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Table of Contents

Introduction to Geostatistics

Section 1Statistics

Learning Outcome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Classical Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Statistics for Assay Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Statistics for Composite Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Statistics within Geology Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

Probability Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

In situ Data Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

Correlation and Scatter Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

Plot Proportional Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

Section 2Variograms

Learning Outcome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Geostatistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

The Variogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Variogram Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Calculating Variograms and Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Modeling Variograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211

Calculating Down-hole Variograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215

Variogram Data Contouring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220

Variogram Parameter File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225

Section 3Point Validation/Cross Validation (for variogram evaluation)Learning Outcome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Interpolation Controls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Point Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

Section 4Declustering


Declustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

Statistics for Assay Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

Histogram of Declustered Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

Section 5Model InterpolationLearning Outcome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

Types of Interpolations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

Interpolation Controls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

IDW Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52


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Advanced Geostatistics

Section 6Kriging


Orginary Kriging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

Kriging with MineSight

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

Section 7Point Validation/Cross Validation of Estimation Methods


Types of Point Interpolations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

Interpolation Controls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

Point Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

Section 8Model Statistics/Geologic Resources


Reserve Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

Model Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82Grade/Tonnage Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

Plot IDW and Histograms Together . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

Model Statistics At and Between Cutoffs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 810

Model Correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 814

Probability Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 818

Section 9Model Calculations


Model Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

Section 10Quantifying UncertaintyLearning Outcome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

Distance to the Closest Composites Calculations . . . . . . . . . . . . . . . . . . . . . . 101

Kriging Variance/RVI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

Combined Kriging Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

Section 11Change of Support

Learning Outcome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

Change of Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

Global Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

Kriges Relationship of Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

Calculation of Block Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

Change of Support on Composite Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

Distribution of Theoretical Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

Volume-Variance Correction on Composite Data . . . . . . . . . . . . . . . . . . . . . 1111

Volume Variance Correction on Model Data . . . . . . . . . . . . . . . . . . . . . . . . 1115


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Section 12Indicator Kriging to Define Geologic Boundary Above a Cutoff


IK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121Assign Indicators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

Variogram of Indicators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

Model the Indicator Variogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

Krige Indicators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

View Results in MineSight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1211

Section 13Multiple Indicator Kriging (M.I.K.)


M.I.K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

Uses of Indicators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

Incremental Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132Determine M.I.K. Cutoffs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

Statistics for M.I.K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

Calculating Indicator Variograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1312

Modeling Indicator Variograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1216

Variogram Parameter File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1317

Multiple Indicator Kriging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1319

M.I.K. Reserves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1323


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Introduction to the Course

MineSightGeostatistics Training Workbook Jan 2001 Page I1


Learning Outcome The objective of this workbook is to provide hands on training andexperience with the geostatistical programs in MineSight. You will use a

typical range of problems from drillhole assay and composite statistics,variogram analysis, to Kriging and conditional simulation. This workbook

does not cover all the capabilities of MineSight, but concentrates on a

typical metal open pit mine evaluation using a given set of data.

How ThisWorkbook IsOrganized

This workbook is divided into sections that follow the steps you would take

to complete a project evaluation. All sections contain a basic step, or series

of steps, for using MineSightwith a project. The sections include:

A brief summary of what is to be done within the section

An outline of the process using the menu system

An example of the results of the process

How to ObtainHelp

MineSightprovides a large volume of programs with wide ranges of

options within each program. This may seem overwhelming at times, but

once you feel comfortable with the system, the volume of programs becomes

an asset because of the flexibility it affords. It is our intent to provide

everyone with a successful experience using MineSight. If any portion of

your training is unclear, ask the consultant to repeat the steps or lesson until

you fully understand the idea. We have more concern for our users than for

an agenda.

This training course is intended to cover a wide number of topics rather than

a few topics in depth. For this reason, practice time to learn everything in

detail may not be sufficient. It will be to your advantage to use MineSight

as soon as possible after your return home while the ideas remain fresh.

For help after training, Mintec provides on-call support weekdays from 6:00

a.m. to 6:00 p.m. (MST). From the US, call 800-533-MEDS (6337); from

Canada call 800-548-MEDS (6337); from Mexico call 95 (800) 548-MEDS

(6337); from Chile call 123-0020-2154; from Peru call 001 (800) 533-MEDS

(6337); from South Africa call 0800-996052; or from other countries call

520-795-3891.

The Mintec website provides the latest in program updates and other useful

files. See the Quick Reference Guide for details on how to use the service,

and read the newsletter for updates on what is available.


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Page I2 MineSightGeostatistics Training Workbook Jan 2001


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Section 1Statistics

MineSightGeostatistics Training Workbook Jan 2001 Page 11

Section 1Statistics

Prior to this section you must have loaded the drillhole data to MineSight.

If you are calculating statistics on the composites, you must have calculated

the composites. In this section you can compute classical statistics on the

assays and composites. This is not required for later work.

Learning Outcome In this section you will learn:

How to produce a histogram of assay values

How to produce a histogram of composite values

ClassicalStatistics

Statistical operations available within MineSight:

Mean and standard deviation

Histograms

Cumulative frequency plots

Correlations

Cumulative probability plots

Use classical statistics to:

Analyze data to determine descriptive parameters

Make inferences about an entire population based on samples

Some difficulties involved with the application of classical statistics to

mineral projects are:

Mineral deposit data is generally not independent. It is for this reason

that geostatistics was developed.

Different geologic zones may have different statistical populations.

Mixing zones may produce incorrect statistics.

Different types of samples have different volumes and should be kept

separate for analysis, e.g., drillhole assays and bulk samples.

Although samples may be equal in size, they may not have an equalvolume of influence. Drilling tends to be closer spaced in higher grade

areas so the statistics may be indicating a higher proportion of ore than

exists.


