Geostatistics 2001

Introduction to Geostatistics and

Advanced Geostatistics

January 2001

MineSight® is a registered trademark of Mintec, inc. © 1994, 1978 Mintec, inc. All rights reserved.

Table of Contents Introduction to Geostatistics Section 1—Statistics Learning Outcome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1—1 Classical Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1—1 Statistics for Assay Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1—2 Statistics for Composite Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1—8 Statistics within Geology Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1—14 Probability Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1—18 In situ Data Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1—23 Correlation and Scatter Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1—27 Plot Proportional Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1—31 Section 2—Variograms Learning Outcome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2—1 Geostatistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2—1 The Variogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2—1 Variogram Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2—2 Calculating Variograms and Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2—7 Modeling Variograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2—11 Calculating Down-hole Variograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2—15 Variogram Data Contouring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2—20 Variogram Parameter File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2—25 Section 3—Point Validation/Cross Validation (for variogram evaluation) Learning Outcome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3—1 Interpolation Controls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3—1 Point Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3—2 Section 4—Declustering Learning Outcome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4—1 Declustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4—1 Statistics for Assay Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4—2 Histogram of Declustered Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4—5 Section 5—Model Interpolation Learning Outcome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5—1 Types of Interpolations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5—1 Interpolation Controls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5—1 IDW Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5—2

Advanced Geostatistics Section 6—Kriging Learning Outcome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6—1 Orginary Kriging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6—1 Kriging with MineSight® . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6—1 Section 7—Point Validation/Cross Validation of Estimation Methods Learning Outcome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Types of Point Interpolations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Interpolation Controls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Point Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7—1 7—1 7—1 7—2

Section 8—Model Statistics/Geologic Resources Learning Outcome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8—1 Reserve Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8—1 Model Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8—2 Grade/Tonnage Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8—7 Plot IDW and Histograms Together . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8—9 Model Statistics At and Between Cutoffs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8—10 Model Correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8—14 Probability Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8—18 Section 9—Model Calculations Learning Outcome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9—1 Model Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9—1 Section 10—Quantifying Uncertainty Learning Outcome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Distance to the Closest Composites Calculations . . . . . . . . . . . . . . . . . . . . . . Kriging Variance/RVI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Combined Kriging Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10—1 10—1 10—5 10—5

Section 11—Change of Support Learning Outcome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11—1 Change of Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11—1 Global Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11—1 Krige’s Relationship of Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11—1 Calculation of Block Variance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11—2 Change of Support on Composite Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11—4 Distribution of Theoretical Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11—8 Volume-Variance Correction on Composite Data . . . . . . . . . . . . . . . . . . . . . 11—11 Volume Variance Correction on Model Data . . . . . . . . . . . . . . . . . . . . . . . . 11—15

Section 12—Indicator Kriging to Define Geologic Boundary Above a Cutoff Learning Outcome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12—1 IK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12—1 Assign Indicators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12—1 Variogram of Indicators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12—4 Model the Indicator Variogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12—6 Krige Indicators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12—8 View Results in MineSight® . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12—11 Section 13—Multiple Indicator Kriging (M.I.K.) Learning Outcome . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13—1 M.I.K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13—1 Uses of Indicators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13—1 Incremental Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13—2 Determine M.I.K. Cutoffs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13—6 Statistics for M.I.K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13—8 Calculating Indicator Variograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13—12 Modeling Indicator Variograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12—16 Variogram Parameter File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13—17 Multiple Indicator Kriging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13—19 M.I.K. Reserves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13—23

Introduction to the Course


Learning Outcome

The objective of this workbook is to provide hands on training and experience 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 This Workbook Is Organized

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 MineSight® with a project. The sections include:

How to Obtain Help

C

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

C

An outline of the process using the menu system

C

An example of the results of the process

MineSight® provides 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.

MineSight® Geostatistics Training Workbook

Jan 2001

Page I—1


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Jan 2001

Section 1&Statistics

Section 1—Statistics 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

Classical Statistics

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 equal volume 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.


Jan 2001

Page 1&1


Statistics for Assay Values

Panel 1

Select Group Name = STATISTICS Operations Type = Calculation Procedure Desc. = Statistics (assays) — p40101.dat

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.

Panel 2


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

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Jan 2001


Panel 3

Panel 4

Optional Data Selection


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


Jan 2001

Page 1&3


Panel 5

Histogram Plot Attributes

This panel provides options for setting up your histogram display.

