+90 degrees is vertical down). The tilt is measured as the clockwise rotation of the plane about the axis with the attitude of the given azimuth and plunge. Optionally, a rake angle within the rotated plane can be specified. These three parameters define the primary search plane for variogram direction N. This definition of the primary search plane is illustrated in Figure 5.1.

                       FIGURE 5.1
                  PRIMARY SEARCH PLANE

The user is then prompted for the WINDOW ANGLE and the TOLERANCE BAND FOR VARIOGRAM DIRECTION N that lie in the primary search plane. The window angle is used to define two "wedges" that lie in the primary search plane. The tolerance band is an offset of a given distance either side of the window angle.

Next, the user is asked to enter the WINDOW ANGLE and the TOLERANCE BAND FOR VARIOGRAM DIRECTION N that lie normal to the primary search plane. The window angle is used to define two "wedges" that lie normal to the primary search plane. The tolerance band is an offset of a given distance either side of the window angle. The use of window angles and tolerance bands are illustrated in Figure 5.2.

                       FIGURE 5.2
           SECONDARY PERPENDICULAR SEARCH PLANE

The CLASS (or LAG) DISTANCE FOR VARIOGRAM DIRECTION N is the distance along the primary search plane which is used to pair the data points. This distance can be replicated along the primary search plane by defining the NUMBER OF CLASS (or LAG) INTERVALS FOR VARIOGRAM DIRECTION N. There must be at least one interval, and there can be as many as 25 lag intervals defined. The total lag distance is the class distance multiplied by the number of lag intervals. Refer to Figure 5.2 for an illustration of lag distance and number of lag intervals.

5.5.4 Print Variogram/Model

The experimental variogram is calculated from the input data for the chosen variogram created by the program described in Section 5.5.3, Calculate and Print Variogram. The variogram model is a user specified mathematical function that represents the experimental variogram.

NOTE: When this program is invoked, the first answerset the user chooses defines which set of variogram results will be printed. The variogram calculation program stores results in a separate file for each variogram run. Thus, it is possible to "go back" and plot, say, the second set of variogram points that were calculated, even though the most recent variogram calculations were performed based on the fifth answerset.

This option allows the user to quickly display any or all of the experimental variograms and/or user specified variogram models on the printer.

The ANSWERSET NAME identifies this set of responses. It also appears as a runtime title along with the project title on the output. The ANSWERSET NAME should contain information that is specific to this run, such as date, operator, important input parameters, etc.

The user must elect to either plot or skip each variogram direction calculated with the program described in section 5.5.3. A check box appears to the left of each variogram description. Select the check box to plot that variogram. Unselect the check box to skip that variogram.

A separate input screen is displayed for each of the variograms the user elects to print. On each of these screens, the user can customize the way the experimental variogram is displayed. The user may also elect to show one or more nested variogram models superimposed on top of the experimental variogram points.

The HORIZONTAL scale of the variogram can be selected AUTOMATICALLY, or a USER SELECTED scale can be entered.

The VERTICAL scale of the variogram can be selected AUTOMATICALLY, or a USER SELECTED scale can be entered.

The user can elect to print the VARIANCE LINE, or skip printing. If this option is chosen, a line of equal signs is printed at the value of the sample variance for all data points that were used to calculate the variogram.

The user must specify the NUMBER OF NESTED MODELS. If zero (0) is entered, then no models are plotted. Otherwise, the user must specify the nested model type (linear, spherical, exponential, or gaussian), the range, and the sill value for each. In addition, the user enters the nugget effect value for the nested structure.

5.5.5 Plot Variogram/Model

The experimental variogram is calculated from the input data for the chosen variogram created by the program described in Section 5.5.3, Calculate and Print Variogram. The variogram model is a user specified mathematical function that represents the experimental variogram.

NOTE: When this program is invoked, the first answerset the user chooses defines which set of variogram results will be plotted. The variogram calculation program stores results in a separate file for each variogram run. Thus, it is possible to "go back" and plot, say, the second set of variogram points that were calculated, even though the most recent variogram calculations were performed based on the fifth answerset.

This option allows the user to display the experimental variograms and/or user specified variogram models as unscaled plots.

The majority of input for this option is exactly the same as that for Print Variogram/Model (Section 5.5.4). The difference is that this option creates an unscaled plot file, instead of a printer file.

In addition to all of the input parameters listed in the previous section, the user must also enter a pen color for each of the following items: PLOT BOX, TIC MARKS, SCALE NUMBERS, SCALE LABELS, EXPERIMENTAL VARIOGRAM, MODEL VARIOGRAM, PLOT KEY.

The Variogram Plotting program produces an unscaled plot (see Volume I, Section 6.3.9). For further explanation on SCALE OF PLOTS, see chapter 11, Plotting.