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Section 1Statistics

Page 12 MineSightGeostatistics Training Workbook Jan 2001

Statistics forAssay Values

Select Group Name =STATISTICS

Operations Type = Calculation

Procedure Desc. = Statistics (assays) p40101.dat

Panel 1 Assay Data Statistical Analysis

Enter Cu as the base assay for cutoffs and also report the MO values. Weight

the statistics by the assay length.


A frequency interval of .1 will be used and all values below .0 will beignored.


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Section 1Statistics


Panel 3 Optional Data Selection


You have the option of limiting the area of data selection.


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Section 1Statistics


Panel 5 Histogram Plot Attributes

This panel provides options for setting up your histogram display.

Files Used RUN401.CU RPT401.CU,

DAT401.CU HIS401.CU,

PLT401.CU RUN122.FRQ

Programs Used M401V1 M122V1

Run File as it appears

in the report file


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Section 1Statistics


The report file shows a summary of the statistics calculated.

Another page of the report file showing that 66 of the assays were below the minimum Cu.


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Section 1Statistics


Second report showing summary statistics and histogram


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Section 1Statistics


MPLOT Panel Select Vto view the histogram on the screen.

(From Viewer, Click on Xto Exit & go back to MPLOT Panel.)

Select X to Exit MPLOT Panel.

Plot Reference

RUN122.FRQ


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Section 1Statistics


Statistics forComposite Values

Select Group Name = Statistics


Procedure Desc. =Statistics (comps) p40201.dat

Panel 1 3-D Composite Data Statistical Analysis

Enter Cu as the base assay for analysis and histogram generation. Also report

the Mo values..


A frequency interval of .1 will be used and all values below .0 will be

ignored.


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Section 1Statistics



Panel 4 3-D Coordinate Limits for Data Selection



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Section 1Statistics




Files Used RUN402.CU RPT402.CU

DAT402.CU HIS402.CU




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Section 1Statistics


Run File as it

appears in the

report file

The report file shows a

summary of the statistics

calculated.


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Section 1Statistics



summary by bench for the

distribution of Cu Grades.

Second report with

summary statistics

and histogram


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Section 1Statistics


MPLOT Panel Select Vto view the histogram on the screen.

(From Viewer, Click on Xto Exit & go back to MPLOT Panel.)

Select X to Exit MPLOT Panel.

Plot Reference

RUN122.FRQ

Exercise 1 Generate composite statistics for those composites that have ALTR = 1 and

2 only.(Hint: this can be done with a change to Panel 3)

Exercise 2 Repeat the exercise for those composites that have ROCK = 1 and 2 only.

Exercise 3 Generate lognormal composite data statistics for those composites that haveROCK = 1.


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Section 1Statistics


Statistics withinGeology Types

Select Group Name = STATISTICS


Procedure Desc. = Statistics (comps) - P40201.dat


Enter ROCK ad the first item. This item will be used to determine the

cutoffs. Enter CU as the second item. This item will be used for statistical

analysis.


A frequency interval of 1 will be used because the CU statistics will bereported at cutoffs of ROCK item. Also check the box Dont report the

first item and dont accumulate ints?


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Section 1Statistics


The report file shows a summary of the Cu Grades at ROCK Cutoffs.

Exercise Generate Cu statistics within ALTR codes.


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Section 1Statistics


Probability Plots Select Group Name = STATISTICSOperations Type = Plot

Procedure Desc. = Probability Plotp41201.dat

Panel 1 Select File or Drillholes to Use

Select File 11 Assays to do the cumulative probability plot.

Panel 2 Parameters for Probability Plot

Enter Cu for the item to be plotted. Generate the first plot with logtransformation.


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Section 1Statistics


Panel 5 Optional Plot Parameters

This panel provides options for setting up your probability plot features. You

can try out different parameters until you get a display you like.

Files Used RUN412.CU RPT412.CU

PLT412.CU RUN122.PRB



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Section 1Statistics


MPLOT Panel Select Vto view the probability plot on the screen.

(From the Viewer, Click on Xto exit & go back to MPLOT Panel.)

Select Xto Exit MPLOT Panel.

Plot Reference

RUN122.PRB


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Section 1Statistics


Exercise 1 Generate probability plots for those assays that have ALTR = 1 and 2 only.(Hint: this can be done with a change to Panel 3.)

Exercise 2 Repeat the exercises using the composites.

Exercise 3 Overlay the composite probability plot on the assay probability plot andcompare. (Hint: Output only the cumulative probability curve for composites

and overlay it on the full assay probability plot.)

Exercise 4 Generate probability plots without using log transformation.


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Section 1Statistics


In situDataStatistics



Procedure Desc. = In Situ Statistics p40301.dat

Panel 1 Select the File for Statistical Analysis

Enter9 for the file selection.

Panel 2 Select the item for Statistical AnalysisEnter Cufor the composite grade to analyze. Also specify the file extensions.


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Section 1Statistics


Panel 3 Optional Data SelectionUse ROCK Types 1 and 2 only.

Panel 4 Parameters for Grid SelectionSpecify the parameters of the 3-D grid for the statistical analysis of Cu. Also specify

plot parameters for the selected slice to be plotted.

Files Used RUN403.CU RPT403.CU,PLT403.CU RUN122.STU

Programs Used M403V1M122V1


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Section 1Statistics


Run file as it appears in the

report file

The report file

shows a summary

of the statistics

calculated in

each grid cell.


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Section 1Statistics


Correlation andScatter Plots



Procedure Desc. = Correlationsp41101.dat

Panel 1 File and Data SelectionWe will use File 11 assays and all the drillholes

Panel 2 Scatter Plot ParametersEnter Cufor the y-axis, andMofor the x-axis of the plot.


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Section 1Statistics



Panel 4 Optional Data SelectionLimit the correlation statistics to Rock Types 1 and 2 only.

Files Used RUN411.CU RPT411.CU,PLT411.CU RUN122.SG



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Section 1Statistics


Run File as it

appears in the

report file


summary of correlation

statistics for Cu and Mo

grades.


