Multivariate Estimation Editor

Use the Multivariate Estimation Editor option to perform cokriging grade estimations on your block model. The Multivariate Estimation Editor allows you to set up parameters used to perform Simple CoKriging, Ordinary CoKriging, Standarised CoKriging, and Traditional Ordinary CoKriging for multiple variables.

Note

To set up parameters to perform calculations for a single variable, use the Univariate Estimation Editor instead.

To use Jack Knife and Cross Validation, use the Validation Editor.


Instructions

On the Block menu, point to Grade Estimation, then click Multivariate Estimation Editor.

Samples Selection

Follow these steps:

  1. Enter a name for the Estimation file, or select it from the drop-down list. The drop-down list displays all files found in the current working directory that have the (.bef) extension. Click Browse to select a file from another location.

    Note:  The information entered here is also used to provide the name of the report that is generated and stored in your project folder. The naming convention used for the report is <bef_file>_<estimation id>.bef_report. The reports can be opened with Vulcan"s Text Editor, or any other text editor.

    Tip

    You can make changes to an existing estimation file, then click the Save As icon to save the edited version under a new name. This allows you to transfer all the parameter settings from the Estimation Editor to the new file without having to enter everything in again.

  2. Enter or select an Estimation ID. To create a new estimation ID, click the New icon as shown below, and provide a unique name for the current panel settings. Up to nine separate IDs can be created for each BEF file.

    Figure 1 : Click to create a new estimation ID.

    The ID Description is optional and is not required. However, they can be very helpful, especially when you are creating multiple IDs.

    If you need to edit these fields you may do so by clicking the icon to open the estimation file options, then make your changes.

    ID Options

    Figure 2 : Click to open the estimation file Options panel.

    Setting up multiple estimation passes

    Click the Estimation Passes icon located at the top of the panel, as shown below.

    Tip:  This should be done after you have completed the main panel entries for the initial estimation pass.

  3. Select the type of Estimator you want to apply. The options will change depending on your selection of estimator. The Multivariate Estimation Editor allows you to set up parameters used to perform Simple CoKriging, Ordinary CoKriging, Standarised CoKriging, and Traditional Ordinary CoKriging for multiple variables.

    Note:  Since there is one Estimation Mode option available, Block Model Estimation, you will not need to select from the drop-down list.

  1. Select the Block Model from the drop-down list. The drop-down list displays all files found in the current working directory that have the (.bmf) extension. Click Browse to select a file from another location.

    Note

    When setting up a previously saved BEF file, if you attempt to use a block model that does not include the variables that were previously selected, a warning will be displayed asking if you want to add them to the block model.

    Clicking Yes will automatically add the missing variables to the block model.

  2. Specify the name of the database or mapfile that contains the sample data. The drop-down list labelled Select Database or Map File contains all of the Vulcan database files and mapfiles found within your current working directory. Click Browse to select a file from another location.

    Alternatively, you can use an ODBC link to connect to a database that contains the sample data. Click here for information about ODBC databases.

  3. Select the field that the estimates will be calculated from using the Grade variable drop-down list.

  4. Enter the name of the Sample Group (database key) to be loaded. Wildcards (* multi-character wildcard and % single character wildcard) may be used to select multiple groups.

    Note:  Multiple groups only apply to Isis databases (ASCII mapfiles consist of one group).

  5. Select the names of the fields containing the X, Y and Z coordinates from the Location field drop-down lists.

  6. In the section labelled Sample Database Manipulation you can apply the base logarithm function to all sample values. Click Apply logarithm, and then enter the constant that you want to use.

    Note:   All original sample values must be positive for the logarithm to be defined.

    The specified logarithm constant is added to the calculated logarithm.

  7. Click Use cut grades if you want to apply cut-offs to the grades used in the estimation. Specify a lower grade cut value (grades lower than this value are set to this value) and an upper grade cut value (grades above this value are set to this value).

  8. Enable the option labelled Use database and location of the Primary variable in the rest of the variables if you want to use the same database for both the primary and secondary variables. If you choose not to use this option you will need to specify the database used when selecting the secondary variable.

  9. Highlight the Secondary label in the Sample Variables window to select the secondary variable from the drop-down list.