5.6 Point Validation Presort

The point validation presorting and point validation options allow the user to test the results of a given set of modeling parameters before actually creating the grade model. The point validation programs accomplish this by estimating the value of the current label for each known drill hole interval based on surrounding data. The estimated value is then compared statistically against the known value.

Before the user can proceed to Point Validation (Section 5.7), the assay data for the current label must be presorted. The purpose of the presort is to create a temporary file that instructs the Point Validation program which data values can be used to estimate each drill hole interval. This extra step makes point validating faster and more convenient. Since all point validation modeling runs can be made on the same presort file, it is not necessary to presort the drill hole data for each modeling run of the current label unless the search parameters are changed.

The ANWSERSET NAME identifies this set of answers, and should contain information that is specific to this run, such as date, operator, important input parameters, etc. This input serves no other purpose but to identify each run.

The TYPE OF INPUT DATA determines if the input data is to come from the current data label in either the SAMPLED or COMPOSITED drill hole databases.

There are two search options for the point validation presort. The first search option is SEARCH FOR CLOSEST POINTS which searches for the nearest user specified number of data points (drill hole intervals) regardless of the locations of the data points relative to the estimated drill hole interval. With this option, it is possible to find points from a clustered location. The system then prompts for the MAXIMUM NUMBER OF POINTS (32 max) to be used to estimate each cross validated drill hole interval. The presorting runtime increases as the maximum number of points increases. Generally, 16 to 24 points is adequate, since there may be only a few data points within the user specified search ellipsoid or sphere.

The second search alternative is the SECTOR SEARCH FOR DATA. With this option, a user specified maximum number of points is found in each sector. A sector can be visualized as a square-based pyramid whose apex is at the estimated point. Six (6) sectors all containing apices at the point to be estimated make up the three-dimensional space surrounding that point. The MAXIMUM NUMBER OF POINTS PER SECTOR, N, (5 max) instructs the program to find the N closest points within each sector of the search ellipsoid.

The user can control the way drill hole intervals are estimated by limiting the rock type intervals from the input drill hole data (Rock Code Input Selection). The user can either specify that ALL rock codes are used, or can specify a subset of rock codes to use. If a subset of codes is selected, then the number of codes and the actual rock numbers are entered on a later screen.

In the same manner that the user controls which data intervals are used in the estimation process, control of the drill hole interval rock types to be interpolated can also be specified (Rock Codes to Interpolate). The user can either specify that ALL rock codes will be interpolated, or can specify a subset of codes to interpolate. If a subset of codes is selected, then the number of codes and the actual rock numbers are entered on a later screen.

In the second input screen, the user must select whether the data is isotropic or anisotropic. For isotropic data, the same search distance limit applies in all directions (a sphere). For anisotropic data, the search distance is varied, depending on the search direction (a search ellipsoid). A search ellipsoid is used for data that exhibits a trend that is supported by geologic or geostatistical analysis.

For ANISOTROPIC DATA the search ellipsoid is defined by its orientation and size as shown in Figure 5.3. The orientation is specified by the PRIMARY ROTATION ANGLE (azimuth) from North to the Primary (generally longest) axis, the PLUNGE OF THE PRIMARY AXIS from horizontal, and the ROTATION ANGLE ABOUT THE PRIMARY AXIS (TILT). Note that there is a second way in which to define the third angle, which is easier to visualize. The user can specify that the third angle is a RAKE angle. The RAKE angle, if used, is the angle within the plan defined by the first two rotations. A negative RAKE angle signifies a counter-clockwise rotation, which a positive RAKE angle signifies a clockwise rotation. The size of the ellipsoid is specified by the maximum search range (radius) and the ratio of the secondary and tertiary axes radii to the primary axis radius. This relationship is defined as follows:

                                           FIGURE 5.3
                                  THREE DIMENSIONAL ELLIPSOID

The user must enter the LENGTHS OF THE PRIMARY, SECONDARY, AND TERTIARY AXES. These "lengths" can be expressed in any consistent units the user desires, such as axes lengths, axes radii, percents, ratios, etc. The maximum and minimum search ranges (radii) ultimately determine the actual size of the inclusion and exclusion ellipsoids. The axes "lengths" simply describe the relative size of the primary, secondary, and tertiary axis radii (ellipsoid shape). See Volume I, Section 3.8 for further discussion of ellipsoid conventions.

     PRIMARY AXIS RADIUS = MAXIMUM SEARCH RADIUS

    SECONDARY AXES RATIO = (SECONDARY AXIS RADIUS)/(PRIMARY AXIS RADIUS)
     TERTIARY AXES RATIO = (TERTIARY AXIS RADIUS)/(PRIMARY AXIS RADIUS)

   SECONDARY AXIS RADIUS = (SECONDARY AXES RATIO) x (MAXIMUM SEARCH RADIUS)
    TERTIARY AXIS RADIUS =  (TERTIARY AXES RATIO) x (MAXIMUM SEARCH RADIUS)

The user may now define the maximum distance from an estimated drill hole interval for which data are used in the point validation. This distance is the MAXIMUM SEARCH RANGE. It is also called the MAXIMUM SEARCH RADIUS. The maximum search radius is defined to be the longest radius of the search ellipsoid, which is entered later on in the program.