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Section 1Statistics


MPLOT Panel Select Vto view the scatter plot on the screen.

(From Viewer, Click on Xto Exit and go back to MPLOT Panel.)


Plot Reference

RUN122.SG


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Section 1Statistics


Panel 3 Optional Data SelectionUse ROCK Types 1 and 2 only.

Panel 4 Parameters for Grid SelectionSpecify the parameters of the 3-D grid for the statistical analysis of Cu. Also specify

plot parameters for the selected slice to be plotted.


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Section 1Statistics


Panel 5 Parameters for plotting

Files Used RUN403.CU RPT403.CU DAT403.CUPLT403.CU RUN122.STU


M607V4


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Section 1Statistics


MPLOT Panel SelectXto exit MPLOT Panel.


Operation Type = Calculations

Procedure Desc. = Correlation using ASCII data p41102.dat

Panel 1 Select file for statistical analysis. Use output from previous procedure.

Panel 2


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Section 1Statistics


Panel 3


Files Used RUN403.CU RUN122.SG rpt411.CUplt411.CU DAT403.cu



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Section 1Statistics



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Section 2Variograms


Section 2Variograms

Prior to this section you must have calculated the composites. In this section

you can develop variograms of the composites. Following this, you can

initialize the mine model and do Kriging.


Definition of geostatistics

How to make an h-scatterplot

Types of variograms within MineSight

Procedure for creating variograms

Geostatistics Geostatistics recognizes the fact that geologic samples such as assays orthickness values are not independent samples.

Samples in proximity to one another are usually correlated to some degree.

As the distance between samples increases this degree of correlation declines

until the samples are far enough apart where they can be considered to be

independent of one another.

The Variogram The variogram is a graph that quantifies the spatial correlation betweengeologic samples. It is a plot with the average squared assay difference

between all pairs of samples h distance apart plotted along the y-axis

( (h)), and the distance h plotted along the x-axis.

Logically you would expect this squared difference (h) to increase as the

distance h between the sample pairs increases. Once you reach a distancewhere the sample pairs are independent, the average squared differnece is

not related to the distance h anymore and the curve levels off.

This distance where the samples are no longer correlated is called the range

of the variogram and the value of (h) where it levels off is called the sill.

Theoretically the sill is equal to the variance of samples.

The distance over which the samples are correlated can be and usually is

different in different directions. This is called Anisotropy and simply states

that mineralization may be more continuous in one direction than another.

Therefore, variograms are computed in different directions.

At DISTANCE h=0 (i.e., 2 samples at the same location) the sample values

should be identical. In reality they usually are not. This is described in

geostatistics as the Nugget effect. Its value should be small if correct

sampling and assaying procedures are used.


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Section 2Variograms


Variogram Models The variogram model is the equation of a curve that best fits the variogramgenerated with your data. Variogram models available in MineSightare:

Spherical

Exponential

Linear

Nested

Exercise Select Group Name = STATISTICSOperations Type = Plots

Procedure Desc. = H-Scatter plots p31101.dat

Panel 1 File and Data Selection

We will use File 8 composites and select Cu as the item.



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Section 2Variograms



Use Rock Type 1 data only.

Panel 4 Coordinate Limits


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Section 2Variograms


Run Fileas it appears in

the report file

Panel 5 Parameters for Data Pair Selection

Select all pairs 15mapart vertically (-90 dip.)


PLT311.CU RUN122.HSP

Programs Used M311V1

M122V1


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Section 2Variograms


MPLOT Panel Select Vto view the h-scatterplot on the screen

(From Viewer, Click on to Exit and go back to MPLOT panel.)


Plot Reference

Run122.HSP

Exercise Generate h-scatter plots for pairs 0-50mapart in different horizontaldirections.


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Section 2Variograms


CalculatingVariograms andModeling


Operations Type = Calculations

Procedures Desc. = Variograms (comps) p30302.dat

Panel 1 Compute Experimental Variograms for 3-D CompositesUse File 8 and normal variogram type to compute the initial variograms.

Panel 2 Optional Variogram Parameters


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Section 2Variograms



Limit the data input to Rock Type 1 only.

Panel 4 Optional Coordinate Limits



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Section 2Variograms


Panel 5 Parameters for Multi-Directional Composite Variograms

Compute 4 normal variograms (4x1), starting at horizontal angle 0.0 with 45

degree increments and at a vertical angle 0.0. Use 10 intervals with 120m lag

distance.

Files Used RUN303.A

RPT303.001

DAT303.001

Program Used M303V2

Run file as listed in

the report file


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Section 2Variograms


In the report file, a

summary appears for

each variogram

calculated.

The variogram value is

under the column V(H).

It is plotted along the y-

axis on the graph. The

distance h is under

the column DISTANCE.

It is plotted along the x-

axis on the graph.

This is the plot of the

variogram points listed

above.


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Section 2Variograms


ModelingVariograms



Procedures Desc. = Variogram Modeling p30002.dat

Panel 1 Variogram File Input


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Section 2Variograms


Program M300V1 will display on the screen a list of the 4 directional

variograms plus the 2-D Global variogram and the 3-D Global variogram.

Clickon3-D Globaland then onExit Panel.


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Section 2Variograms


Exercise 1 Interactively fit a spherical variogram model to the experimental variogramby following these steps:

1. Select New Model from menu.

2. Using the mouse, select Nugget location on y axis (Point 1).

3. Using the mouse, select Sill & Range Values which are defined by the

second point that you specify.

4. Click rightto display Model Parameter Values based on your selection.

Exercise 2 Interactively modify the spherical variogram model you just created byfollowing these steps:

1. SelectEdit Modelfrom the menu

2. Click on your Nugget Value (Point 1) and move it around with the

mouse to a new location. Clickrightto store the new location.

