22b Module 22 -- Resource Estimation -- Exercises

MICROMINE Training v10.1 Module 22 Resource Estimation

Copyright Micromine Pty Ltd 2006

MODULE 22 TABLE OF CONTENTS

Lesson 1 Resource Estimation Concepts ............................................................................................................................... 1

CONCEPTS ............................................................................................................................................................................. 1 THE TRAINING PROJECT ........................................................................................................................................................ 2 NUMERIC EXCEPTIONS .......................................................................................................................................................... 2

Lesson 2 - Classical Statistics ................................................................................................................................................... 4

CLASSICAL STATISTICAL ANALYSIS ...................................................................................................................................... 4 Tables................................................................................................................................................................................ 4

Lesson 3 Generate Downhole Coordinates .......................................................................................................................... 11

WIREFRAMING ..................................................................................................................................................................... 13

Lesson 4: Assay Data Flagging .............................................................................................................................................. 15 FLAGGING/SELECTION ................................................................................................................................................. 15

Flagging using Solid wireframes .................................................................................................................................... 15 Flagging using DTMs ..................................................................................................................................................... 15

Lesson 5 Balancing Cut ....................................................................................................................................................... 18

Lesson 6 - Compositing .......................................................................................................................................................... 21

Lesson 7 - Geostatistics .......................................................................................................................................................... 25

THEORY ............................................................................................................................................................................... 25 Variography .................................................................................................................................................................... 25 Anisotropy ....................................................................................................................................................................... 27 Semi variogram formula ................................................................................................................................................. 27 Semi variogram model formula ...................................................................................................................................... 27

PRACTICE ............................................................................................................................................................................ 30 Review ............................................................................................................................................................................. 30 Nugget ............................................................................................................................................................................. 30 Using Semi Variograms .................................................................................................................................................. 32 Optimum Lag .................................................................................................................................................................. 33 Directional variogram, main: ......................................................................................................................................... 39 Direction of maximum continuity, primary variogram; .................................................................................................. 40 Model the variograms:.................................................................................................................................................... 41 Indicator variograms: ..................................................................................................................................................... 44 Relative variograms: ...................................................................................................................................................... 48 Cross Validation: ............................................................................................................................................................ 51

Lesson 8 Empty Cell Model ................................................................................................................................................ 55

BLOCK MODEL CELL SIZE ................................................................................................................................................... 55 Flagging.......................................................................................................................................................................... 55 Checklist ......................................................................................................................................................................... 55 How to decide the block size ........................................................................................................................................... 56 Subcelling ....................................................................................................................................................................... 57

Lesson 9 Modelling Principles ............................................................................................................................................ 61

Declustering .................................................................................................................................................................... 61 Specific gravity and block size ........................................................................................................................................ 62 Change of Support .......................................................................................................................................................... 62 Proportional effect .......................................................................................................................................................... 62 Interpolate parent blocks only ........................................................................................................................................ 63 Multiple runs ................................................................................................................................................................... 63

Lesson 10 Grade Interpolation ............................................................................................................................................. 65 INTERPOLATION ............................................................................................................................................................. 65

Search ellipse .................................................................................................................................................................. 66

Module 22 Resource Estimation MICROMINE Training v10.1


How to decide search ellipse size ................................................................................................................................... 67 INVERSE DISTANCE WEIGHTING ......................................................................................................................................... 68

Recommended Values ..................................................................................................................................................... 69 ORDINARY KRIGING ............................................................................................................................................................ 70

Ordinary kriging formula: .............................................................................................................................................. 71 ORDINARY KRIGING, RELATIVE VARIOGRAMS ..................................................................................................................... 72 MULTIPLE INDICATOR KRIGING .......................................................................................................................................... 73 KRIGING VARIATIONS.......................................................................................................................................................... 78

Lesson 11 Model validation ................................................................................................................................................ 81

Global validation: .......................................................................................................................................................... 82 Declustered global estimate ........................................................................................................................................... 82 Local validation: ............................................................................................................................................................ 83 Model validation: ........................................................................................................................................................... 84

Lesson 12 - Block Model Display .......................................................................................................................................... 86

Lesson 13 Resource Classification ...................................................................................................................................... 88

Kriging variance: ........................................................................................................................................................... 89

Lesson 14 Resource reporting ............................................................................................................................................. 91

Lesson 15 Cut-off grades and grade tonnage curves ........................................................................................................... 95

Lesson 16 - Example NVG data Ordinary kriging start to end .............................................................................................. 98

Step 1: Classical statistics exhaustive population .......................................................................................................... 98 Step2: Generate downhole coordinates .......................................................................................................................... 99 Step 3: Assign the wireframe to the assay file .............................................................................................................. 100 Step 4: Classical statistics orezone .............................................................................................................................. 100 Step 5: Apply a balancing cut ....................................................................................................................................... 101 Step 6: Composite the data to equal intervals .............................................................................................................. 102 Step 7: Geostatistics ..................................................................................................................................................... 103 Step 8: Cross validation ............................................................................................................................................... 109 Step 9: Build blank model ............................................................................................................................................ 110 Step 10: Ordinary Kriging ........................................................................................................................................... 111 Model report ................................................................................................................................................................. 114 Validation ..................................................................................................................................................................... 114



Table of Exercises

Exercise 22.1 Classical Stats .................................................................................................................................................... 6

Exercise 22.2 Generate Downhole Coordinates ..................................................................................................................... 11

Exercise 22.3 Flagging using solid wireframe ........................................................................................................................ 16

Exercise 22.4 Balancing Cut ................................................................................................................................................... 18

Exercise 22.5 Compositing ..................................................................................................................................................... 21

Exercise 22.6 Nugget .............................................................................................................................................................. 30

Exercise 22.7 Omni Variogram .............................................................................................................................................. 33

Exercise 22.8 Horizontal Fan Variogram ............................................................................................................................... 35

Exercise 22.9 Vertical Fan Variogram.................................................................................................................................... 37

Exercise 22.12 Creating a Blank Block Model ....................................................................................................................... 58

Exercise 22.13 Inverse Distance Weighting ........................................................................................................................... 70


Copyright Micromine Pty Ltd 2006 Page 22.1

Notes:

Lesson 1 Resource Estimation Concepts After this lesson you will understand:

What are we attempting to model;

What decisions do we need to make;

What are the most important decisions affecting the modelling;

How do we check how good our model is.

Concepts Resource estimation can be conducted for 1D, 2D and 3D models. The resource sector generally requires 3D models except for gridding and other 2D techniques

which use surface data to identify anomalous areas that are indicative of

prospective subsurface mineralisation.

Important considerations for 3D modelling are the search ellipse, compositing, domaining, the interpolation method, dealing with erratic high grades, anisotropy,

block sizes and validation? (1) The search ellipse includes sample grades relevant to the estimation of block

grades and excludes redundant (not required) grades;

(2) The compositing ensures the grades used for estimation are weight averaged back to the same length so the estimation process is not biased.