It is possible to search a rectangular portion of the grid. This is referred to as submodeling. The rectangular area is defined by the STARTING and STOPPING ROWS, COLUMNS, AND LEVELS. Only samples that are located within this rectangle "box" are modeled. This feature is useful to submodel portions of the grid under different parameters due to radically different data or when only small portions of the grade model are necessary.

To more closely simulate the Grade Modeling and Presort programs, the Point Validation Presort program has the facility to exclude data that is close to the estimated drill hole interval. Often, these close intervals are from the same drill hole as the estimated point. To exclude this nearby data, the user enters a MINIMUM SEARCH RADIUS. If an ellipsoid is specified, the minimum search radius is adjusted by the search ellipsoid in the same manner as the Maximum Search Radius.

The user has the option to run point validation using a UNIVERSAL KRIGING estimation method. If the user selects to use universal kriging, several additional input parameters must be specified.

First, the NUMBER OF UNIVERSAL KRIGING VARIABLES, N, to be used must be entered. Currently, the maximum number of variables is one (1). The system also prompts for the sample (or composite) label name that is to be used. This label number must exist, and must contain universal kriging values to be used in the point validation estimation.

MicroMODEL allows the user to limit the search to samples that have the universal kriging zone values which fall within a specified range of values. If the user selects this option, he must then enter the MAXIMUM DIFFERENCE ALLOWABLE BETWEEN input Sample and Interpolated Sample. For example, if the user specifies a maximum difference of 3.0 in the search, a sample location with a universal kriging zone code of 5.0 is only modeled by other samples with zone codes ranging from 2.0 and 8.0.

Upon completion of the Point Validation Presort, the user can proceed to Point Validation Modeling and evaluate several different modeling parameters based on the presorted drill hole data for the current label.

5.7 Point Validation

The point validation presorting and point validation programs allow the user to test the results of a given set of presorting and validation parameters before actually creating a grade model grid for a given sample or composite data label. The point validation programs accomplish this by estimating the value of the current label for each known drill hole interval based upon surrounding data. The estimated value is then compared statistically against the known value.

This program produces a printed output showing the mean and variance of both known and estimated values and the errors of estimation. The correlation coefficient of the estimated vs. known values and the Student-T Statistic are also displayed.

The user can also use the Correlation Analysis program (Section 5.12) to produce a linear regression plot of Estimated Values vs. Known Values.

With the Point Validation program, the user can try different presorting and modeling parameters until reaching the minimum error of variance and best correlation is established between the known and estimated values for the current data label. Once these parameters are discovered, the user can be confident of the results of the presorting and modeling of the corresponding grade model using the same parameters.

The ANSWERSET NAME identifies this set of answers.

Two point validation modeling options are available to the user, KRIGING and INVERSE DISTANCE TO A POWER (IDP). The user must select kriging, or IDP.

For IDP, the user must specify the POWER OF INTERPOLATION. A power of 1.0 represents linear interpolation while a power of 5.0 approaches a polygonal estimation. Powers less than 1.0 should not be used.

The program has the facility to calculate ERROR OF ESTIMATION for the IDP interpolation. If the user requests to store variance of error values (error of estimation), a Variogram TYPE, NUGGET, SILL, and RANGE are needed as input. Instead of calculating and saving an ERROR OF ESTIMATION, the user may elect to store the distance to the closest data point

The user must choose either a BRIEF LISTING or a DETAILED LISTING. A detailed listing produces a listing of each point's coordinate, known value, estimated value, and error of estimation if calculated. The detailed listing can become very large for large databases. A BRIEF LISTING consists of only a summary of the point validation run.

The user can request to reset all values to unestimated before this run by selecting the check box labeled "YES, Reset all values to missing". It is highly recommended that the user always choose this option for the first in a series of modeling runs. This insures that any values that were interpolated previously, say with a larger search radius, will not erroneously persist if a smaller search radius is tried.

The user can require that a MINIMUM NUMBER OF POINTS be found meeting the search criteria for the estimated point before an estimation is made. This facility prevents points from being estimated when only very few data points are within the search envelope.

For both kriging and IDP modeling options, the program asks for the NUMBER OF ANISOTROPIES to use. Choosing zero (0) anisotropies implies the data is isotropic. For data that is isotropic, the program gives points that are equidistant from the estimated point equal weighting in the interpolation. If the data is ANISOTROPIC, the user may enter from 1 up to 5 anisotropic weighting ellipsoids. MicroMODEL does not require the presorting ellipsoid and weighting ellipsoid(s) to be identical. For instance, the user may choose to presort with a sphere (isotropic) and model with one or more ellipsoids (anisotropic).