3. SelectEdit Modelagain. Click on your Sill/Range Value (Point 2) and

move it around with the mouse to a new location. Clickrightto store the

new location.

4. SelectEdit ModelandFix Range

5. Point to the desired value for range on the X-axis (e.g., 500) and click.

6. Click on Point 2 and move it around. (Note that only the Sill Value is

changing.) Clickrightto store the new Sill.

7. SelectEdit ModelandFix Sill (Make sureFix Rangeis off)

8. Point to the desired value for Sill on the y-axis (e.g., .1) and click.

9. Click on Point 2 and move it around. (Note that only the Range is

changing.) Clickrightto store the new Range

10. Click onXto exit Variogram Modeling Program.

Exercise 3 Try an exponential model and compare the fit (visually) with the spherical.

Exercise 4 Try to model the directional variogram at 0,45,90, and 135degrees.

Exercise 5 If the directional variograms are difficult to model, add an absolute lagtolerance of25. Dont use composite values above3. Use extension 002.

Exercise 6 Try a different horizontal angle increment (30). Use extension 003.


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Section 2Variograms


Exercise 7 Try to compute variograms using different vertical angle orientations.Compare horizontal variograms to the vertical ones. Use extension 004.

Exercise 8 Compute variograms using different variogram type options, such as

correlogram. Use extension 005.

Exercise 9 Run variograms (as in Exercise 5) for rock type2. Use extension 006.


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Section 2Variograms


Calculating Down-hole Variograms



Procedure Desc. = Down-hole Variogramsp30101.dat

Panel 1 File and Variogram Type SelectionYou have the option to use the assay or composite files.

Panel 2 Input Parameters

Use Cu for variogram analysis.


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Section 2Variograms



Panel 4 Optional Data Selections

Limit input data to Rock Type 1 and 2 only.


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Section 2Variograms


Panel 5 Optional Coordinate Limits


Panel 6 Parameters for Down-hole Variograms

Compute variograms for each hole. Use20intervals with5mlag distance.

Files Used RUN301.A

RPT301.CU

DAT301.CU



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Section 2Variograms


Run File as listed in

the report file

In the report file, a

summary appears for each

variogram calculated, as

well as a summary for a

combined variogram.

The variogram value isunder the column V(H). It

is plotted along the y-axis

on the graph. The distance

h is under the column

DISTANCE. It is plotted

along the x-axis on the

graph.


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Section 2Variograms


This is the plot of the

variogram points listed on

the previous page.

Exercise 1 Model the combined down-hole variogram. Pick up a nugget value.

Exercise 2 Calculate and model a down-hole variogram for rock type 2. Pick up anugget value.

Exercise 3 Generate down-hole variograms using composite data.


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Section 2Variograms


Variogram DataContouring



Procedure Desc. = Contour variogram data - pvgctr.dat

Panel 1 File Data Selection

Use the variogram data file generated for ROCK1.

Panel 2 Plot Parameters


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Section 2Variograms


Panel 3 Variogram Contour Parameters

Panel 4 Optional User Plot Files


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Section 2Variograms


Panel 5 Standard Title Box Set up

Files Used RUN607.A RPT607.TMP

PLT607.PAA RUN122.CON

Programs Used GNV2CN

M607V4

MPLOT Panel Select Vto view the contours on the screen

(From Viewer, click on Xto Exit to go back to MPLOT panel.)



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Section 2Variograms


Plot Reference

RUN 122.CON

Exercise 1 Overlay an ellipse to the variogram contours using200mmajor axis and125mminor axis. What is the major axis orientation? Adjust lengths until

the ellipse fits the contours. If you find an orientation that you dont have

variograms for, rerun the variograms programs for a new orientation.


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Section 2Variograms


Exercise 2 Repeat for rock type 2.


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Section 2Variograms


VariogramParameter File


Operations Type = Edit

Procedure Desc. = Variogram Parameter File pvgpar.dat

Having studied the individual variograms, down-the-hole variograms, and

the contour maps for each rock type, decide on one set of variograms.

For example:

Rock

type

Nugget Sill Range

(major)

Range

(minor)

Model

type

1 0.014 0.240 70 (10o) 40 (100o) Exponentia

l

2 0.007 0.085 80 (45o) 60 (135o) Exponentia

l

Assume for the vertical axis the same ranges as the minor axis.

If you use an exponential model, use three times the range as search

distances.

Panel 1 Output and Description File

Variogram parameters will be written to the output file specified.


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Section 2Variograms


Panel 2 Variogram Parameters

The variogram file will be printed on the screen.


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Section 2Variograms


Exercise 1 Set up variogram parameter file for Rock Type 2.

Exercise 2 Set up variogram parameters for both Rock Types 1 and 2 in the same file.(Hint: specify the geology label as ROCK in the first panel.)


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Section 2Variograms



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Section 3Point Validation/Cross Validation (for variogram evaluation)


Section 3Point Validation/Cross Validation (for variogram

evaluation)

Prior to this section, you must have calculated the variograms and modeled

them. In this section you can use the Kriging method to determine the error

between the estimated and the actual known value of composite data atselected locations, using different variograms. The theoretical variogram that

produces the smallest error can be assumed as the better fit.


How to use point validation for variogram evaluation

InterpolationControls

There is a large range of parameters for controlling the point interpolation.

Search distance N-S, E-W, and by elevation

3-D ellipsoidal search

Minimum and maximum number of composites to use

Maximum distance to the nearest composite

Use or omit geologic control

Inverse distance powers and variogram parameters

Point interpolation program M524V1 outputs the results for each composite

used to an ASCII file. These results are evaluated using program M525TS

and the statistical summaries are output to the report file.

In this case we will assume search parameters as indicated by the

variograms. If a specific search scenario has been determined for the model

interpolation, it should be used instead.