(3) Domaining divides the deposit into separate areas such as lodes that have

unique geological or grade characteristics that must be interpolated and modelled independently.

(4) The interpolation method is the method selected for modelling. This may be Inverse distance weighting (which does not require variography); ordinary kriging; median indicator kriging or multiple indicator kriging. Classical statistics,

in particular the shape of the histogram, the shape of the probability plot and the

coefficient of variation are useful to select the most appropriate interpolation method.

(5) Erratic high grades can be allowed for by applying balancing cuts to grades

or by using nonlinear methods such as multiple indicator kriging. An allowance must be made for high grades so that they do not bias the entire model and

affect large areas of the model to bias the model higher.

(6) Anisotropy is the preferred continuity of grade in one direction; isotropy means the grade is equal in all directions. All deposits should exhibit anisotropy

and this reflects the nature of deposition and the style of mineralisation. Gold in particular is very changeable and more prone to continuity in one direction to

another

(7) The size of the blocks required can be directed by the engineers who

indicate the SMU (Smallest Mining Unit) or by the drillhole spacing, and by the


Page 22.2 Copyright Micromine Pty Ltd 2006

Notes:

style of the deposit. The parent cells can be used for estimation and subcells can improve the definition to provide an accurate volume.

(8) Validation can be both global and local. Global validation means the raw sample data and the wireframe envelope are compared to the block model

tonnes and grade to ensure the model reflects the data that was used for the estimation.

The Training Project A good example for resource estimation is an iron project because the data is more regular and can produce strong models. For the resource estimation we

will use iron data

Files used in this training project:

Collar: IRON COLLAR.DAT

Survey: IRON SURVEY.DAT

Assay: IRON ASSAY.DAT

Assay: IRON ASSAY COMP2.DAT

Wireframe: Iron.tdb

Numeric Exceptions Always have the numeric exceptions ticked on for all three categories: Ignore characters, Ignore blanks and



Notes:

Lesson Summary

This lesson has introduced some of the fundamental concepts involved in

Resource Estimation. In the following lessons, we will put these concepts into use:

search ellipse

compositing

domaining

the interpolation method

dealing with erratic high grades

anisotropy

block sizes

validation

numeric exception

Good Practice

Use Numeric Exceptions throughout.

Help Topics

For information on: See:

Numeric Exceptions Numeric Exceptions



Notes:

Lesson 2 - Classical Statistics

Classical Statistical Analysis The aim of the classical statistical analysis is:

To check for the mixing of grade populations and the necessity of

separation of grade populations if there are more than one population, To derive the top cut grades for grade interpolation process, To determine the natural cut-off grades for interpretation of mineralisation, To determine the distribution of grades, To assess the validity of Kriging interpolation process, and To obtain the statistical parameters for grades.

Classical statistics are used to examine initially the global population and then the mineralisation population. The histogram, the cumulative frequency plot and

the probability plot all reveal information about the distribution of population grades.

Tables

To obtain statistical parameters, run Stats | Descriptive | Normal/Ln for

each element and for each potential domain separately. The statistical parameters are to be recorded in the output file, tabulated and included into the

report.

Histogram

The histogram bin size is selected so the shape of the distribution is apparent, it must be small enough to show the shape and large enough to contain sufficient

data. The histogram shows two populations, one at low background grades and another at higher grades; there is a discreet break between the two. The

moments such as mean, medium etc are displayed on the right of the histogram.

Probability plot

The change in the angle of the line on the probability plot helps to indicate the grade at which mineralisation grades occur as opposed to background grades.

In other words this is the cut-off grade separating country rock from the ore

zone. This grade is used for the grade to design the outlines on the drillholes for the ore zone interpretation. This grade is applied for the delineation of

mineralisation polygons.

Histograms, Log Histograms and (Log) Probability Plots should be generated for each element and potential domain using Stats | Distribution process. Use

filters to separate domains if possible. All graphs should be plotted, studied and



Notes:

included into the report. The potential mixing of grade populations, grade cut-offs for interpretation and top-cuts for grade interpolations should be determined

from the histograms and cumulative frequency plots. One of the most important

questions is to identify the number of grade populations. The number of populations can be estimated using the Stats | Distribution, (select

Probability Plot and Natural Log options). When the probability plot is displayed, run Model | Decompose from the top menu to obtain the statistical

parameters of grade populations. This can subsequently be displayed on the drill

traces and checked against the geological model and structures.

Obtain the grade value that separates background grades from mineralization grades. This is the inflection point on the probability plot. Alternatively this

figure may be stated by the Government. This grade value is the grade at which all mineralization polygons will be interpreted in section.

This Stage can take from several hours to several days depending on number of

elements and number of domains. Domains are separated data for different block models, such as different lodes, or weathering or very high grade, high

grade and low grade areas.

Please note, it is a good practice to calculate a coefficient of variation that might indicate a potential quality of variograms (COV = St. Dev. / Mean) and the

nature of interpolation method required. For a COV of 1 or less than 1.5 IDW

may be appropriate, above 1.5 a kriging method should be applied.

Interpretation

When interpreting the orebodies and wireframing the ore zones and mineralisation, a decision needs to be made whether a hard boundary or soft boundary is used. A typical hard boundary is where mineralisation is truncated

by a fault; a typical soft boundary may be where a stockwork of veins extends

from the main mineralisation zone into the country rock. A wireframe can be used for the hard boundary, however grades outside the wireframe or indeed no

wireframe may be used when modelling the soft boundary.

CHECKLIST

Classical stats tables are generated for all elements and domains COV values are calculated

Histograms, log histograms and probability plots are generated for all

elements and domains Tables and graphs are studied and modelling methodology is determined Use numeric exceptions if there are any character values in numeric fields The distributions are described



Notes:

Exercise 22.1 Classical Stats

1. Select Stats | Descriptive | Normal/Ln.

2. Fill in the dialog box:

Prompt Setting

Input File IRON ASSAY

Type DATA

Fields | Field Name (1)

Fields | Field Name (2)

T FE

SIO2

Output File DESCRIPT IRON

As discussed in Lesson 1, all Numeric Exceptions should be selected.

3. Click Run. You should see a window displaying the Normal and

Logarithmic descriptive stats showing T Fe. Click Next to review the SIO2 stats.

4. Click Close to exit. You can right-click on the Output File: DESCRIP IRON.REP to view the file. Copy and paste to you Resource document and then

Close.