Files Used

Programs Used

RUN401.CU DAT401.CU PLT401.CU

RPT401.CU, HIS401.CU, RUN122.FRQ

M401V1

M122V1

Run File as it appears in the report file

Page 1&4


Jan 2001


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.


Jan 2001

Page 1&5


Second report showing summary statistics and histogram

Page 1&6


Jan 2001

Section 1&Statistics MPLOT Panel

Select V to view the histogram on the screen. (From Viewer, Click on X to Exit & go back to MPLOT Panel.) Select X to Exit MPLOT Panel.

Plot Reference RUN122.FRQ


Jan 2001

Page 1&7


Statistics for Composite Values Panel 1

Select Group Name = Statistics Operations Type = Calculation Procedure Desc. = Statistics (comps) — p40201.dat 3-D Composite Data Statistical Analysis

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

Panel 2

3-D Composite Data Statistical Analysis

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

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Jan 2001


Panel 3

Panel 4


3-D Coordinate Limits for Data Selection



Jan 2001

Page 1&9


Panel 5



Files Used

Programs Used

Page 1&10


RPT402.CU HIS402.CU RUN122.FRQ

M402V1 M122V1


Jan 2001



The report file shows a summary of the statistics calculated.


Jan 2001

Page 1&11


The report file shows a summary by bench for the distribution of Cu Grades.

Second report with summary statistics and histogram

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Jan 2001


Select V to view the histogram on the screen. (From Viewer, Click on X to Exit & go back to MPLOT Panel.) Select X to Exit MPLOT Panel.


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 have ROCK = 1.


Jan 2001

Page 1&13


Statistics within Geology Types Panel 1

Select Group Name = STATISTICS Operations Type = Calculation Procedure Desc. = Statistics (comps) - P40201.dat 3-D Composite Data Statistical Analysis

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.

Panel 2


A frequency interval of 1 will be used because the CU statistics will be reported at cutoffs of ROCK item. Also check the box “Don’t report the first item and don’t accumulate ints?”

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Panel 3

Panel 4





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Page 1&15


Panel 5



Files Used

Programs Used

Page 1&16

RUN402.RCK RPT402.RCK DAT402.RCK HIS402.RCK PLT402.RCK RUN122.FRQ M402V1 M122V1


Jan 2001


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

Exercise

Generate Cu statistics within ALTR codes.


Jan 2001

Page 1&17


Probability Plots

Panel 1

Select Group Name = STATISTICS Operations Type = Plot Procedure Desc. = Probability Plot—p41201.dat 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 log transformation.

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Jan 2001


Panel 3


Select Rock Types 1 and 2 for plotting.

Panel 4

Optional Plot Files


Jan 2001

Page 1&19


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

Programs Used

Page 1&20

RUN412.CU PLT412.CU

RPT412.CU RUN122.PRB

M412V1

M122V1


Jan 2001


MPLOT Panel

Select V to view the probability plot on the screen. (From the Viewer, Click on X to exit & go back to MPLOT Panel.) Select X to Exit MPLOT Panel.

Plot Reference RUN122.PRB


Jan 2001

Page 1&21


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 and compare. (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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Jan 2001


Select

In situ Data Statistics

Group Name = STATISTICS Operations Type = Calculation Procedure Desc. = In Situ Statistics — p40301.dat

Panel 1

Select the File for Statistical Analysis Enter 9 for the file selection.

Panel 2

Select the item for Statistical Analysis Enter Cu for the composite grade to analyze. Also specify the file extensions.


Jan 2001

Page 1&23


Panel 3

Optional Data Selection Use ROCK Types 1 and 2 only.

Panel 4

Parameters for Grid Selection Specify 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

Programs Used

Page 1&24

RUN403.CU PLT403.CU

RPT403.CU, RUN122.STU

M403V1 M122V1 MineSight® Geostatistics Training Workbook

Jan 2001


Run file as it appears in the report file

The report file shows a summary of the statistics calculated in each grid cell.


Jan 2001

Page 1&25


MPLOT Panel

Select V to view the plot on the screen. (From Viewer, Click on X to Exit & go back to MPLOT Panel.) Select X to Exit MPLOT Panel.

Plot Reference RUN122.STU

Exercise

Page 1&26

Generate In situ statistics for assays in elevation range 2500 to 3000.