    Select the variable using the same method you used to select the primary variable. If you selected the option to use the same database and location as the primary variable, the controls for the Sample Location of any additional variables will be disabled. However, you will be given the option to apply logarithms and set lower and upper grade cut values.

    Add extra secondary variables by clicking the icon on the right side of the window.

    Note:  A maximum of five variables can be selected.

Select Using Filter

Use this panel to filter your sample data by setting restrictions on samples values, triangulations used, character values within database fields, and field attributes. You can use any combination of the four filters, or not use any at all. This panel is optional.

To set up a filter for each variable, highlight the variable that you want to apply the filter to in the Sample Variables window, then edit the filter parameters.

Example:  The example above shows one possible way to filter the data. The filters will ignore all default assay values of -99.0 and include only samples that fall within the three vein triangulations.

The following steps show how to set your filters.

Estimation Result Variables

Use this panel to select the grade variable you want to run estimations on, along with any additional output variables.

Follow these steps:

  1. Select the primary variable you want to use for the estimations by selecting it from the Grade variable drop-down list.

    Only valid variables will be displayed in the list.

  2. Enter a default value for blocks that are not estimated.

  3. Select any output variables you want to include in your estimation run. Depending on which estimation method you are using, the available output variables will change. The table below shows the entire list of output variables and the estimation methods in which they are used.

    To quickly populate the table with all the variables, click the Fill output variables button.

    Output Variable Type Output Variable Default Value ID SK OK IK UC
    Distance to Closest Sample (Anisotropic) au_ids_dist_c_an -99.0 * * *   *
    Distance to Closest Sample (Cartesian) au_ids_dist_c_ca -99.0 * * *   *
    Flag when Estimated au_ids_flag_variable 0.0 * * * * *
    Grade of the Closest Sample (Anisotropic) au_ids_grade_c_an -99.0 * * *   *
    Grade of the Closest Sample (Cartesian) au_ids_grade_c_ca -99.0 * * *   *
    Maximum Weight au_ids_max_weight -99.0 * * *    
    Minimum Weight au_ids_minimum_weight -99.0 * * *    
    Number of Holes au_ids_num_holes 0.0 * * * * *
    Number of Samples au_ids_num_samples 0.0 * * * * *
    Sample Coeff. of Variation au_ids_sample_coeff -99.0 * * *    
    Sample Grade Minus Estimation au_ids_sample_grade_diff -99.0 * * *    
    Sample Mean au_ids_sample_mean -99.0 * * *    
    Sample Standard Deviation au_ids_sample_stddev -99.0 * * *    
    Sample Variance au_ids_sample_variance -99.0 * * *    

    The first column labelled Output Variable Type shows a description of the variable. This field cannot be edited.

    The second column labelled Output Variable is the variable name that your block model will use. This field can be edited if desired.

    Note:  The name of a variable can have a maximum of 30 alphanumeric characters. The variable, which can only be entered using lowercase characters, must start with a letter and can only contain alphanumeric characters and/or underscores, for example, variable_1.

    This is followed by the Default Value. This field can also be edited.

  4. If you are using Simple Kriging as your estimation method, the option to manually define a mean will be enabled.

    There are three options to choose from:

    1. Use stationary mean - Select this option if you want to manually define the stationary mean value.

    2. Use mean variable - Select this option to take the locally varying mean into consideration. The mean variable is used for the sample mean and the block mean.

      With this option, you can set the default value for all samples that are located outside the model area by entering a value into Drift value.

      Note:  The mean variable value is used if a block is found on XYZ coordinates (of the sample), and the stationary mean value is used if not. In earlier version of Vulcan these were exclusive. To keep the previous behaviour, set a value of 0.0 for the stationary mean.

    3. Use block mean variable - Select this option to use the variable that holds just the block mean and not the sample mean.

Variography

Use this panel to enter the variogram parameters.

Note

Use the tabs at the top of the main panel to access the settings for the secondary and extra variables.

Follow these steps:

  1. Select a variogram file. This step is optional. You can choose to enter the variogram information directly into the table if you desire to do so. To select the file, use the drop-down list labelled Read variogram from file, or click the Browse button if the file is located somewhere other than your current working directory.

    All the files that have a (.vrg) extension will be shown in the list.

    Note:  To generate a variogram file, you can use an exported file from the Data Analysis tools located in the Analyse menu.