5. Select Stats | Distribution with:

Prompt Setting

File IRON ASSAY

Type DATA

Graph field T FE

Graph type HISTOGRAM

Values used NORMAL

6. Numeric Exceptions are all set.

7. Graph Limits are set to:

Prompt Setting

Graph min 0

Bin Size 1

Graph max 71

Graph increment 10



Notes:

8. Graph Options are:

9. Click OK and you should see the histogram graph below:

The histogram of the exhaustive (total) iron population shows a very strong normal distribution suitable for Inverse Distance Weighting or Ordinary Kriging

interpolation, which will be explored in later lessons.



Notes:

11. From the menu, select Mode to change the Graph type to CUM FREQUENCY to display the following cumulative frequency graph:

The cumulative frequency curve shows the frequency of grades at varying grade cut-offs.

12. Change the Graph type again to PROBABLITY PLOT for this graph:

With the probability plot set Normal, the major inflection point around a grade of 10% indicates the change from background to the mineralised grades.



Notes:

13. Change the Values used to NATURAL LOG.

When the probability plot is set to natural log and the population plots as a

straight line then the distribution is normal, this is the case for the iron population.



Notes:

Lesson Summary

This lesson has introduced the concepts of:

Descriptive stats

Histograms

Cumulative frequency graphs

Probability plots

Natural Log scales

To create these outputs and graphs, we used Stats | Descriptive and Stats | Distribution.

Good Practice

Keep saving your outputs into a document or folder so that you can build a resource estimation report as you work through the process. This will be easier

while you have the data fresh in your mind.

Label everything carefully so that it will be easy to understand what it is in a months time or to a third party reader.

Help Topics


Descriptive stats Descriptive stats

Distribution stats Distribution stats



Notes:

Lesson 3 Generate Downhole Coordinates Prior to interpolation, the assay data file should be desurveyed (i.e. 3D co-ordinates should be calculated for the centroid of each sample interval) using

Dhole | Generate | Downhole Coordinates.

All geological domains and mineralised envelopes (or seams) can be interpreted

interactively on screen using Strings or Outlines in VizEx. These Strings or Outlines are used to generate solid wireframes; Strings are generally used to

create surfaces or DTMs such as weathering surfaces.

When all strings or outlines have been generated, they should be loaded into the 3D Viewer and checked for potential errors (missing interpreted sections or

drillholes etc).

Interpretation can take from 1 to 2 days, to several weeks depending on the complexity of deposit, necessity to interpret geology, domains and multiple

elements.

Internal dilution can also be automatically integrated into the interpretation process. MICROMINE can use Dhole | Compositing | Grade to set a trigger grade at which compositing occurs in conjunction with various settings for internal dilution, minimum grade, minimum and maximum waste intervals. Once the settings are enabled then a new grade composite file incorporating the internal dilution can be produced. The new file is then set up in section and the interpretation is performed on this file instead of the assay file.

Exercise 22.2 Generate Downhole Coordinates

1. From the menu, select Dhole | Generate | Downhole Coordinates and

fill in as below:



Notes:

2. The Collar/survey File More button needs to be filled in as follows:

3. You will need to write in new field names for the new Interval file fields (East, North and RL):

4. Close the Collar/Survey Setup form and Run.

5. Examine the modified Interval File by right-clicking on it.

If you are using the Drillhole Database option on the 3D Coordinates form, you can just tick the Create new Coordinate fields tickbox and the new fields in the Interval file will be generated in accordance with you Form Options under Options | Forms.



Notes:

Wireframing The geological model is an attempt to model by wireframing the mineralisation in

the ground, there are no economic decisions at this stage, it is a mineralisation model.

Wireframing was covered in a previous section of the training.

At the completion of the wireframing, assign the wireframe to the assay file to allow the wireframed mineralised data to be segregated from the unmineralised data outside of the wireframe. The finished wireframe is Iron.tdb. A tdb file is a

database file and is short for triangle database. Use Iron.tdb for all work.



Notes:

Lesson Summary

This lesson has introduced the concepts of

Wireframing

Good Practice

Checklist

All sections are interpreted for mineralised zones and/or geology;

All Strings/Outlines are snapped to drillhole intervals;

Interpretation is visually checked in 3D.

Help Topics




Notes:

Lesson 4: Assay Data Flagging

FLAGGING/SELECTION When all the wireframes are generated, they should be used to code the assay

database in order to select the part of the database to be used for geostatistics and grade interpolation. If the wireframing stage was not required, the

interpreted outlines can also be used to flag the Assay database. Prior to flagging, additional fields should be generated in the files where the flags will be

recorded. The Assay file should be de-surveyed. By this method the assay file will be coded for those intervals inside the wireframe and those outside of the

wireframe, and then a filter can be applied to consider grades only in the

wireframe.

Flagging using Solid wireframes

If solid wireframes are used to flag assays (or points), this should be done using

Modelling | Assign |Wireframes. There is no necessity to use the sub blocking option; because we are flagging assay data and sub blocking factors are

not required. If there are several overlapping solid wireframes, the flagging process should be run several times using the solids in the required order or

recording flags into different fields.

Flagging using DTMs

DTMs can be used to flag any point data (e.g. samples) for their location below,

above and outside of the DTM using process Strings | DTM | Assign. It is always a good practice to avoid absent values in numeric fields if possible.

Therefore, it is recommended to use all three options in the process and to generate flag values for the point data below, above and outside of the DTM

(e.g. generate values 1, 2 and 3). Make sure the DTM covers all samples. A grid

file can be generated and converted to a DTM to get sufficient coverage.



Notes:

Exercise 22.3 Flagging using solid wireframe

1. 6HOHFWModelling | Assign |Wireframes and fill in as below:

2. We will not use a Block Model here so select Point Data.

3. The Input file will be IRON ASSAY.DAT. Once it is selected, you will need to

right-click on the filename and select Modify. You will need to insert a new Field after SiO2. The Field Name is WFcode, Type C (Character) and Width 5. You do

not need to give decimals as this will default to 0.

4. The Wiretrame will be selected from the IRON.TDB for the Type and the orebody Name is also iron.

5. Under Attributes to Assign you can tick Clear target field and Overwrite target field. Click the More button.and fill in (by double-clicking) as below:

6. Create a Report file name, eg WFassign.

7. Click Run.

8. Right-click the Report file to show 3933 records were updated.

9. Check the Input file (IRON ASSAY) by right-clicking.



Notes:

Lesson Summary


Good Practice

The flagged samples are displayed in 3D and checked visually

It is a good practice not to have absent values (blanks) for flags

DTMs cover all samples involved in the resource estimation

Help Topics


M M



Notes:

Lesson 5 Balancing Cut The balancing cut is used for block models produced using a linear estimation method such as Inverse distance weighting or ordinary kriging. A balancing cut

is the use of a more conservative grade instead of a few higher grades in the interpolation process. A balancing cut is determined by using a Cumulative

Frequency plot for the mineralized grades only, mineralised grades are those inside the wireframe. At the grade where 97.5 percent of the grades occur, read

from the cumulative frequency curve, is the grade to be used for the balancing cut.