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Point Validation Select Group Name = STATISTICSOperations Type = Calculation

Procedure Desc. = Point Validation p52401.dat

Panel 1 File and Area Selection

Panel 2 Search Parameters for Interpolation


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Panel 7 Optional IDW powers and Other Parameters

Use the default IDW powers.

Files Used RUN524.CU1 RUN525.CU1

RPT524.CU1 RPT525.CU1


M525TS


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This report shows

summary statistics for

actual composite grades

versus the results from

different interpolations.

This section of the report

shows the statistics of the

differences between actual

and kriging values The

histogram is the

histogram of the errors.


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file shows correlation

statistics between the

actual and kriging values.

Exercise Modify the variogram parameter file. Use nugget of 0.02. Rerun the pointvalidation procedure. Compare results (you should get a lower correlation

and a higher standard error).


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Prior to this section you must have calculated the composites and sorted

statistics.

In this section you will use cell declustering technique to decluster thecomposite data. This is not required for later work.


How to decluster composite values

How to produce a histogram of declustered composite values

DeclusteringThere are two declustering methods that are generally applicable to any

sample data set. These methods are the polygonal method and the cell

declustering method. In both methods, a weighted linear combination of all

available sample values are used to estimate the global mean. By assigning

different weights to the available samples, one can effectively decluster the

data set.

In this section you will be using the cell declustering method which divides

the entire area into rectangular regions called cells. Each sample received a

weight inversely proportional to the number of samples that fall within the

same cell. Clustered samples will tend to receive lower weights with this

method because the cells in which they are located will also contain several

other samples.

The estimate one gets from the cell declustering method will depend on the

size of the cells specified, If the cells are very small, then most samples will

fall into a cell of its own and will therefore receive equal weights of 1. If the

cells are too large, many samples will fall into the same cell, thereby causing

artificial declustering of samples.


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Statistics forAssay Values



Procedure Desc. = Decluster Datap52301.dat

Panel 1 Composite Data Selection

Enter Cu as the composite data item to be used.


Use all the values of Cu.


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Run File as itappears in the

report file

Panel 3 Area limits and Cell Size

Files Used RUN523.50 RPT523.50



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The report file shows

summary statistics for the

original and the

declustered samples.

Exercise 1 Obtain declustered data using cell sizes 45 x 45 and 40 x 40.

Exercise 2 Create a graph of the cell sizes vs mean values. The cell size that gives thelowest value should be the best choice.

Exercise 3 Try declustering using Rock Type 1 only.


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Histogram ofDeclustered Data


Operation Type= Calculations

Procedure Description= ASCII Data Stats p40204.dat

Panel 1 ASCII Data Statistical Analysis

Enter ASCII output (for cell size equal to 45) from the previous procedure.


Enter column number for item to analyze from ascii file.


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Use a frequency interval of .1

Panel 4 Histogram plot attributes

Files used RUN122.FRQ RUN402.45

DAT402.45 RPT122.LA

RPT402.45 HIS402.45

DAT523.45 PLT402.45

Programs used M402V1 M122V1

Mplot Panel Select Vto view the histogram on the screen.

(From viewer, click on Xto Exit & go back to MPLOT Panel)

Select Xto Exit MPLOT panel.


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Plot Reference

RUN122.FRQ


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Section 5Model Interpolation



Prior to this section you must have calculated the composites and sorted them. You

must have initialized the mine model and added any necessary geology to it. In this

section you can use inverse distance weighting to add grades to the mine model. This

is required before displaying the model, calculating reserves or creating pit designs.


The types of interpolations available

The use of controls on the interpolation

How to interpolate grades with MineSight

Types ofInterpolations

There are several methods of interpolation provided to you.

Polygonal assignment

Inverse distance weighting

Relative elevations

Trend plane

Gradients

Kriging


There is a large range of methods for controlling the interpolation available.


Minimum and maximum number of composites to use for a block



In the following example, inverse distance weighting is used without the octant

search.


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IDW Interpolation Select Group Name = 3D DEPOSIT MODELINGOperations Type = Calculation

Procedure Desc. = IDW Interpolation p62001.dat

Panel 1 M620V1 File and Model Area Specifications

Panel 2 M620V1 Input Search ParametersSpecify a 3-D search to use all composites within 210m (based on variograms)

horizontally and 50m vertically of a block. A weighting power of 2 is used.


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Panel 3 Interpolation Control ItemsInterpolate the Cu and Mo grades.

Panel 4 Store Local Error


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Panel 7 Optional Geologic CodesUse only Rock Type 1.

Panel 8 Optional Data SelectionInclude Rock Type 1 and 2 data only.


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Files Used RUN620.id1RPT620.id1


Exercise Rerun for Rock Type2. Change search distances and use optionomit.

Change the following panels:


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Section 6Kriging


Section 6Kriging

Prior to this section you must have calculated the composites and sorted

them. You must have also initialized the mine model and added any

necessary geology to it. In this section you can use kriging to add grades to

the mine model.


How to set up and run a Kriging interpolation

Ordinary Kriging Ordinary kriging is an estimator designed primarily for the local estimationof block grades as a linear combination of the available data in or near the

block, such that the estimate is unbiased and has minimum variance. It is a

method that is often associated with the acronym B.L.U.E. for best linear

unbiased estimator. Ordinary kriging is linearbecause its estimates areweighted linear combinations of the available data; it is unbiasedsince the

sum of the weights add up to 1; it is bestbecause it aims at minimizing the

variance of errors.

The conventional estimation methods, such as inverse distance weighting

method, are also linear and theoretically unbiased. Therefore, the

distinguishing feature of ordinary kriging from the conventional linear

estimation methods is its aim of minimizing the error variance.