  2. Enter the Nugget. This represents the random variability and is the value of the variogram at distance (h) ~ 0.

  3. Complete the table defining the variogram parameters to be used. Enter the information by typing into the space provided for each column.

    Tip:  If you want to use block model variables instead, enable the Use block model variables checkbox, then use the drop-down lists to populate each field. The drop-down lists will automatically display all eligible variables from the block model selected at the top of the panel.

    Note

    Click the icon in the Extra Secondary Variable tab to display the tables needed to setup the variograms for extra secondary variables as shown here.

    Explanation of table columns:

Search Region

Use this panel to set the search direction and how far to look for samples.

Follow these steps:

  1. Select the shape of your search area by choosing Ellipsoid or Box.

    Figure 5 : The major radius is "a", the semi-major radius is "b" and the minor radius is "c".

    Note:   The volume of a box with sides 2a, 2b, and 2c is about twice the volume of an ellipsoid with radii a, b, and c. Therefore, when using the box search you collect about twice as many sample points. This causes an estimation using a box search to take from two to eight times as much time as an estimation with a search ellipsoid.

  2. Set the search orientation. The Bearing, Plunge, and Dip values are angles, in degrees, that specify the orientation of the search ellipsoid and orientation of variogram structures.

    Care must be taken with these parameters as there are several common misunderstandings about the meaning of these parameters.

    To understand these parameters, imagine an ore body with a primary axis. To find the bearing of the ore body, project the ore body axis straight up onto the surface plane and call this line the bearing line. The bearing is the angle clockwise from north to the bearing line.

    Figure 6 : Bearing

    Plunge is the angle between the horizontal plane and the ore body axis. Note that the plunge should be negative for a downward pointing ore body.

    Figure 7 : Plunge

    To find the dip of an ore body, imagine the ore body is located in a plane. First rotate around the Z axis by the bearing so that the ore body is pointing north. Then rotate around the east-west axis by the plunge so that the ore body is level with the ground. At this point the ore body is parallel to the north-south axis. The dip is the angle of rotation to bring the plane into the horizontal plane. Looking north, if the plane must be rotated clockwise around the north-south axis, then the dip is positive (other software packages may use the opposite convention).

    Figure 8 : Dip

    Note:   The terms bearing, plunge and dip have been used by various authors with various meanings. In this panel, as well as kriging and variography, they do not refer to true geological bearing, plunge, and dip. The terms X', Y', and Z' axis are used to denote the rotated axes as opposed to X, Y, and Z which denote the axes in their default orientation.

  3. Enter the dimensions of the search box. The search box has sides with length twice the numbers given. The major axis radius is the search distance along the axis of the ore body. The semi-major radius is the search distance in the ore body plane perpendicular to the ore body axis. The minor axis radius is the search distance perpendicular to the ore body plane.

    Note

    The search radii are true radii. If you set your major search radius to '100', then the ellipsoid has a total length of 200. The following diagram shows the relationship between the axes with the ellipse in the default orientation (bearing 90°, plunge and dip 0.00°).

    Figure 9 : Relationship between radii

  4. If you are using a tetrahedral model has been created, you can select the Unfold checkbox to select a (.tetra) file from the Unfolding spec file drop-down list. This list will contain all (.tetra) files found within your current working directory. Refer to the Unfolding section for more information on tetrahedral modelling.

  5. Click the Interactive button to display the Edit Interactive Ellipsoid panel define search ellipsoids on screen in Vulcan.  Once defined in Vulcan, the parameters will then be written back into the panel.

Distance to Samples

Use this panel to set the parameters to store the search distances used to look for your samples. Any, all, or none of the different distance measures can be stored by putting a block model variable name in the appropriate panel item. If you do not want to store a value, then leave the panel item blank.

Follow these steps:

  1. Enter a variable name into the appropriate box. There are two different kinds of distances that can be stored:

  1. Enter a number into Default distance when no estimate is made. This will be stored as an average distance if there aren't enough samples available to make an estimate.

Sample Count

Use this panel to set the minimum and maximum number of samples that will be used to estimate the grade of a block.

Follow these steps:

  1. Enter the lowest number of samples in the box labelled Minimum number of samples per estimate.

    This is the minimum number of samples that needs to be found to generate an estimate. Blocks with less than this number of samples within the search ellipsoid or search box are assigned the default grade value.