Jan 2001


Correlation and Scatter Plots

Select

Group Name = STATISTICS Operations Type = Calculation Procedure Desc. = Correlations—p41101.dat

Panel 1

File and Data Selection We will use File 11 assays and all the drillholes

Panel 2

Scatter Plot Parameters Enter Cu for the y-axis, and Mo for the x-axis of the plot.


Jan 2001

Page 1&27

Section 1&Statistics Panel 3


Panel 4

Optional Data Selection Limit the correlation statistics to Rock Types 1 and 2 only.

Files Used

Programs Used

Page 1&28

RUN411.CU PLT411.CU

RPT411.CU, RUN122.SG

M411V2 M122V1


Jan 2001



The report file shows a summary of correlation statistics for Cu and Mo grades.


Jan 2001

Page 1&29


Select V to view the scatter plot on the screen. (From Viewer, Click on X to Exit and go back to MPLOT Panel.) Select X to Exit MPLOT Panel.

Plot Reference RUN122.SG

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Jan 2001


Plot Proportional Effect

Select

Group Name = STATISTICS Operations Type = Calculation Procedure Desc. = In Situ Statistics — p40301.dat

Panel 1

Select the File for Statistical Analysis Enter 9 for the file selection.

Panel 2

Select the item for Statistical Analysis Enter Cu for the composite grade to analyze. Also specify the file extensions.


Jan 2001

Page 1&31


Page 1&32

Panel 3

Optional Data Selection Use ROCK Types 1 and 2 only.

Panel 4

Parameters for Grid Selection Specify the parameters of the 3-D grid for the statistical analysis of Cu. Also specify plot parameters for the selected slice to be plotted.


Jan 2001


Panel 5

Files Used

Programs Used

Parameters for plotting

RUN403.CU PLT403.CU

RPT403.CU RUN122.STU

DAT403.CU

M403V1 M122V1 M607V4


Jan 2001

Page 1&33


MPLOT Panel

Select X to exit MPLOT Panel.

Select

Panel 1

Group Name = STATISTICS Operation Type = Calculations Procedure Desc. = Correlation using ASCII data – p41102.dat

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

Panel 2

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Jan 2001


Panel 3

MPLOT Panel

Files Used

Programs Used

Select V to view the scatter plot on the screen.

RUN403.CU plt411.CU

RUN122.SG DAT403.cu

rpt411.CU

M411V1 M122V1


Jan 2001

Page 1&35


Page 1&36


Jan 2001

Section 2—Variograms

Section 2&Variograms 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.

Learning Outcome

In this section you will learn: 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 or thickness 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 between geologic 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 distance where 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.


Jan 2001

Page 2—1


Variogram Models

The variogram model is the equation of a curve that best fits the variogram generated with your data. Variogram models available in MineSight® are: • Spherical • Exponential • Linear • Nested

Exercise

Select Group Name = STATISTICS Operations 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.

Panel 2

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Jan 2001


Panel 3


Use Rock Type 1 data only.

Panel 4

Coordinate Limits


Jan 2001

Page 2—3


Panel 5

Parameters for Data Pair Selection

Select all pairs 15m apart vertically (-90 dip.)

Files Used

Programs Used

RUN311.CU PLT311.CU

RPT311.CU, RUN122.HSP

M311V1 M122V1


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Jan 2001


This section of the report file shows summary statistics of correlations between “head” and “tail” of pairs.

This section of the report file shows summary statistics for all the samples in pair data.


Jan 2001

Page 2—5

Section 2—Variograms MPLOT Panel

Select V to view the h-scatterplot on the screen (From Viewer, Click on to Exit and go back to MPLOT panel.) Select X to Exit MPLOT Panel.

Plot Reference Run122.HSP

Exercise

Page 2—6

Generate h-scatter plots for pairs 0-50m apart in different horizontal directions.


Jan 2001


Calculating Variograms and Modeling Panel 1

Select Group Name = STATISTICS Operations Type = Calculations Procedures Desc. = Variograms (comps) — p30302.dat

Compute Experimental Variograms for 3-D Composites

Use File 8 and normal variogram type to compute the initial variograms.

Panel 2

Optional Variogram Parameters


Jan 2001

Page 2—7


Panel 3


Limit the data input to Rock Type 1 only.