Kriging withMineSightBefore producing an interpolation using kriging, you must have developed a

variogram. Three types of variograms are allowed:

Spherical

Linear

Exponential


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Section 6Kriging


Select Group Name = 3D DEPOSIT MODELING


Procedure Desc. = Ordinary Kriging p62401.dat

Panel 1 M624V1 File and Model Area Specifications

Panel 2 M624V1 Krige Search Parameters

Specify a 3-D search to find all composites within 210m horizontally and

50m vertically of a block. Use a maximum of 16 composites.


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Section 6Kriging


Panel 3 Interpolation Control Items

Krige the Cu grades on each bench.

Panel 4 Optional Input Parameters.

Leave blank if not used.


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Section 6Kriging



Enter the variogram parameters used in Kriging.

Panel 6 Optional Sear Parameters


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Section 6Kriging


Panel 7 Optional Rotation Angles

These angles need to be specified when ellipsoidal search is used for

composite selection.

Panel 8 Optional Geologic Codes

Use Rock Type 1.


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Section 7Point Validation/Cross Validation


Section 7Point Validation/Cross Validation of Estimation Methods

and/or Search Parameters

In this section you can use inverse distance weighting and Kriging methods

to determine the error between the estimated and the actual known value ofcomposite data at selected locations. Then, you can decide which method is

more appropriate. You can also validate search parameters.


The types of interpolations available in point validation

The use of controls on the interpolation

How to interpolate point grades with MineSight

Types of PointInterpolations

Each composite is interpolated using different powers of inverse distance

weighting method and Kriging. The results are then summarized showing

the differences between the estimated and actual known data values. The

following interpolations are done by default by the program.

Inverse distance weighting (IDW) of power 1.0

IDW of power 1.5

IDW of power 2.0

IDW of power 2.5

IDW of power 3.0

Kriging


There is a large range of parameters for controlling the point interpolation.


3-D ellipsoidal search

Minimum and maximum number of composites to use



Inverse distance powers and variogram parameters

Point interpolation program M524V1 outputs the results for each composite

used to an ASCII file. These results are evaluated using program M525TS

and the statistical summaries are output to the report file.


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Point Validation Select Group Name = STATISTICSOperations Type = Calculation

Procedure Desc. = Point Validation p52401.dat

Panel 1 File and Area Selection

Panel 2 Search Parameters for Interpolation


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Panel 3 Ellipsoidal Search Parameters

Ellipsoidal Search and use of anisotropic distances are optional. Use the

distances we used for Rock Type 1.

Panel 4 Angle definition for Ellipsoidal Search


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Panel 6 Optional Geologic Codes

Include Rock Type 1 data only.


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Panel 7 Optional IDW powers and Other Parameters

Use the default IDW powers.

Files Used RUN524.CU1 RUN525.CU1

RPT524.CU1 RPT525.CU1

Programs Used M524V1M525TS


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actual and Kriging values.




actual and inverse

distance

values.

Exercise Change some of the search parameters and rerun the above procedure. Whatdo you observe?


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Prior to this section you must have added the grades, topography, and

necessary geology into the mine model. In this section you can summarize

the mine model data with frequency distributions and calculated the geologic

resources.


How to calculate grade and tonnages above different cutoffs

How to calculate grade and tonnages between cutoffs

How to produce a histogram plot of model values

How to generate reserves by bench or geological resources

How to generate probability plots from the model

ReserveCalculations

To calculate initial reserves from the block model, use M608V1 (i.e.,

STATISTICS Calculations Statistics (Model). Refer to the STRIPPERreserves section for a method of developing a more detailed reserve report.

The reserves calculated in this section are the tons and grade above a cutoff.

The topographic values you added to the mine model are used to give you an

accurate reserve report. For different specific gravities, use the run file

created and run each rock type separately.

The menu system has been set to give you the quickest level of reserves.

With the run files, you can customize the run to give reserves by bench, rock

type or any other subset you want. For example, in the menu system, 40

intervals are selected (for plotting purposes). The interval size you choose

will be based on the cutoff grades you wish to show. If you choose 0.1, for

example, you will get a report for blocks above 0.0, above 0.1, above 0.2,

etc. up to 40 cutoffs. If special cutoff values are wanted (such as 0.13 or

0.52) you can use another procedure (P60802.DAT) to calculate reserves at

user specified cutoffs.


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Model Statistics Select Group Name = STATISTICSOperations Type = Calculation

Procedures Desc. = Statistics (Model) p60801.dat

Panel 1 File Selection

Panel 2 Item Selection

Panel 3 Cutoff Grades and Frequency Parameters


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Enter 16.2 as multiplier for resource calculation. This is the Ktonnage/block

for our project.


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file shows the grade and

tonnage of CUID,

CUKRG, CUPLY and

MOID values at specified

cutoffs.

This section of the report fileshows the tonnage and grade

of CUID values at each bench.

The grade is reported at

whatever the minimum value

specified on Panel 3

Files Used RUN608.CUI RPT608.CUI

DAT608.CUI HIS608.CUI

PLT608.CUI RUN122.MFR


A statistical summary and histogram can be found in the report file.


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MPLOT Panel Select V to view the histogram on the screen.

Plot Reference

RUN122.MFR

Exercise Generate model statistics for items from IDW, polygonal and Krigingmethods separately. Use the same cutoff intervals. We will use the data

output files from each run to make grade tonnage plots. Use extension cui,

cup, and cuk respectively.


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Grade/TonnagePlots


Operations Type = Plot

Procedure Desc. = Grade/Tonnage Plots pgtplt

Panel 1 Select Files or Parameters

We will plot grade/tonnage curves from polygonal, IDW and kriging

methods on the same graph. Identify each curve by the symbol, linetype orcolor specified.

MPLOT Panel Select Vto view the curves on the screen.

(From Viewer, Click on Xto Exit and go back to MPLOT Panel)

SelectXto Exit MPLOT Panel.


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Plot Reference

RUN122.MSG


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Plot IDW andKrigingHistogramsTogether

Select Group Name = Adv Plotting/VBM

Operations Type = Plot

Procedures Desc. =Plot any USERF/DATAF anyplt.dat

Panel 1 Plotting panel

Enter scale and x,y limits (plotting units, not project). Plotting files are

USERF. Use appropriate shift command.