  2. Enter the largest number of samples in the box labelled Maximum number of samples per estimate.

    This is the maximum number of samples to be used in any grade estimation. Up to 999 samples per estimate are allowed.

    Example:  The estimation program may find 30 samples near a block centre. If you had specified a maximum of 10 samples, then only the 10 samples closest to the block centre are used. The distance to the block centre is calculated by an anisotropic distance based on the search radii.

  3. Decide whether or not to use an octant search. The space around a block centre is divided into eight octants by three orthogonal planes.

    Note:  An octant search is a declustering tool used to reduce imbalance problems associated with samples lying in different directions. If there are more samples in one direction than another, then this option limits the bias.

    If want to use an octant search, enable the checkbox labelled Use Octant Based Search. This places a limit on the number of samples that can come from a given octant.

  4. Enter the maximum number of samples from each octant to be used in the estimation in the box labelled Maximum samples per octant. Samples closest to the block centre are used first.

    Note:  The maximum number of samples per estimate always applies, regardless of the maximum samples per octant value.

  5. Enable the checkbox labelled Additional restrictions if you want to limit the number of samples for octants. Then enter the number of minimum and minimum samples per octant.

    The minimum octants with samples enables you to specify the number of octants that must contain samples for an estimate to be generated. The minimum samples per octant enables you to specify the number of samples per octant that needs to be found to generate an estimate. These two restrictions work together. An octant is considered filled if it contains at least the minimum number of samples per octant. The minimum number of octants with samples requires that at least that number of octants be filled.

    If you set the minimum number of samples per octant to 2, the minimum number of octants to 3 and have the following number of samples per octant, there are two filled octants. As this is less than the minimum number of octants with samples, the default value is assigned to this block.

    Octant Number

    Number of samples per octant

    Filled / Not Filled

    0 1 Not filled
    1 3 Filled
    2 2 Filled
    3 1 Not filled
    4 1 Not filled
    5 1 Not filled
    6 1 Not filled
    7 0 Not filled
  6. Enable the checkbox labelled Store octants used if you want to save the number of octants in a block model variable.

  7. Enable the checkbox labelled Store octants information if you want to save information concerning which octants were used by each estimated block in a block model variable.

  8. Select octant rotation type. There are three types:

    Rotate axes This consists of three planes perpendicular to axes that have been rotated 45° about the Z axis and 35° about the X' (X axis after rotation about the Z axis), this produces a set of planes in which the first has a bearing of 135°, the second has a bearing of 45° and is at angle of -55° to the horizontal and the third also has a bearing of 45°, but is at an angle of 35° to the horizontal. (See the diagram below.)
    Cartesian axes This consists of three planes perpendicular to the conventional Cartesian axes X, Y, and Z (or East, North, and elevation) axes.
    Ellipsoid axes This consists of three planes that are perpendicular to the major, semi-major, and minor axes of the search ellipsoid.

  9. Select the method by which the samples will be measured by choosing either Select by anisotropic distance or Select by Cartesian distance. The samples are sorted by distance (either anisotropic or Cartesian) prior to the samples being limited. This ensures that the closest samples are kept.

  10. Enter the distance to use in Distance to check duplicate samples to prevent the same sample from being used more than once. Samples less than or equal to the specified distance value are considered to be duplicates, and will result in the entire grade estimation process being stopped. You can disable this feature by specifying a distance value of '-1'.

Sample Limits

Use this panel to limit the effect a high-valued sample will have on distant blocks.

Important:  Using this option will not place a grade cap on the high-yield samples. It will prevent them from being used in the estimation completely.

The high-yield exclusion ellipsoid specified in this section of the Estimation Editor interface has its own major, semi-major, and minor axes that have the same orientation as the ellipsoid defined in the Search Region panel. When selecting the samples for the grade estimation, any samples within the high-yield exclusion ellipse can be chosen whether they are greater than or less than the threshold. However, between the smaller high-yield exclusion ellipse and the normal search region ellipse, only samples that are less than the threshold will be used.

Follow these steps:

  1. Enable the checkbox labelled Exclude distant, high yield samples to ignore sample values at or above the specified threshold and outside the specified ellipsoid.

  2. Specify the database Field for high yield samples. It is usually the same as the input grade field. However, other fields can be used to achieve special sample limits.

  3. Enter the threshold you want to use as a limit for high-yield samples. Only samples that are less than the threshold will be used.