Panel 4

Optional Coordinate Limits


Page 2—8


Jan 2001


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

Program Used

RUN303.A RPT303.001 DAT303.001 M303V2

Run file as listed in the report file


Jan 2001

Page 2—9


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 yaxis on the graph. The distance “h” is under the column DISTANCE. It is plotted along the xaxis on the graph.

This is the plot of the variogram points listed above.

Page 2—10


Jan 2001


Select Group Name = STATISTICS Operations Type = Calculation Procedures Desc. = Variogram Modeling — p30002.dat

Modeling Variograms

Panel 1

Variogram File Input


Jan 2001

Page 2—11


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. Click on 3-D Global and then on Exit Panel.

Page 2—12


Jan 2001


Exercise 1

Interactively fit a spherical variogram model to the experimental variogram by 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 right to display Model Parameter Values based on your selection.

Exercise 2

Interactively modify the spherical variogram model you just created by following these steps: 1. Select Edit Model from the menu 2. Click on your Nugget Value (Point 1) and move it around with the mouse to a new location. Click right to store the new location. 3. Select Edit Model again. Click on your Sill/Range Value (Point 2) and move it around with the mouse to a new location. Click right to store the new location. 4. Select Edit Model and Fix 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.) Click right to store the new Sill. 7. Select Edit Model and Fix Sill (Make sure Fix Range is 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.) Click right to store the new Range 10. Click on X to 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 135 degrees.

Exercise 5

If the directional variograms are difficult to model, add an absolute lag tolerance of 25. Don’t use composite values above 3. Use extension 002.

Exercise 6

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


Jan 2001

Page 2—13


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 type 2. Use extension 006.

Page 2—14


Jan 2001


Calculating Downhole Variograms

Panel 1

Select Group Name = STATISTICS Operations Type = Calculations Procedure Desc. = Down-hole Variograms—p30101.dat

File and Variogram Type Selection

You have the option to use the assay or composite files.

Panel 2

Input Parameters

Use Cu for variogram analysis.


Jan 2001

Page 2—15


Panel 3

Panel 4


Optional Data Selections

Limit input data to Rock Type 1 and 2 only.

Page 2—16


Jan 2001


Panel 5



Panel 6

Parameters for Down-hole Variograms

Compute variograms for each hole. Use 20 intervals with 5m lag distance.

Files Used

Programs Used

RUN301.A RPT301.CU DAT301.CU M301V1


Jan 2001

Page 2—17


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 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.

Page 2—18


Jan 2001


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 a nugget value.

Exercise 3

Generate down-hole variograms using composite data.


Jan 2001

Page 2—19


Variogram Data Contouring Panel 1

Select Group Name = STATISTICS Operations Type = Calculation Procedure Desc. = Contour variogram data - pvgctr.dat File Data Selection

Use the variogram data file generated for ROCK1.

Panel 2

Page 2—20

Plot Parameters


Jan 2001


Panel 3

Variogram Contour Parameters

Panel 4

Optional User Plot Files


Jan 2001

Page 2—21


Panel 5

Files Used

Programs Used

MPLOT Panel

Page 2—22

Standard Title Box Set up

RUN607.A RPT607.TMP PLT607.PAA RUN122.CON GNV2CN M607V4 Select V to view the contours on the screen (From Viewer, click on X to Exit to go back to MPLOT panel.) Select X to Exit MPLOT Panel.


Jan 2001


Plot Reference RUN 122.CON

Exercise 1

Overlay an ellipse to the variogram contours using 200m major axis and 125m minor axis. What is the major axis orientation? Adjust lengths until the ellipse fits the contours. If you find an orientation that you don’t have variograms for, rerun the variograms programs for a new orientation.


Jan 2001

Page 2—23


Exercise 2

Page 2—24

Repeat for rock type 2.


Jan 2001


Variogram Parameter File

Select Group Name = STATISTICS 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 1

Nugget

Sill 0.240

Range (major) 70 (10o)

Range (minor) 40 (100o)

0.014

2

0.007

0.085

80 (45o)

60 (135o)

Model type Exponentia l 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.


Jan 2001

Page 2—25


Panel 2

Variogram Parameters

The variogram file will be printed on the screen.

Page 2—26


Jan 2001


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.)


Jan 2001

Page 2—27


Page 2—28


Jan 2001

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

Section 3&Point 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 at selected locations, using different variograms. The theoretical variogram that produces the smallest error can be assumed as the better fit.

Learning Outcome

In this section you will learn: •

Interpolation Controls

How to use point validation for variogram evaluation

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.