The user has the option to do point validation using a UNIVERSAL KRIGING estimation method. The user must select the label FOR UNIVERSAL KRIGING that is to be used. This label must exist, and must contain universal kriging values to be used in the point validation estimation.

For kriging, decimal LOGARITHMIC TRANSFORMATIONS can be used on data that is approximately log-normally distributed. In this case, the interpolation is performed on the logs of the data after several involved calculations are performed. The results of this computation are transformed back to the decimal system prior to output. An error of estimation grid is automatically generated if kriging is used. If logarithmic transforms are selected the user can enter the THIRD PARAMETER. This parameter allows the user to bias all data values by this quantity. If the third parameter is not required, enter the default value of 0.0. NOTE: Logarithmic transformation should only be selected under a special set of circumstances. Users without a strong geostatistical background should not even consider using this option.

Selecting the kriging option requires the user to input the NUMBER OF VARIOGRAM MODELS TO NEST. Up to nine different variogram model structures may be nested to establish the overall variogram model.

In addition to specifying the number of variograms to nest, the user must enter the NUGGET VALUE for the composite structure, along with an optional total SAMPLE VARIANCE. The SAMPLE VARIANCE should be left at 0.0, unless there is a zonal effect. For each variogram that is nested, the user must enter the VARIOGRAM MODEL TYPE, SILL, and RANGE for each structure. Supported variogram model types are spherical, linear, exponential, and gaussian. See Volume I, Section 3.5 for a discussion of MicroMODEL's variogram model conventions. If any anisotropies have been specified, then the anisotropy number associated with each variogram must be entered.

For ANISOTROPIC DATA, the weighting ellipsoid is defined by its orientation and ratio of its axis "lengths" as shown in Figure 2.4. The orientation is specified by the ROTATION ANGLE (azimuth) from North clockwise to the Primary (generally largest) axis. The user can also specify a second rotation angle (DIP), and third rotation angle (TILT or RAKE). The axes length ratios of the ellipsoid is specified by the ratio of the secondary and tertiary axes lengths to the primary axis length as described below:

    SECONDARY AXES RATIO = (SECONDARY AXIS RADIUS)/(PRIMARY AXIS RADIUS)
     TERTIARY AXES RATIO = (TERTIARY AXIS RADIUS)/(PRIMARY AXIS RADIUS)

The program prompts the user for the LENGTH OF THE PRIMARY, SECONDARY, and TERTIARY AXES for each anisotropy selected. These "lengths" (weighting factors) may be expressed in any consistent units the user chooses, such as axes lengths, axes radii, percents, ratios, etc. The axes "lengths" describe the relative size of the primary, secondary, and tertiary axes radii according to the axes ratio. Further discussion of weighting ellipsoid conventions can be found in Volume I, Section 3.8.

If the user is not satisfied with the resulting point validation, the data can be presorted again (if the presort parameters require change) and point validated using different parameters, until the desired result is obtained. If other rock types are to be point validated, the current sample or composite label assay data must be point validation presorted and validated for the new rock type(s).

5.8 Grade Modeling Presort

The Grade Modeling program (Section 5.9) assigns values based on the current sample or composite data label to each block of the current grade label model according to user specified constraints. Before the user can proceed to modeling, the sampled or composited drill hole data must be presorted.

The Grade Modeling Presort option allows the user to presort data for each grid block centroid within user specified bounds. The advantage of separating the presorting and modeling routines is that, once presorting is accomplished, several modeling runs with different modeling criteria can be made on the same presorted file while using a minimum of computer time. It is not necessary to presort the assay data for each grade modeling run unless the search (presort) parameters must be changed.

The ANWSERSET NAME identifies this set of answers, and should contain information that is specific to this run, such as date, operator, important input parameters, etc. This input serves no other purpose but to identify each run.

The TYPE OF INPUT DATA determines if the input data is to come from the current data label in either the SAMPLED or COMPOSITED drill hole databases.

There are two search options for the grade modeling presort. The first search option is SEARCH FOR CLOSEST POINTS which searches for the nearest user specified number of data points (drill hole intervals) regardless of the locations of the data points relative to the estimated block centroid. With this option, it is possible to find points from a clustered location. The system then prompts for the MAXIMUM NUMBER OF POINTS (32 max) to be used to estimate each cross validated drill hole interval. The presorting runtime increases as the maximum number of points increases. Generally, 16 to 24 points is adequate, since there may be only a few data points within the user specified search ellipsoid or sphere.

The second search alternative is the SECTOR SEARCH FOR DATA. With this option, a user specified maximum number of points is found in each sector. A sector can be visualized as a square-based pyramid whose apex is at the estimated point. Six (6) sectors all containing apices at the point to be estimated make up the three-dimensional space surrounding that point. The MAXIMUM NUMBER OF POINTS PER SECTOR, N, (5 max) instructs the program to find the N closest points within each sector of the search ellipsoid.