Exercise 22.4 Balancing Cut

1. Select Stats | Distribution with:

Prompt Setting

File ASSAY IRON

Type DATA

Filter Selected

WFCODE = 1 numeric

Graph field T FE

Graph type HISTOGRAM

Values used NORMAL

2. Save your Filter as Mineralisation.

3. In the plotted example the grade at which 97.5 percent of the population

occurs is 65.



Notes:

4. Select Fields | Calculate with the following settings:

Prompt Setting

File IRON ASSAY

Type DATA

Filter Selected

Mineralisation

5. Right-click on IRON ASSAY and select Modify.

6. Insert a new row before T Fe:

Prompt Setting

Field TFe Cut 65

Type N

Width 5

Decimals 2

7. Close and Save.

8. Fill the table on the right hand side:

Prompt Setting

Input T Fe

Function Cut highs to

Input 65

Result TFe Cut 65

9. Click Run.

10. Right-click IRON ASSAY and you can check that rows 11 and 12 have been reduced down to 65.

The cut grades will be used for the interpolation process and for reports on the resource and the reserve.

The 97.5 percent figure is a western standard discovered from the modelling of many projects, generally the grade at 97.5 percent is sufficient to reduce the influence of the high grades in the estimation avoiding sections of the model biasing the overall result too high. A balancing cut is required because if another hole was drilled down beside the high grade samples it is quite likely that a much lower sample grade will be returned, this is the nugget effect, and as such the model must be more conservative for very high grades.



Notes:

Lesson Summary

This lesson covered the concepts of :

Cumulative Frequencies for just the minerealisation.

Applying a cut to the data

Good Practice

Help Topics


Fields Calculate Core | Files | Fields | Calculate



Notes:

Lesson 6 - Compositing When deciding upon interval length, if the composite length is not obvious, a histogram should be produced for the Assay file, it should be calculated in File |

Fields | Calculate by subtracting FROM from TO. Then run the process Stats | Distribution for the INTERVAL field, study the obtained histogram and

make a decision on the composite length. Produce the balancing cut prior to compositing.

Samples can be composite using Dhole | Compositing | Downhole process. Set up sample composite length equal to average sample interval length. Avoid mixing of samples from different populations or geological domains when

composites are generated. It can be achieved by applying filters and then

appending the result files together.

Generally wireframes will be assigned to the assay file before compositing, if so then use the wireframe assign field as the Constant field in the compositing

routine.

CHECKLIST:

Run stats and make sure there are no strange composite interval

lengths Use weighted average method for compositing

Run compositing separately for each domain

Set up minimum composite length (usually equal to the half of the

composite length) Use numeric exceptions if there are any character values in numeric

fields

Exercise 22.5 Compositing

1. We already have interval lengths in the field INT. Determine the most

frequent sample interval to composite to for the iron data. Plot the interval size

on the histogram as follows



Notes:

2. The image below should be produced.

Clearly a two metre interval should be used for the composite length, by using two metres most assays will remain unaltered for the estimation but ultimately all will be of equal length.

3. Select Dhole | Compositing | Downhole and fill in as below (Output File is IRON ASSAY COMP1):

There will be errors reported but they are only where there are breaks in mineralisation within a given drillhole. The first item in the report file rep will be in hole CK2 at a depth of 326.3m. This is the start of the second mineralisation

in that drillhole.

Where the last interval of the mineralisation is less than 2 metres, the same TO

value is used and the actual interval is written in.



Notes:

4. Intervals (INT) in uncomposited IRON ASSAY.DAT file vary. The image below has less relevant fields hidden.

5. Recalculate your intervals by right-clicking on IRON ASSAY COMP1 and

selecting Edit, then select Calculations from the toolbar.

Prompt Setting

Input TO

Function Minus

Input From

Result INT

Clear result field Selected

Overwrite result field Selected

6. The composited IRON ASSAY COMP1.DAT file has 2 metres intervals and values for the mineralisation only (again some fields are hidden). This file is

then used for all further interpolation.



Notes:

Lesson Summary


Compositing the mineralisation

Good Practice

Help Topics




Notes:

Lesson 7 - Geostatistics

Theory Classical statistical analysis should be repeated using the same procedures described in the Lesson 2. However, this classical stats analysis will have the

following differences: The analysis will be run for sample composites

Only flagged composites will be used for the analysis, those assays inside the wireframe

Stats will be run for each geological / lithological / structural / mineralogical domain separately

Final decisions will be made regarding the method of grade interpolation,

variography, mixing of population and top cuts. Mixing of grade populations within each domain should be carefully considered using the same process

described in Lesson 2. If it is not possible to separate grade populations using domaining, then the MIK grade interpolation method should be used.

Variography

Variography will be run for each element and domain separately. For every domain there are three variograms, each at right angles to each other. For

example, if we have three elements and five domains, the task will be to generate 45 directional variograms. If MIK is applied, then the number of final

variograms will be 450 (if 10 thresholds are used).

The first step would be to generate omni variograms. Omni variograms will indicate the general ranges and variances of grade populations and whether the

chances of getting good directional variograms are good or bad. They also assist

with the lag sizes. Variograms are to be generated using the process Stats | Semi Variograms.

The second step would be to identify the main axis of directional anisotropy if

any. If omni variograms are reasonable, a rosette of horizontal directional variograms should be generated. Ideally, a variogram map should also be

generated which will clearly show the minimum and maximum ranges and directional anisotropy of grade distribution.

A direction of maximum continuity should be identified from the horizontal variogram rosette. That will be the azimuth of the main axis. Then a rosette of vertical variograms should be generated with the azimuth of dipping equal to the

azimuth of the longest continuity of horizontal variograms. A variogram with

longest ranges will show the angle of dipping of the main axis of directional anisotropy.

Downhole variograms are to be used to model nugget effect.

Once the azimuth and dipping of the main axis of directional anisotropy is

identified, three variograms are to be generated and modelled. The first variogram will be in the direction of the main axis, the second one



Notes:

perpendicular to the first variogram, and the third one perpendicular to the first two variograms.

If geology and mineralisation are well studied and interpreted, sometimes the main directions of directional anisotropy are obvious and the above steps could

be simplified or skipped. The directional variograms are to be displayed and modelled in Stats | Semi Variograms. It would be a good practice to

generate Direct, Log and Relative semi variograms to obtain the main features.

When experimental variograms are displayed on screen, they can be modelled using the Model menu. Select the variogram type (e.g. Model | New |

Spherical). Then you will be prompted for the number of structures. Select the number of structures (for example 2). Then you will be able to model the

nugget effect and sills of every structure using the mouse. When you specify the

model parameters with the mouse, MICROMINE will display the modelled variogram parameters. Please note that Sill parameters there are actually C

values. Sill values will have to be calculated (Sill = C partial sill + Nugget).