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Model Statistics Atand BetweenCutoffs



Procedures Desc. = Statistics at User Cutoffs (Model)

p60802.dat




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Panel 3 Cutoff Specification

Check the box not to accumulate intervals.


Select blocks with Rock code 1 only. Enter 16.2as multiplier for resource

calculation. This is the Ktonnage/block for our project.


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Panel 5 Mine Model Statistical Analysis

Calculate the statistics for benches 21-40.


Files Used RUN608.Ci2 RPT608.Ci2

DAT608.Ci2 HIS608.Ci2

PLT608.Ci2 RUN122.MFR



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ModelCorrelations



Procedure Desc. = Correlations (Model)p61801.dat


We will use File 15 model file.

Panel 2 Scatter Plot Parameters

Enter CUID for the y-axis and CUKRG for the x-axis of the plot.


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Panel 3 Optional Plot Parameters and Data Selection

Select benches 21-40.


Limit the correlation statistics to Rock Types 1 only.


PLT618.CU RUN122.MSG


M122V1


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file shows the summary of

correlation statistics

between CUID and

CUKGR values.


(From Viewer, Click on Xto Exit and go back to MPLOT Panel)

SelectXto Exit MPLOT Panel.


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Plot Reference

RUN122.MSG

Exercise Calculate the correlations between polygonal and Kriging grades. What doyou observe?


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Probability Plots Select Group Name =3D DEPOSIT MODELINGOperation Type= Plot

Procedure Description= Probability Plots (model)-p61901.dat



Select item CUKRG.


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Panel 4 Optional Plot Files


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Files used RUN619.A RPT619.LA

RUN122.MCP RPT122.LA

PLT619.LA

Programs used M619V1 M122V1

Mplot Panel Select Vto view the probability plot on the screen.(From viewer, click on Xto Exit & go back to MPLOT Panel)

Select Xto Exit MPLOT panel.


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Plot Reference

RUN122.MCP

Exercise Create separate probability plots for Rock Types 1 and 2. Compare results.


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In this section you will calculate block values for item EQCU and store them

in the model.


How to perform calculations using information stored in the model

ModelCalculations

Select Group Name = 3-D DEPOSIT MODELING


Procedure Desc. = User-Calcs (Model)p61201.dat

Panel 1 Mine Model/Surface File Data Items

Specify number of levels, rows, and columns.


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Panel 2 Mine Model/Surface File Data Items

We will calculate EQCU values from values stored for CUID and MOID.


Restrict EQCU calculations to blocks in Rock Types 1 and 2 only.


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Panel 4 Define Special Project Calculations

In this panel the EQCU calculation is defined and the item in the model

(EQCU) where the result is to be stored is specified.

Panel 5 Store Item Back to Model


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Section 10Quantifying Uncertainty



Prior to this section you should have calculated the distance to the closest

composite and the Kriging variance.

Learning Outcome In this section, you will learn how to quantify your confidence in the resultsof the block model calculations.

We will use different approaches:

Distance to the closest composite,

Kriging variance,

Combined Kriging variance

Relative Variability Index

Distance to theClosestCompositesCalculations

Assign the value of 1to model item ZONE, when DISTP = 0 to 39(since weused the same search distances for IDW and Kriging, item DISTP represents

the distance to the closest composite for both methods).

Distance of 39m corresponds more or less to 25% of the model. Fifty

percent of the model was assigned distances up to57m, and 75% up to 77m.

Distances are not true (they are anisotropic).

Select Group Name = 3-D DEPOSIT MODELING

Operation types= Calculations

Procedure Desc. = User-Cals (Model) p61201.dat

Panel 1 Mine Model/Surface File


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Panel 2 Undefined values

Do not substitute undefined values



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Panel 4 Define calculation

Panel 5 Store item back to model


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Repeat the procedure for:

Zone = 2 when DISTP = 40 to 57

Zone = 3 when DISTP = 57 to 77

Zone = 4 when DISTP >77

These values for ZONE will be used to define proven ore (ZONE =1 or 2),

probable ore (ZONE =3) and possible ore (ZONE =4).

Exercise Make a model view of item ZONE.


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Kriging Variance Make a model view of the item CUKVR as it was calculated by runningprocedure P62401.DAT. Use cutoffs of 0.039, 0.055 and 0.087 (quartiles).

Combined KrigingVariance

Rerun the Kriging procedure for each rock type. Calculate combined

variance instead of Kriging variance. Store in item CUKCV. Make a model

view. Use cutoffs of 0.005, 0.010, and 0.021(quartiles).


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Relative VariabilityIndex

Rerun the Kriging procedure for each rock type. Calculate RVI instead of

Combined variance. Store in item RVI. Make a model view. Use cutoffs of

0.22, 0.34, and 0.65(quartiles). What do you notice?


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MineSightGeostatistics Training Workbook January 2001 Page 111


Prior to this section you must have the composite and 3-D model files

initialized and loaded. You must also have calculated the classical statistics

and the grade variograms of the composites.


What change of support means

How to determine indicator cutoffs

How to calculate block variance for different size blocks

What is Kriges relationship of variance

How to determine change of support correction factor

How to do global change of support correction

Change of support methods

Change of Support The termsupportat the sampling stage refers to the characteristics of thesampling unit, such as the size, shape and orientation of the sample. For

example, channel samples and diamond drillcore samples have different

supports. At the modeling and mine planning stage, the termsupportrefers

to the volume of the blocks used for estimation and production.

It is important to account for the effect of the support in our estimation

procedures, since increasing the support has the effect of reducing the spread

of data values. As the support increases, the distribution of data gradually

becomes more symmetrical. The only parameter that is not affected by the

support of the data is the mean. The mean of the data should stay the same

even if we change the support.