The user can control the way blocks are estimated by limiting the rock type intervals from the input drill hole data (Rock Code Input Selection). The user can either specify that ALL rock codes are used, or can specify a subset of rock codes to use. If a subset of codes is selected, then the number of codes and the actual rock numbers are entered on a later screen.

In the same manner that the user controls which data intervals are used in the estimation process, control of the block rock types to be interpolated can also be specified (Rock Codes to Interpolate). The user can either specify that ALL rock codes will be interpolated, or can specify a subset of codes to interpolate. If a subset of codes is selected, then the number of codes and the actual rock numbers are entered on a later screen.

In the second input screen, the user must select whether the data is isotropic or anisotropic. For isotropic data, the same search distance limit applies in all directions (a sphere). For anisotropic data, the search distance is varied, depending on the search direction (a search ellipsoid). A search ellipsoid is used for data that exhibits a trend that is supported by geologic or geostatistical analysis.

For ANISOTROPIC DATA the search ellipsoid is defined by its orientation and size as shown in Figure 5.3. The orientation is specified by the PRIMARY ROTATION ANGLE (azimuth) from North to the Primary (generally longest) axis, the PLUNGE OF THE PRIMARY AXIS from horizontal, and the ROTATION ANGLE ABOUT THE PRIMARY AXIS. The size of the ellipsoid is specified by the maximum search range (radius) and the ratio of the secondary and tertiary axes radii to the primary axis radius. This relationship is defined as follows:

     PRIMARY AXIS RADIUS = MAXIMUM SEARCH RADIUS

    SECONDARY AXES RATIO = (SECONDARY AXIS RADIUS)/(PRIMARY AXIS RADIUS)
     TERTIARY AXES RATIO = (TERTIARY AXIS RADIUS)/(PRIMARY AXIS RADIUS)

The user must enter the LENGTHS OF THE PRIMARY, SECONDARY, AND TERTIARY AXES. These "lengths" can be expressed in any consistent units the user desires, such as axes lengths, axes radii, percents, ratios, etc. The maximum and minimum search ranges (radii) ultimately determine the actual size of the inclusion and exclusion ellipsoids. The axes "lengths" simply describe the relative size of the primary, secondary, and tertiary axis radii (ellipsoid shape). See Volume I, Section 3.8 for further discussion of ellipsoid conventions.

The user may now define the maximum distance from an estimated drill hole interval for which data are used in the point validation. This distance is the MAXIMUM SEARCH RANGE. It is also called the MAXIMUM SEARCH RADIUS. The maximum search radius is defined to be the longest radius of the search ellipsoid, which is entered later on in the program.

It is possible to search a rectangular portion of the grid. This is referred to as submodeling. The rectangular area is defined by the STARTING and STOPPING ROWS, COLUMNS, AND LEVELS. Only samples that are located within this rectangle "box" are modeled. This feature is useful to submodel portions of the grid under different parameters due to radically different data or when only small portions of the grade model are necessary.

The user has the option to run point validation using a UNIVERSAL KRIGING estimation method. If the user selects to use universal kriging, several additional input parameters must be specified.

First, the NUMBER OF UNIVERSAL KRIGING VARIABLES, N, to be used must be entered. Currently, the maximum number of variables is one (1). The system also prompts for the sample (or composite) label name that is to be used. This label number must exist, and must contain universal kriging values to be used in the point validation estimation.

The user must also specify the 3-D grade label and model type (IDP or Kriged) for the corresponding block model universal kriging value.

MicroMODEL allows the user to limit the search to samples that have the universal kriging zone values which fall within a specified range of values. If the user selects this option, he must then enter the MAXIMUM DIFFERENCE ALLOWABLE BETWEEN data input value and Interpolated value. For example, if the user specifies a maximum difference of 3.0 in the search, a block location with a universal kriging zone code of 5.0 is only modeled using samples with zone codes ranging from 2.0 and 8.0.

Upon completion of the Grade Modeling Presort, the user can proceed to Grade Modeling and evaluate one or more modeling methods based on the presorted drill hole data for the current label.

5.9 Grade Modeling

This option allows the user to interpolate assay values and assign grade values to the current label grade model, according to user specified parameters. The input data for this program is contained in the presorted drill hole data file created by the previous program, Grade Modeling Presort (Section 5.8).

The first time this program is run, a background grid of unestimated block values (-999.99) is created for the grade model associated with the current grade label and the chosen modeling method. This background grid is then updated with the interpolated block values by the Grade Modeling program. The update may overwrite the entire grid, or may only overwrite a portion of the grid because of submodel clipping or modeling with different rock types. The user can ensure that a grid is reinitialized on a subsequent run by deleting the grade file (and error or distance files, if appropriate) prior to that run.

With the Grade Modeling program, the user can try different presorting and modeling parameters until a satisfactory model has been created.