All modelled variogram parameters should be saved to a Form.

Variography can take from several days to several weeks depending on the number of elements, domains and selected interpolation method. If MIK is

selected, the exercise could be very time consuming due to the large number of variograms to be modelled.

CHECKLIST:

Note the Sill in MICROMINE is actually, the partial sill. Use downhole variograms (or vertical) to estimate nugget effect

Make sure all 3 variograms have the same nugget, C value and total

sill

Handle zonal anisotropy (if any) by adding another structure to

variograms

Variogram properties

Nugget co

gamma

Sill co + c

Range m



Notes:

Anisotropy

There are two types of anisotropy:

1. Zonal. The sills and the ranges are different in the three directions. If this occurs two structures must be used with a second long range to

get the sills back to the same level at a very large range, such as 10,000 metres

2. Geometric. The sills are the same but the ranges are different for the three directions

Semi variogram formula

The semi variogram and variogram is basically the same thing, technically they are different as the semi variogram is divided by two.

Algorithm as follows, semi variogram

( ) ( ) ( )( ) 2

121

=

=

hN

iii yxhN

h

Once the semi variogram has been displayed then a model must be fitted to the

gamma values.

Semi variogram model formula

The rule of thumb is that a spherical model is fitted to most gold data; in some circumstances an exponential model may be used.

3D modelling requires three variograms orthogonal to each other, the nuggets

should be the same and the partial sills must be the same, the ranges can differ for each direction

The nugget is best determined from the downhole data as the data is the most closely spaced, the lag can be determined from the omnidirectional variogram which is an average of the lag spacing.

Fitting the variogram model is done interactively, the Noel Cressie statistic can show the quality of the fit using a least squares regression, however the best

guide is a visual fit of the line to the gamma values.

The smaller the Noel Cressie statistic then the better the variogram model fit, theoretically. However in practice the first and second gamma values greatly

influence this result. Use the visual fit in conjunction with the test button.

Ordinary kriging requires the data to resemble a normal population. If there are mixed populations (this is apparent on the histogram and probability plot) then a

method such as multiple indicator kriging must be used.

The variograms are saved together in a form that retains the model parameters and the attitude; azimuth and plunge of the variogram. The weighting is then

performed automatically within the ordinary kriging routine.



Notes:

Search ellipsoid parameters

The parameters entered here define a search ellipse used to select samples for

modelling. That is, the samples that will be used to calculate the estimated value.

Radius - Enter the primary radius of the search ellipse. This value is a length or

distance that becomes the base value by which the three factors below are multiplied to determine the dimensions of the search ellipse.

Azim (deg)

Enter the Azimuth (bearing in degrees) of the long axis of the search ellipse. This

has a range of values 0 - 360 measured clockwise from north = zero. It corresponds to geological strike, or the trend of the long axis of a plunging body.

Azim factor

Enter the factor for the length of the long axis of the ellipse. This will be

multiplied by the Radius to determine the actual length of the Azimuth axis.

The Azimuth factor is generally the longest dimension of the search ellipse. Commonly the Radius is set equal to the along-strike search, typically 1.25 to 1.5

times the average section spacing, and the azimuth factor set to 1. The other two factors would then be defined as decimal values between zero and one.

Plunge (deg)

The plunge is the downward inclination of the orebody along the strike. It must

be positive; plunge values are always in the range 0 - 90.

For example, a tabular structure with Azimuth 30 degrees and a Dip of 60 degrees to the South-East will have Azim = 30 and Dip = -60. If the plane



Notes:

contains a tubular or elliptical structure that plunges downward at 30 degrees to the north-east then the value required is Plunge = 30.

If the same tabular structure has a tubular or elliptical structure that plunges downward at 30 degrees to the south-west then the value required is still Plunge

= 30 but the Azim must be 210 and the Dip required is 60.

Thick factor

This describes the thickness component of the search ellipsoid. Enter a factor for the length of the search axis perpendicular to the plane of the Azimuth and Dip

values. This value is multiplied by the Radius value to determine the actual length of the Thickness search axis. The thickness factor usually describes the

short axis of the search ellipsoid.

Dip (+/- deg)

Dip is an angle, with range -90 to 90 measured from the horizontal, perpendicular to the azimuth axis. It corresponds to geological dip. The

convention used throughout MICROMINE is that clockwise rotation, looking in the Azimuth direction, has negative dip values and counterclockwise rotation has

positive dips. Thus a bed striking at zero degrees and dipping 60 degrees east will have a Dip angle of -60.

Dip factor

Enter a factor for the length of the dip axis of the ellipse. This value is multiplied by the Radius value to determine the actual length of the Dip axis search. This is the down dip search dimension of the search ellipsoid.



Notes:

Practice Iron deposit (3d): The iron deposit will be modelled using ordinary kriging and

median indicator kriging. The iron deposit is a good example because it has an excellent linear population and produced strong variogram models with

geometric anisotropy.

Files:

Collar: IRON COLLAR.DAT

Survey: IRON SURVEY.DAT Assay: IRON ASSAY.DAT

Assay: IRON ASSAY COMP.DAT Wireframe: IRON.TDB

Review

After the 3d coordinates were created for the assay file, the wireframe was assigned to the assay file. This ensures we know which grades are the relevant

mineralised grades and which grades fall outside the wireframe and are

redundant. This file has already been produced and is IRON ASSAY.DAT; the code field should be WFCODE with the code iron. A 2 metre composite file was

also created called IRON ASSAY COMP.DAT.

Nugget

The IRON ASSAY.DAT file is now used to calculate the variograms and so, to create the variogram models. Do not use the composite file at this stage

because it may inadvertently display zonal anisotropy because compositing

smooths the data in the file and will change the variance to a greater degree in one direction than another. The composite file is only used for the interpolation.

Exercise 22.6 Nugget

1. Open the semi variogram form by selecting Stats | Semi variograms.



Notes:

2. The Semi Variogram Type will be Downhole in this instance.

3. Select the IRON ASSAY.DAT as the Raw Data file. We initially have to create a semi variogram file from a raw data file. Later these semi variogram

files can be re-used by clicking the second option.

4. Apply a filter to the Raw Data file in order to only use data inside the wireframe. Make sure you save this filter using Forms | Save as.

5. Select Show Variance under Data Values and complete the form as

shown below:

6. Under Semi Variograms, select Show semi variograms and Write semi variograms to file. The name of the File will be Vario DH of Type DATA.

7. You will of course have set Numeric Exceptions and then saved the form using the Forms button (third from left on the Toolbar) as Downhole Nugget.

8. This will display a Downhole variogram to determine the nugget size.

9. This gives a Nugget Coefficient established at about 50.



Notes:

Using Semi Variograms

When you create a semi variogram, you will notice that the menu at the top of

the screen changes. The two menu items of particular interest are Display and Variogram.