Jan 2001

Page 3—1


Point Validation

Page 3—2

Select Group Name = STATISTICS Operations Type = Calculation Procedure Desc. = Point Validation &p52401.dat

Panel 1

File and Area Selection

Panel 2

Search Parameters for Interpolation


Jan 2001


Panel 3

Ellipsoidal Search Parameters

Ellipsoidal Search and use of anisotropic distances are optional.

Panel 4

Angle definition for Ellipsoidal Search


Jan 2001

Page 3—3

Section 3—Point Validation/Cross Validation (for variogram evaluation) Panel 5

Optional Parameters

If the variogram parameter file name is not entered in this panel, you will be asked to enter the variogram parameters.

Panel 6

Optional Geologic Codes

Include Rock Type 1 data only.

Page 3—4


Jan 2001


Panel 7

Optional IDW powers and Other Parameters

Use the default IDW powers.

Files Used

Programs Used

RUN524.CU1 RUN525.CU1 RPT524.CU1 RPT525.CU1

M524V1 M525TS


Jan 2001

Page 3—5

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

Page 3—6


Jan 2001

Section 3—Point Validation/Cross Validation (for variogram evaluation) This section of the report file shows correlation statistics between the actual and kriging values.

Exercise

Modify the variogram parameter file. Use nugget of 0.02. Rerun the point validation procedure. Compare results (you should get a lower correlation and a higher standard error).


Jan 2001

Page 3—7


Page 3—8


Jan 2001

Section 4—Declustering

Section 4&Declustering

Prior to this section you must have calculated the composites and sorted statistics. In this section you will use cell declustering technique to decluster the composite data. This is not required for later work.

Learning Outcome

In this section you will learn: How to decluster composite values How to produce a histogram of declustered composite values

Declustering

There 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.


Jan 2001

Page 4—1


Statistics for Assay Values

Panel 1

Select Group Name = STATISTICS Operations Type = Calculation Procedure Desc. = Decluster Data & p52301.dat

Composite Data Selection

Enter Cu as the composite data item to be used.

Panel 2


Use all the values of Cu.

Page 4—2


Jan 2001


Panel 3

Files Used Programs Used

Area limits and Cell Size

RUN523.50

RPT523.50

M523V1



Jan 2001

Page 4—3


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 the lowest value should be the best choice.

Exercise 3

Try declustering using Rock Type 1 only.

Page 4—4


Jan 2001


Histogram of Declustered Data

Panel 1

Select Group Name = STATISTICS Operation Type= Calculations Procedure Description= ASCII Data Stats— p40204.dat

ASCII Data Statistical Analysis

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

Panel 2


Enter column number for item to analyze from ascii file.


Jan 2001

Page 4—5


Panel 3


Use a frequency interval of .1

Panel 4

Files used

Programs used Mplot Panel

Page 4—6

Histogram plot attributes

RUN122.FRQ DAT402.45 RPT402.45 DAT523.45

RUN402.45 RPT122.LA HIS402.45 PLT402.45

M402V1 M122V1 Select V to view the histogram on the screen. (From viewer, click on X to Exit & go back to MPLOT Panel) Select X to Exit MPLOT panel.


Jan 2001

Section 4—Declustering Plot Reference RUN122.FRQ


Jan 2001

Page 4—7


Page 4—8


Jan 2001

Section 5—Model Interpolation

Section 5&Model 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.

Learning Outcome

Types of Interpolations


In this section you will learn:

The types of interpolations available

The use of controls on the interpolation

How to interpolate grades with MineSight®

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.


Jan 2001

Page 5—1


IDW Interpolation

Page 5—2

Select

Group Name = 3D DEPOSIT MODELING Operations Type = Calculation Procedure Desc. = IDW Interpolation &p62001.dat

Panel 1

M620V1 File and Model Area Specifications

Panel 2

M620V1 Input Search Parameters Specify 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.


Jan 2001


Panel 3

Interpolation Control Items Interpolate the Cu and Mo grades.

Panel 4

Store Local Error


Jan 2001

Page 5—3


Page 5—4

Panel 5

Optional Search Parameters

Panel 6

Optional Rotation Angles These angles need to be specified when ellipsoidal search is used for composite selection


Jan 2001


Panel 7

Optional Geologic Codes Use only Rock Type 1.

Panel 8

Optional Data Selection Include Rock Type 1 and 2 data only.