  4. Select Use angles if you want to use a customised orientation for the search ellipsoid. If you do not use this option, the samples will be selected using the ellipsoid defined in the Search Region panel.

    When a high yield region is defined, the value used puts a threshold on the samples outside of your specified distance and angle parameters. The high yield exclusion ellipsoid specified through this section of the Estimation Editor interface has its own major, semi-major and minor axes that have the same orientation as the ellipsoid defined through the Search Region section. When selecting the samples for the grade estimation, any samples within the high yield exclusion ellipse can be chosen whether they are greater than or less than the threshold. However, between the smaller high yield exclusion ellipse and the normal Search Region ellipse, only samples that are less than the threshold can be chosen. This is commonly used to avoid estimation from high gold nugget values to distant blocks.

    Example:  Using the settings in the screenshot above, we have several high-value samples that we would still like to use in our estimation and they outside of our high value spatial limits, so we set the Threshold value to 20. Then, we set our XYZ distance and rotation. Within that bubble, the high-value samples will be used without capping. Outside of that bubble, the value will be reduced to 20.

  5. Enter the search distance into the spaces provided for Major, Semi-Major, and Minor axes radii.

    Click the Interactive button to display an ellipsoid that can be edited by manipulating it with the mouse or entering the rotation and axis parameters directly.

  6. Select Use Capping Options to set threshold values for the lower and upper grade values that will be used in your estimations.

    You can use a Fixed value or use a Block Model value.

  7. Select Do not cap grades inside High Yield region if you do not want a threshold applied to the region specified in Step 4 above.

  8. Select Limit samples per drillhole if you want to limit how much influence a single drillhole or its samples will have.

  9. Specify the name of the database field containing the drillhole name by selecting the field from the drop-down list labelled Field for drillhole ID. The default is DHID.

Soft Boundaries

Use this panel to setup soft boundaries. Sometimes samples that are at a different estimation domain share similar grade properties when they are located close to the limit between the domains. This is often known as a soft boundary between the domains. In this case, it could be useful to include samples from a different domain but only at short distances from the blocks in the current domain.

Follow these steps:

  1. Select this checkbox labelled Use soft boundaries to make the rest of the panel available.

  2. Enter or select from the Soft boundary drop-down list the variable that will be used as a criteria to identify the estimation domains. The list is populated with the names of the database fields.

  3. If you want block model variables to be used as radii for restricted search ellipsoid or the bearing, plunge, and dip values of the restricted search region, click the option labelled Use block model variables. All the block model variables will populate the drop-down list of the respective fields.

    Explanation of table headings:

    Note:   If the sample selection criteria does not allow for samples in soft boundaries domains to be selected, then no samples will be applied to the definitions specified here.

  4. Click the Interactive button to display the Edit Interactive Ellipsoid panel define search ellipsoids on screen in Vulcan.  Once defined in Vulcan, the parameters will then be written back into the panel.

    Note:  Clicking on a row to highlight it will enable the Interactive button.

Cross Variography

This pane will display a matrix created from the selected variables.

Follow these steps:

  1. Click the icon for the cross variogram pair you want to edit. A new panel will be displayed that allows you to edit the input parameters for the variograms.

  2. If you want to use the parameters from an existing variogram, such as one created using the Vulcan Data Analyser, click Read variogram from file, then select the file you want to apply.

  3. Enter a value to use as the nugget.

  4. For the parameters listed in the table, you can use block model variables by enabling Use BM variables. This will convert each of the cells in the table to a drop-down list from which you can select the variables.

  5. You also have the option of entering the values for each cell by double-clicking in a cell, then entering a new value.

  6. Click OK to close the panel when completed.

  7. Do the same for each variogram you wish to edit.

Block Options

Use this panel to set up various block options.

Available options.

Note:  During the grade estimation process, any blocks that have been selected but don't get an estimation value will receive the grade estimation default value. All blocks that have not been selected will retain their block creation default value. As a result, you could end up with two default values within the block model. If block selection criteria has not been specified, i.e. all blocks are selected, then the blocks not receiving an estimated value will have their block creation default value overwritten with the grade estimation default value, that is, one default value exists.

Tip

You can test whether or not the selected block options will flag any blocks by clicking either of two buttons located at the bottom of the panel.