The menu items with icons are available from the Semi Variogram Toolbar. The ones that are probably used the most under Display menu are:

Form you should always save your forms so that you can easily reproduce a result.

Dump creates a screen shot of the active window that you can paste into a report that you might be generating as you work.

Zoom + Area allows you to zoom into the area of interest. The relevant scale will also be shown automatically.

Display Mode takes you to the variogram parameters page where you can make changes or check entry details.

Show Together if you have more than one set of parameters, all of them can be shown on the screen at the same time. This is an alternative to leafing

throught them by using the Page Up and Page Down keys on your keyboard.

When using Show Together, you might want to use Display Mode first and change the Display Mode of some of the less likely candidates to None. This will

simplify the display and let you focus on the more likely candidates.

All of the items under the Variogram menu are of use:

Previous lets you leaf back through individual variograms. This can be done more easily by using the Page Up key on the keyboard.

Next lets you leaf forward through individual variograms. This can be done

more easily by using the Page Down key on the keyboard.

Model lets you model a curve through the points to represent a best fit representation of an ideal curve.



Notes:

Optimum Lag

Determine the optimum lag size by using an omni directional variogram with

various lag sizes. The omni directional variogram displays the average of lags. We will use the composited data found in the IRON ASSAY COMP.DAT file.

For this iron example, lags of 50 to 60 metres produce well behaved variogram results. This distance can now be used to find the direction of maximum

continuity.

Exercise 22.7 Omni Variogram


2. The Semi Variogram Type will be Omnidirectional.

3. Select the IRON ASSAY COMP.DAT as the Raw Data File. Keep the filter WFcode = iron and select TFECUT65 as the Semi variogram field.



Notes:

4. Select Show Variance under Data Values, click the Omnidirectional Semi Variograms button and complete the form as shown below:

5. Save the above form as Optimal Lag Omni Comp.

6. Under Semi Variograms, select Show semi variograms and Write semi

variograms to file. The name of the File will be Var Omni Comp of Type DATA.

7. Save the main form also as Optimal Lag Omni Comp.

8. These will display Semi Variograms. To leaf through the displays, use the Page Up and Page Down buttons on your keyboard. It is advisable to zoom in to

the left-hand side using the magnifying glass with the square inside it from the toolbar

9. The screenshot below shows the orange 60_50 values. This gives a

reasonable fit.



Notes:

10. We should now repeat the search with a tighter range of say 35 to 75, or even tighter.

We will use a value of 50 for our lag or interval for now. The next step is to discover the direction of maximum continuity. This will have the longest total

range. Set the variogram fan for 30 degree increments for 180 degrees, it is not necessary to do 360 degrees as one half is the mirror of the other. Set the

tolerance to 15 degrees so they do not overlap and apply a conical search. The geology is often a very good guide to the direction of maximum continuity.

The Mode button applies the value in the first row to all other valid rows. The display modes you can choose from are:

None: The data for that azimuth will not be displayed. Useful when you want to

switch a direction off temporarily to simplify the display. Line: Data for the azimuth will be plotted as a simple line graph. You can enter

a symbol number when LINE is selected. The corresponding symbol will appear at each interval distance. Its size will vary proportionally to the

number of pairs in that interval.

Graph: The data will be displayed as a graph with two lines. The area between the lines can be hatched. To generate the lines, alternate values from

interval one to the maximum calculated distance interval are connected. The intervening values are then connected back to the first interval value.

This displays the difference between values in adjacent intervals (but loses information on the number of pairs in each interval).

Symbol: The interval semi-variogram value for the azimuth will appear as a

symbol. The symbol size is relative to the number of pairs in the interval. Pairs: The Pairs display option displays a fixed size symbol with the number of

pairs written beside the symbol.

Exercise 22.8 Horizontal Fan Variogram

1. We will use the Semi Variograms form again. The Semi Variogram

Type will be Directional.



Notes:

2. Change the Semi Variograms File to Var Horiz Comp. The rest of the form stays unchanged.

3. You will notice that the button under Data Values has changed to Semi Variograms Directions. Click this and complete the form as shown below:

4. Save the above form as Horizontal Fan.

5. Notice that we are using the Display Mode of Lines. Lines are easier to

read than Pairs but there is much more information in Pairs.

6. Save the main form also as Horizontal Fan.

7. Again leaf through the displays using the Page Up and Page Down buttons on your keyboard. It is advisable to zoom in to the left-hand side using the

magnifying glass with the square inside it from the toolbar.

8. Your graphs should show that the best fit will be between 35 and 55 degrees for the Azimuth. The screenshot below comes from a second run from 35 to

55. Blue 39 was slightly better than Pink 41. We will use 40.



Notes:

Exercise 22.9 Vertical Fan Variogram


2. The Semi Variogram Type will again be Directional.

3. Change the Semi Variograms File to Var Vert Comp. The rest of the form stays unchanged.

4. Click the Semi Variograms Directions button and complete the form as shown below:

5. Save the above form as Vertical Fan.

6. Save the main form also as Vertical Fan.

7. Click Run to display the variograms as shown below.



Notes:

8. Again leaf through the displays using the Page Up and Page Down buttons on your keyboard. It is still advisable to zoom in to the left-hand side using the

magnifying glass with the square inside it from the toolbar.

9. Your graphs should show that the best fit will be -6.

Omni directional variogram to determine optimum lag:

The setup for defining the Omni directional variogram;



Notes:

The display of the Omni directional variograms;

Directional variogram, main:

Step 4:

Finding the principle direction;

Defining the settings to narrow down the principle direction variogram;



Notes:

Display of the variograms for the principle direction;

Direction of maximum continuity, primary variogram;

Step 5: Directions of maximum continuity; once the approximate direction of maximum continuity is known from step 4, then the lag can be experimented

with and then the exact direction of maximum continuity in terms of azimuth and

plunge can be investigated and modelled.



Notes:

Clearly the lag of 50 or 60 metres and a zero degree plunge produce the best

behaved semi variograms. The variograms have a good regular pattern, sill out close to the variance and do not have a saw toothed appearance.

Model the variograms:

Step 6: The azimuth is 142 degrees, the lag 50 and the plunge zero. Then fit a spherical model to the gamma values on the variogram. Retain the same nugget as the downhole, vertical variogram with the same partial sills, one and two

retained for all three orthogonal variograms.

Principal direction: 142 degrees azimuth;



Notes:

Principal direction: 142 degrees azimuth, fitted model;

Intermediate: Directional variogram 232 degrees azimuth;



Notes:

Intermediate: Directional variogram 232 degrees azimuth, fitted model;

3rd direction: 180 degrees azimuth, 90 degrees dip;



Notes:

3rd direction: 180 degrees azimuth, 90 degrees dip, fitted model;

These are the required variogram models for Ordinary kriging or to establish the search ellipse dimensions for Inverse distance weighting.