Global Correction There are some methods available for adjusting an estimated distribution toaccount for the support effect. The most popular ones are affine correction

and indirect lognormal correction. All of these methods have two features

in common:

1. They leave the mean of the distribution unchanged.

2. They change the variance of the distribution by some adjustment

factor.

KrigesRelationship ofVariance

This is the special complement to the partioning of variances, which simply

says that the variance of point values is equal to the variance of block values

plus the variance of points within blocks. The equation is given below:

p2= b

2+ 2p b


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Page 112 MineSightGeostatistics Training Workbook January 2001

Calculation ofBlock Variance



Procedure Desc. = Block variance - psblkv.dat

Panel 1 Block Variance Calculation

The output report file summarizes the following:


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Files Used VARIO.RK1

MSBLKV.PAR

MSBLKV.RPT

Programs Used MSBLKV

Exercise 1 Change block size to 10x10 and re-run the procedure. What change do yousee in the block variance?

Exercise 2 Change block discretization to 10x10x5 and see the effect on the blockvariances of 20x20 blocks.

Exercise 3 If you have another variogram parameter file, try running the procedure withit. What do you observe?


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Change of Supporton CompositeValues

Select Group Name = Statistics


Procedure Desc. =Statistics (comps) p40201.dat


Enter Cu as the base assay for analysis and histogram generation.


Make sure to check the change of support option.


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Panel 3 Change of Support Parameters


Select Rock Type 1.


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Files Used RUN402.CU RPT402.CU BLOCK.DAT

DAT402.CU HIS402.CU




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Look into BLOCK.DAT using Notepad or another editor. The first column

in this file is the theoretical block grades after the change of support

correction is made. The second column is the original data as input.


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Distribution ofTheoretical Blocks



Procedure Desc. = Statistics - ASCII - p40204.dat


Use Block.dat as the input file with free format.

Panel 2 Free Format Specs

Select Column #1 to read.


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Files Used RUN402.D RPT402.BLK

DAT402.BLK HIS402.BLK

PIT402.BLK RUN122.FRQ

BLOCK.DAT



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MPLOT Panel Click on the Preview/Create Metafile (M122MF) Button.

Plot Reference

RUN122.FRQ


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Volume-VarianceCorrection onComposite Data



Procedure Desc. = Volume-variance (comps) - pcmpvc.dat

Panel 1 Select the File to Use

Panel 2 Volume-Variance Correction in Composite grades

Store the results in item CUBLK. Select the affine correction option(default).


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Select Rock Type 1.

Panel 4 Volume-Variance Correction Parameters

The Volume-variance Correction factor will be block to point variance

ratios: 0.17699/0.247 = 0.716

Files Used RUN508.A

RPT508.LVC


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RPT508.LVC A summary of the results from Volume-variance Correction is displayed.

Exercise 1 Run stats on item CUBLK to look at the new distribution. Use extensionAFF.

Exercise 2 Run the Volume-Variance Correction using the indirect lognormal method.Then compare the results with affine correction. (Store back to CUBLK, run

statistics, use extension ILM.)

Exercise 3 Combine all histograms in one plot:

original data (plt402.cu)

hermite polynomials transformation (plt404.blk)

affine correction (plt402.aff), and

indirect lognormal method (plt402.ilm)


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Volume VarianceCorrection onModel Data



Procedure Desc. = Volume-variance - pmodvc.dat

Panel 1 Select the File to Use

Enter benches 21-30.

Panel 2 Select Items to be UsedSelect indirect lognormal correction option.


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Select Rock Type 1.

Panel 4 Volume-Variance Correction Parameters

Files Used RUN612.A

RPT612.LVC


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Section 12Indicator Kriging


Section 12Indicator Kriging to Define Geologic Boundary above aCutoff

Prior to this section you should have the composite and 3-D model initialized

and loaded.


How to calculate the indicator function (0 or 1) based on a grade cutoff

How to calculate the probability of a block having a grade value above the

cutoff

How to view the probabilities (from block model) in MineSight

IK The basis of the technique is transforming the composite grades to a (0 or 1)function. All composite grades above cutoff can be assigned a code of 1

whereas all the composites below can be assigned a code of 0. Then a

variogram can be formed from the indicators which can be used for Kriging the

indicators. The resulting Kriging estimate represents the probability of eachblock having a grade value above the cutoff.

Assign Indicators Select Group Name = COMPOSITESOperation Type = Calculations

Procedure Desc. = User-Calcs (comps) - p50801.dat

Panel 1 Labels of Composite Items to use

Use itemaltrxas the item to store the indicators.


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Use RANGE for the calculation on rock type and cu grade.

Panel 3 Limits for Data Selection


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Panel 4 Special Project Calculations

Assign an initial code of 0to itemaltrx.

Files Used RUN508.A

RPT508.LA

Program used M508RP

Repeat the procedure, but this time enter a range for cu from 0.3to99, and use

altrx =1.


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Variogram ofIndicators

Select Group = COMPOSITES

Operation types = Calculation

Procedure Desc. = Variograms (comp)- p30302.dat

Panel 1 Experimental Variograms for 3-D Composites

Enter ALTRX as the item to use.



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Use both rock types.



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Panel 5 Parameters for Multi-Directional Variograms

Files used RUN303.ALT

DAT303.ALT

RPT303.ALT

Programs used M303V2

Model theIndicator

Variogram

Select Group =COMPOSITES

Operation Type = Calculations

Procedure Desc. = Variogram Modeling - p30002.dat

Panel 1 Variogram File Input

Enter output from previous exercise.


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Pick the 3-D global variogram from the list and exit panel. Make a new model.

(nugget = .068, sill = .234, range = 370).

Files used RUN300.A

DAT303.ALT

Programs used M300V1


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Page 128 MineSightGeostatistics Training W

geostatistics 2001

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