The ANSWERSET NAME identifies this set of answers.

Two grade modeling options are available to the user, KRIGING and INVERSE DISTANCE TO A POWER (IDP). The user must select kriging, or IDP.

For IDP, the user must specify the POWER OF INTERPOLATION. A power of 1.0 represents linear interpolation while a power of 5.0 approaches a polygonal estimation. Powers less than 1.0 should not be used.

The program has the facility to calculate ERROR OF ESTIMATION for the IDP interpolation. If the user requests to store variance of error values (error of estimation), a Variogram TYPE, NUGGET, SILL, and RANGE are needed as input. Instead of calculating and saving an ERROR OF ESTIMATION, the user may elect to store the distance to the closest data point

The user must specify whether to use point estimation, or block estimation. In Point estimation, one grade interpolation is made to the center of each block being estimated. Block estimation generally produces a smoother grid than point estimation, but takes longer to run.

With BLOCK ESTIMATION, interpolations are made to several locations in each block, with the average of the interpolations being assigned to the block. If Block Estimation is chosen, the user must specify the DETAIL OF ESTIMATION. This controls the number of locations in each block for which interpolations are calculated. These locations are distributed evenly throughout the block according to the following table:

Block Gridding
Detail of Estimation Number of Locations
1 4
2 9
3 16
4 25
5 36

Runtimes increase proportionally with increased detail of estimation. Generally, Block Estimation with a detail of 1-3 is adequate.

The user can request to reset all values to unestimated before this run by selecting the check box labeled "YES, Reset all values to missing". It is highly recommended that the user always choose this option for the first in a series of modeling runs. This insures that any values that were interpolated previously, say with a larger search radius, will not erroneously persist if a smaller search radius is tried.

The user can require that a MINIMUM NUMBER OF POINTS be found meeting the search criteria for the estimated point before an estimation is made. This facility prevents points from being estimated when only very few data points are within the search envelope.

For both kriging and IDP modeling options, the program asks for the NUMBER OF ANISOTROPIES to use. Choosing zero (0) anisotropies implies the data is isotropic. For data that is isotropic, the program gives points that are equidistant from the estimated point equal weighting in the interpolation. If the data is ANISOTROPIC, the user may enter from 1 up to 5 anisotropic weighting ellipsoids. MicroMODEL does not require the presorting ellipsoid and weighting ellipsoid(s) to be identical. For instance, the user may choose to presort with a sphere (isotropic) and model with one or more ellipsoids (anisotropic).

The user has the option to perform grade modeling using a UNIVERSAL KRIGING estimation method. The user must select the label FOR UNIVERSAL KRIGING that is to be used. This label must exist, and must contain universal kriging values to be used in the grade estimation.

For kriging, decimal LOGARITHMIC TRANSFORMATIONS can be used on data that is approximately log-normally distributed. In this case, the interpolation is performed on the logs of the data after several involved calculations are performed. The results of this computation are transformed back to the decimal system prior to output. An error of estimation grid is automatically generated if kriging is used. If logarithmic transforms are selected the user can enter the THIRD PARAMETER. This parameter allows the user to bias all data values by this quantity. If the third parameter is not required, enter the default value of 0.0. NOTE: Logarithmic transformation should only be selected under a special set of circumstances. Users without a strong geostatistical background should not even consider using this option.

Selecting the kriging option requires the user to input the NUMBER OF VARIOGRAM MODELS TO NEST. Up to nine different variogram model structures may be nested to establish the overall variogram model.

In addition to specifying the number of variograms to nest, the user must enter the NUGGET VALUE for the composite structure, along with an optional total SAMPLE VARIANCE. The SAMPLE VARIANCE should be left at 0.0, unless there is a zonal effect. For each variogram that is nested, the user must enter the VARIOGRAM MODEL TYPE, SILL, and RANGE for each structure. Supported variogram model types are spherical, linear, exponential, and gaussian. See Volume I, Section 3.5 for a discussion of MicroMODEL's variogram model conventions. If any anisotropies have been specified, then the anisotropy number associated with each variogram must be entered.

For ANISOTROPIC DATA, the weighting ellipsoid is defined by its orientation and ratio of its axis "lengths" as shown in Figure 5.4. The orientation is specified by the ROTATION ANGLE (azimuth) from North clockwise to the Primary (generally largest) axis. The user can also specify a second rotation angle (DIP), and third rotation angle (TILT or RAKE). The axes length ratios of the ellipsoid is specified by the ratio of the secondary and tertiary axes lengths to the primary axis length as described below:

    SECONDARY AXES RATIO = (SECONDARY AXIS RADIUS)/(PRIMARY AXIS RADIUS)
     TERTIARY AXES RATIO = (TERTIARY AXIS RADIUS)/(PRIMARY AXIS RADIUS)

The program prompts the user for the LENGTH OF THE PRIMARY, SECONDARY, and TERTIARY AXES for each anisotropy selected. These "lengths" (weighting factors) may be expressed in any consistent units the user chooses, such as axes lengths, axes radii, percents, ratios, etc. The axes "lengths" describe the relative size of the primary, secondary, and tertiary axes radii according to the axes ratio. Further discussion of weighting ellipsoid conventions can be found in Volume I, Section 3.8.