Indicator variograms:

Only use indicator variograms if you intend to interpolate using a non linear

model method such as median or multiple indicator kriging.

For median indicator kriging determine the median of the grades inside the wireframe by plotting the cumulative frequency curve of the data. The also find

the grade ranges at 10 percent, 20 percent etc up to 90 percent. These grade cut-offs will be used for the bins in the median indicator kriging routine and the

50th percentile or median will also be used at the cut-off grade in the indicator

variogram modelling procedure.



Notes:

Grade thresholds for the bins:

% of data Fe %

10 26.3

20 29

30 33.8

40 37.6

50 42

60 46.8

70 51.8

80 56.9

90 61.1



Notes:

The median occurs at a cut-off grade of 42% Fe; use this cut-off grade for the indicator variograms. Use the same procedure as for semi variograms to find the

direction of maximum continuity, the intermediate variogram and the third

direction. Note the nugget and partial sill must still be the same for all three indicator variograms.



Notes:

Once the three indicator variograms are modelled then go to Modelling | 3d block estimate | multiple indicator kriging and save the indicator variogram form,

this should be used in the cut-off box.



Notes:

Relative variograms:

If the model area exhibits proportional effect, where the mean and variance change in proportion to each other across the model area then a relative

variogram must be used to ensure the sills of the lags are all at the same level so

the variograms appear sensible and will allow the fitting of a variogram model. A test for proportional effect can be conducted by using modelling | 3d block

estimate | statistical.

Display the result in Stats | scattergrams | simple linear, plotting the mean on one axis versus the standard deviation on the other axis.

If the result plots as close to a straight line then a proportional effect is present,

if the cloud is wide as is the case with the iron example then no proportional effect exists and relative variograms are not required.



Notes:

To produce an ordinary kriged model using relative variograms the variograms

will be modelled using the relative gamma values. When the normal direct variograms are modelled the relative gamma value is also stored inside the file.

Use the relative gamma values for the 142, 232 and vertical normal direct variogram output files by selecting display relative variogram from file. Then fit a

model and save the form for all three relative variograms.



Notes:



Notes:

Cross Validation:

Cross validation is conducted by removing a raw data value and using the surrounding raw data values to estimate the removed value. The value is then compared to the estimate and is repeated throughout the dataset. The total

average estimates are compared to the actual estimates; if the variogram model

is robust the figures should be very close.



Notes:

The average error statistic should be close to zero and the standard deviation of

the error statistic close to one.

The results of the iron estimation by cross validation were 8.0575 for the standard error and -0.005125 for the error statistic. The standard error is a little

high and could be improved but the error statistic is close to zero and is a good result.



Notes:

Actual versus estimated values can be plotted on a scattergram to see how well the kriging process reproduces the sample data. Actual value versus the error

statistic demonstrates the conditional bias

The Means are very close so the global cross validation is good, the precision is

19%, and the result was influenced by some low grades that did not produce a low estimate because of the amount of data found by the search ellipse. The

cross validation is reasonable for the direct variograms to be used for ordinary kriging.



Notes:

Lesson Summary


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Notes:

Lesson 8 Empty Cell Model Grades can also be interpolated into an empty cell block model generated (or imported) earlier.

Block Model Cell Size Model cell size should be selected depending on the following parameters:

Drilling density

Variability of grade

Smallest mining unit SMU

Final model sizeThe cell size should be sized to be small enough to produce a grade map for

grade distribution and big enough that it reflects available data.

When block model cell size is selected and the extent of model is calculated, an empty cell block model should be generated using Modelling| 3D Block | blank

block model. The block sizes should be saved in a form and restrict to wireframe option should be used to save only the blocks in the mineralisation.

Flagging

If wireframe solids and DTMs are modelled, then they should be used to flag the block model. Basically, flagging should be carried out the same way as

described in the section 6. The only difference would be if sub blocking is required.

When the block model is flagged for all possible domains / zones / ore bodies

etc, all other cells (unflagged) should be deleted from the model to reduce the size of the file and number of records (File | Filter | Subset). That will also help

to control the interpolation process.

The process should not take more than several hours.

Checklist

The model should not have too many cells. An average block model has

several hundreds of thousands cells. Generate sub blocks to represent volume more accurately.

Generate as many new fields for flags, as there are wireframe/string/outline

types that are used for flagging. It is easy to combine them later, if

necessary.



Notes:

How to decide the block size

The block size of 10 metres east, 20 metres north and 5 metres in rl is displayed at the centre of the search ellipse. This block size for iron estimation is

appropriate given the sample spacing of 100 metres. The blocks must reflect grade distribution, showing a local map of grade occurrence, so the block cannot

be too big as the grade change will not be shown and cannot be too small

because the file will be unnecessarily large and the grade estimate will become less reliable.

The block size for an iron deposit will be bigger than the block size for more

densely spaced shear hosted gold deposits or VMS hosted base metals because the samples are more closely spaced and the geology is far more variable.



Notes:

If the sample spacing for a gold deposit was 25m between sections, 10m between the drillholes along the section and 1m sample intervals then an

appropriate block size would be 5m by 2m by 2.5m in rl.

Subcelling

Subcelling is the creation of smaller blocks on the edge of the wireframe when

the parent cell is not fully inside the wireframe. The numbers entered into the sub block boxes are how much the parent cell is divided by to define the subcell

in metres. If the parent cell is 10 metres in east and the sub blocks east is entered as 5 then the subcells will be 2 metres in the easterly direction. A sub

block factor is different, the cells are not subblocked, rather a number between

zero and one is defined for the percentage of the block inside the wireframe.



Notes:

Exercise 22.12 Creating a Blank Block Model

1. We know we are going to be asked for the extents of the Iron wireframe, so firstly open that in Vizex in Plan view. Jot down values to encompass the

wireframe in Eastings and Northings. You should have jotted down something like: 19000mE-19900mE and 35000mN-36500mN.

2. Switch to Looking North view and note the RLs as well. You should have something like -650mRL-0mRL.

3. Select Modelling | 3D Block Estimate | Blank Block Model and fill in as below. The Output entries are all typed in as we are creating a new file.

4. Under Restrictions | Wireframes click on the More button. Fill in the details as shown below. Again, the Block Factor Field is going to be created

and the Sub-block values represent the number of times you want the block sub-divided not the size to which you want it sub-divided.

5. Close the Restrict With Wireframes form.



Notes:

6. Click on the Block Definitions button. This is where we use the values that we jotted down earlier.

7. Enter the values but notice that you are asked for the Block Centre. To

accommodate this and keep our blocks on round number co-ordinates, add half the relevant block size (Spacing) to each Origin Block Centre and subtract

half the relevant block size from each End Block Centre.

8. Select Forms | Save As and save the form for later use as Iron OBM.

9. Close the Block Defintions form.

10. Select Forms | Save As and save the form as Iron OBM.

11. Click the Run button. This may take a couple of minutes and progress is

shown in the bottom left of the screen.

12. Right-click on Iron OBM in the Output File box and firstly select Min/Max. You will notice various details including the creation of about

110,000 records and that the data does not start until 19025mE.

13. Right-click on Iron OBM a second time and select view. Notice that the BF field stores a value between 0 and 1 representing the number of virtual sub-

blocks inside the wireframe as a fraction.



Notes:

Lesson Summary


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Notes:

Lesson 9 Modelling Principles Declustering

If samples are clustered then the samples must be declustered to allow a fair estimation of the unknown value in the search ellipse. Declustering is required to

minimise interpolation bias from high-density assay areas, which often occur in high-grade zones. If data is not declustered the clustered data has an undue

overwhelming influence in the grade interpolation on the surrounding area. If a large number of raw data values are picked up by the search ellipse from one

area then these points will preferentially ensure that this area weights the

interpolation of the point of estimation more so than the scattered data points.

Sectors or cells can be employed to decluster the data, a maximum and minimum number of points can be stipulated for each sector.

MICROMINE currently employs a sector method in some model modules to

subdivide the search ellipse and allow the thinning of the number of points to be interpolated by specifying the maximum number of points allowed within the

sector.



Notes:

Specific gravity and block size

Block size is determined by drill spacing and the smallest mining unit required for

the resource, the SMU. The SMU is often suggested by the mining engineer, even at the stage of resource estimation. Specific gravity can be defaulted or

interpolated for the blocks.

Change of Support

Discretisation is where ordinary kriging in this case estimates point grades inside

the block which are then averaged to produce the block grade. Block kriging was designed to combat the change of support, where the grade of a truck load of

ore is more even and reliable compared to the grade of a far smaller often more variable sample. Block kriging is now not considered the best method of dealing

with the change of support but there are few practical alternatives.

Proportional effect

When the local variability of data changes across the model area this is known as

heteroscedasticity, the proportional effect is a form of this. For the positively skewed distributions the local variance increases with the local mean. The

proportional effect is detected from a scatterplot of the local mean versus the variance-calculated from moving window statistics. The proportional effect can

be calculated in Micromine by using the Modelling | 3d | statistical, defining a block size and writing a file containing the local mean and variance.

Proportional effect will render the sample semi variogram uninterpretable. Clustering combined with the proportional effect results in the high clustered

values contributing to the lower lags. The corresponding lag mean is large and because of the proportional effect the lag variance is also large. As distance (h)

increases the data that contributes to the lag becomes more representative, the



Notes:

lag mean and variance decrease. The trend results in the lag variance results in overestimation of the semi variogram value at short range and also the relative

nugget effect. An inaccurate variogram model generates inaccurate weighting. A

relative variogram is required as opposed to a traditional variogram. The relative variogram is standardised by the gamma value divided by the lag variance.

Interpolate parent blocks only

If parent cells only are interpolated then it means that if the parent block was

divided into subcells because it was on the wireframe border, then the subcells will be assigned the grade estimate for the parent cell and they will not be

independently estimated.

Multiple runs

Often when the blank model is created and interpolated into the first search ellipse size is not sufficiently large enough to populate all blocks. When the name

of the block model file is the same for Define blocks from file and the output

block model file then the grades will be written into the blank model. Note that the input field name, width, type and decimals must be the same in the input file

as the define blocks from file data file. If they are different then a result will not be written. After the first run with the first search ellipse then increase the

search ellipse size for run 2 and possibly run 3 until all blocks been populated

with an estimated value.



Notes:

Lesson Summary


Good Practice

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Notes:

Lesson 10 Grade Interpolation

INTERPOLATION The block model is generated simultaneously with interpolation of grades. This means the following routine should be used:

1. Specify all input parameters, files, search ellipse and variogram parameters in the processes Modelling | 3D Block Estimate | IDW or Modelling |

Kriging. Run the interpolation. 2. The generated block model should now be flagged for domains etc. using

wireframes or outlines (as specified in chapter 8).

All unflagged cells (above the surface, outside of wireframes etc.) should be filtered out (File | Filter | Subset). All the assigned cells should be checked for whether all cells are populated with grades or not (Stats or Min/Max).There should be no missing grades in the block model.5. If not all cells are all populated, then repeat the steps from 1 to 4 with

altered (increased) search parameters until all cells are informed with grades. Generate a Run Number field in the output model file. You will have several

saved search ellipses that increase in size, each one represents a grade interpolation run.

6. Add all the generated models together in such a way, that earlier models would update the later ones (File | Merge | MM).

7. Repeat all steps from 1 to 6 for all domains and for all elements.

The interpolation process can take from several hours to several days.

CHECKLIST:

Apply top cuts if necessary

Interpolate grades using several methods for validation

All cells in the Resource model should be informed with grades.

If Kriging was used, run cross validation to check if the variogram is

appropriate. Run the variogram model that produces a good estimate with

the lowest kriging error.

If MIK is used, make sure the search parameters are the same for all bins

for a particular interpolation run

The number of interpolation runs should be equal minimum to: No of

elements x No of domains x No of interpolation volumes x No of

interpolation methods. It is a good idea to save all these runs in a macro.



Notes:

Search ellipse

When defining the search ellipse in MICROMINE

Define the number of sectors, if there is a large amount of data, then eight or sixteen is an appropriate number of sectors to employ.

Define the maximum and minimum number of points to be used in the search ellipse, a maximum of 6 means a total number of six per sector will

be used, the six nearest samples to the point of estimation will be used for the estimate; the other points in the sector will not be used. With the

minimum set to 2, if only one sample is found then the point of estimation

will not be estimated. This is data declustering performed on the fly by MICROMINE in the estimation process.

Define the attitude of the search ellipse, the azimuth, dip and plunge. This

should be defined to include the relevant samples for estimation and to

exclude the redundant points. Several different search ellipses of increasing sizes may be required to interpolate all of the blocks in the

model. Often three runs may be needed to populate the model, the search ellipse will be increased in radius with each run, the blocks that have

already been estimated will not be overwritten, only empty blocks will be

populated by each new run.



Notes:

How to decide search ellipse size

The search ellipse radius is determined from the variogram parameters or from the sample spacing. For the iron example the radius of 250 metres above

contains around seven drillholes in the ellipse each with two metre interval samples, so there are abundant samples for the first pass estimation because the

drillholes are spaced around 100 metres apart.

Save the search ellipse forms. Load the search ellipse in 3D Viewer, bring up the grid and look from different angles with the ellipse transparency on to observe

that the attitude of the search ellipse is the required design. This is an important

validation step.



Notes:

Inverse Distance Weighting Inverse distance weighting uses the inverse of the dis

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22b Module 22 -- Resource Estimation -- Exercises

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