If the user is not satisfied with the resulting grade model values, the data can be presorted again (if the presort parameters require change) and then modeled using different parameters, until the desired result is obtained. If other rock types are to be modeled, the current sample or composite label assay data must be presorted and modeled for the new rock type(s).

The user can require that a MINIMUM NUMBER OF POINTS be within the presorted file for the estimated point before a block estimation is made. This facility prevents blocks from being estimated when only very few data points are within the search envelope.

The grade model can be displayed using any of the options in the Graphical Display Menu (Section 5.13). The statistics programs offered in this module enable the user to run statistics on the grade model for comparisons against the drill hole statistics.

If the user is not satisfied with the resulting grade model, the data can be presorted again (if the presort parameters require change) and remodeled using different parameters, until the desired result is obtained. If other rock types are to be modeled, the current sample or composite label assay data must be presorted and modeled for the new rock type(s).

5.10 Model Frequency Analysis and Basic Statistics

This option allows the user to perform basic statistics on a specified grade model for the current grade model label. The printed output produced by this program includes population information, mean and variance analysis, cumulative frequency analysis, and a histogram printout.

Since MicroMODEL allows Polygon, IDP, IDP Error of Estimation, Kriged, and Kriged Error of Estimation grids to exist for the same label, the user must first specify the TYPE OF INPUT GRID.

Following this, the input options are the same as those for Sample Frequency Analysis and Basic Statistics (Section 1.11). The user should refer to this section for more details.

The one difference in the Model Frequency vs. Sample Frequency programs is that the Model Frequency program allows the user to calculate statistics for a range of levels. The user enters the STARTING and ENDING LEVEL NUMBERS for statistics calculation.

5.11 Model Cumulative Frequency Analysis

This option allows the user to produce an unscaled plot of the cumulative frequency curve of the specified grade model for the current grade model label. The user can enter a variety of controls to isolate certain data populations and may use logarithmic transformations, if needed.

Since MicroMODEL allows Polygon, IDP, IDP Error of Estimation, Kriged, and Kriged Error of Estimation grids to exist for the same label, the user must first specify the TYPE OF INPUT GRID.

The remaining input for this program is similar to that for the Sample Cumulative Frequency Analysis (Section 1.12). There is an additional screen for limiting the analysis to blocks within a given range of levels. The user enters the MINIMUM and MAXIMUM LEVEL number. Also, if the user specifies that the values should be weighted by another second grade model, the user must specify the GRADE MODEL LABEL and MODEL TYPE.

The Cumulative Frequency program produces an unscaled plot (see Volume I, Section 6.3.9). For further explanation on SCALE OF PLOTS, see chapter 11, Plotting.

5.12 Model Correlation Analysis

This option allows the user to produce a correlation analysis (linear regression) plot between two grade models of the same or different labels.

Input for this program is essentially the same as that for Sample Correlation Analysis (Section 1.13). The only additional input required from the user is that the user must specify model types (IDP, Kriged, etc.) For the primary and secondary labels. Also, the user can limit the correlation calculations to a MINIMUM and MAXIMUM level number.

The Correlation Analysis program produces an unscaled plot (see Volume I, Section 6.3.9). For further explanation on SCALE OF PLOTS, see chapter 11, Plotting.

5.13 Graphical Display of Grade Model (Menu)

5.13.1 Introduction

This submodule allows the user to display the grade models that have been previously created by MicroMODEL. The types of grid displays available are:

    GRAPHICAL DISPLAY OF GRADE MODEL (MENU)
  1. Return to Submenu
  2. Command Shell
  3. Printer-plot of grid values
  4. Plan View Cell plot of grid values
  5. Contour grid values
  6. Perspective view of grid values
  7. Plot Cell Values in Section

The graphic output produced by these options are:

  1. Printer Plot (digit map - not to scale)
  2. Plan View Cell Plot showing numeric cell values (scale map)
  3. Contour Plot (scale map)
  4. Perspective View (three-dimensional fishnet - not to scale)
  5. Raised Contour View (Three-dimensional perspective contour - not to scale)
  6. Cell Plot of values in section (scale map)

The Printer Plot, Contouring, and Perspective Fishnet plotting programs only access a specified model type for the current grade model label from this submodule. The Plan View Cell and Cross Section Cell plotting programs use the current rock model and/or specified model types for any grade model label as input from this submodule.

Generally, the Printer Plot, Plan View Cell Plotting, and Cross Section Cell Plotting programs are the most useful for displaying the grade models. The contouring, and three dimensional plots are useful for visualization and demonstration.

5.13.2 Command Shell

This menu choice enables the user to invoke commands and run external programs without exiting MicroMODEL. Refer to Section 1.2.

5.13.3 Printer Plot of Grid Values

This program produces a quick digit map of the specified grade model for the current grade model label. Each digit represents a range of grade values, and the key for the digits is printed below the digit map. Unestimated blocks (-999.99) are indicated by a space. This map is generally used for quick verification only, as it is not to scale.

This program works exactly the same as the choice described in section 3.8.3. The exception is that the user must also specify which grid modeling method created the desired grid for the current grade label digit map. The type of grid can be Polygon, IDP, IDP Error of Estimation, Kriged, or Kriged Error of Estimation.

5.13.4 Plan View Cell Plot of Grid Values

The Plan View Cell Plotting program produces a plot that numerically displays the assigned grid values for any existing grid in MicroMODEL. The plots can be produced at any map scale needed. Several options are available which enable the user to design his plots as needed. Refer to section 3.8.4, Cell Plot of Grid Values, for details.

5.13.5 Contour Grid Values

When accessed from the Grade Modelling submenu, the Contouring program produces isopleth maps of a user specified grade model for the current grade label on a particular bench. This program may be applicable in some conditions. Some experimentation with the program parameters may be necessary to produce the desired results.

The user can design the contour maps as needed by invoking a variety of plotting options. The contour plots can be produced at any map scale.

The user should refer to section 2.9.5, Contour Grid Values (Surface Data), for details. There are two additional input choices.

First, the TYPE OF INPUT GRID must be specified to instruct MicroMODEL which grid modelling method created the desired grid for the current label digit map. The type of grid can be Polygon, IDP, IDP Error of Estimation, Kriged, or Kriged Error of Estimation. Also, the user must specify the level number to contour.

The Contour Grid Values program produces a scaled plot that can be output at any user specified map scale (see Volume I, Section 6.3.7). For further explanation on SCALE OF PLOTS, see chapter 11, Plotting.

5.13.6 Perspective View of Grid Values

This option allows the user to produce a three-dimensional fishnet view of a user specified grade model for the current grade model label, on a user specified bench. The output created by this program displays grade values as peaks and valleys. The plots generated by this program are usually used for verification of modelling, visualization assistance, and report preparation rather than producing actual working maps.

The user should refer to section 2.9.6, Perspective View of Grid Values (surface Data), for details. There are two additional input choices.

First, the TYPE OF INPUT GRID must be specified to instruct MicroMODEL which grid modeling method created the desired grid for the current label digit map. The type of grid can be Polygon, IDP, IDP Error of Estimation, Kriged, or Kriged Error of Estimation. Also, the user must specify the level number to display.

The Perspective Plotting program produces a scaled plot that can be output at any user specified map scale (see Volume I, Section 6.3.7). For further explanation on SCALE OF PLOTS, see chapter 11, Plotting.

5.13.7 Plot Cell Values in Section

The Cell Cross Section option produces a cross section of the block values for the rock model and any grade model through any row or column in the model. It does not work on any diagonal. In the same manner as the Plan View Cell Plotting program, this program produces a plot that numerically displays the assigned grid values for any existing grid in MicroMODEL. The plots can be produced at any map scale needed. Several options are available which enable the user to design his plots.

The user should refer to section 3.8.7, Plot Cell Values in Section (Rock Modeling), for details.

The Block Cross Section Plotting program produces a scaled plot that can be output at any user specified map scale (see Volume I, Section 6.3.7). For further explanation on SCALE OF PLOTS, see Chapter 11, Plotting.

5.13.8 Plot Cell Values in Angled Section

The Angled Cell Cross-Section option produces a cross-section of the block values for rock or grade models along any diagonal in the model.

This program works in exactly the same manner as the previous option (15.13.7 - Plot Cell Values in Section), with one exception. Instead of plotting block values along a section or row, this program plots the values along any diagonal in the model. Refer to Volume 2, Section 3.8.8 for details.

5.14 Model Manipulation

This option allows the user to perform several different types of mathematical and logical operations on up to eight grade labels. Manipulations may also be made with the rock model. The results of the operations can be written into any existing grade label, or the rock model. This option is especially useful for the creation of synthesized data, such as data that has been limited to a given minimum or maximum value.

This option works in exactly the same manner as the program described in section 1.14, Sample Manipulation. The user should refer to that section for details. The only difference is that, in addition to specifying the input and output label type(s), the user must also specify the model type(s).

5.15 Clean-Up Directory

This option allows the user to delete all output files created in the Data Entry Module that are no longer needed in the MicroMODEL system. The files that will be deleted are listed when the program is invoked. The output files that are deleted can always be recreated by MicroMODEL at a later date as needed. Periodically running this program increases usable disk space.