Jan 2001

Page 5—5


Files Used

Programs Used

Exercise

RUN620.id1 RPT620.id1

M620V1

Rerun for Rock Type 2. Change search distances and use option omit. Change the following panels:

Page 5—6


Jan 2001



Jan 2001

Page 5—7


Page 5—8


Jan 2001

Section 6—Kriging

Section 6&Kriging

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.

Learning Outcome

In this section you will learn: C

Ordinary Kriging

How to set up and run a Kriging interpolation

Ordinary kriging is an estimator designed primarily for the local estimation of 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 linear because its estimates are weighted linear combinations of the available data; it is unbiased since the sum of the weights add up to 1; it is best because 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 with MineSight®

Before producing an interpolation using kriging, you must have developed a variogram. Three types of variograms are allowed: C

Spherical

C

Linear

C

Exponential


Jan 2001

Page 6—1

Section 6—Kriging

Select Group Name = 3D DEPOSIT MODELING Operations Type = Calculations 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.

Page 6—2


Jan 2001

Section 6—Kriging Panel 3

Interpolation Control Items

Krige the Cu grades on each bench.

Panel 4

Optional Input Parameters.

Leave blank if not used.


Jan 2001

Page 6—3

Section 6—Kriging

Panel 5


Enter the variogram parameters used in Kriging.

Panel 6

Page 6—4

Optional Sear Parameters


Jan 2001

Section 6—Kriging

Panel 7

Optional Rotation Angles

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

Panel 8


Use Rock Type 1.


Jan 2001

Page 6—5

Section 6—Kriging Panel 9


Include Rock Type 1 and 2 data only.

Files Used

Programs Used

Exercise

Page 6—6

RUN624.KRG RPT624.KRG M624V1

Repeat calculations for Rock Type 2. Use variograms calculated in Section 2. Change search distances as you did for IDW.


Jan 2001

Section 7—Point Validation/Cross Validation

Section 7&Point 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 of composite data at selected locations. Then, you can decide which method is more appropriate. You can also validate search parameters.

Learning Outcome

Types of Point Interpolations



The types of interpolations available in point validation

•

The use of controls on the interpolation

•

How to interpolate point grades with MineSight®

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.


Jan 2001

Page 7—1


Point Validation

Page 7—2

Select Group Name = STATISTICS Operations Type = Calculation Procedure Desc. = Point Validation —p52401.dat

Panel 1

File and Area Selection

Panel 2

Search Parameters for Interpolation


Jan 2001


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


Jan 2001

Page 7—3

Section 7—Point Validation/Cross Validation Panel 5

Panel 6




Page 7—4


Jan 2001


Panel 7

Optional IDW powers and Other Parameters

Use the default IDW powers.

Files Used

Programs Used

RUN524.CU1 RUN525.CU1 RPT524.CU1 RPT525.CU1

M524V1 M525TS


Jan 2001

Page 7—5


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.

Page 7—6


Jan 2001

Section 7—Point Validation/Cross Validation This section of the report file shows correlation statistics between the actual and Kriging values.

This section of the report file shows correlation statistics between the actual and inverse distance values.

Exercise

Change some of the search parameters and rerun the above procedure. What do you observe?


Jan 2001

Page 7—7


Page 7—8


Jan 2001

Section 8—Model Statistics/Geologic Resources

Section 8&Model Statistics/Geologic Resources

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.

Learning Outcome

In this section you will learn: C C C C C

Reserve Calculations

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

To calculate initial reserves from the block model, use M608V1 (i.e., STATISTICS Calculations Statistics (Model). Refer to the STRIPPER reserves 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.


Jan 2001

Page 8—1


Model Statistics

Page 8—2

Select Group Name = STATISTICS Operations Type = Calculation Procedures Desc. = Statistics (Model) — p60801.dat

Panel 1

File Selection

Panel 2

Item Selection

Panel 3

Cutoff Grades and Frequency Parameters


Jan 2001


Panel 4


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


Jan 2001

Page 8—3


Panel 5

Selection of Mine Model Limits

You may optionally select a portion of the model to calculate the reserves.

Panel 6

Page 8—4



Jan 2001


Files Used

Programs Used

RUN608.CUI RPT608.CUI DAT608.CUI HIS608.CUI PLT608.CUI RUN122.MFR M608V1 A statistical summary and histogram can be found in the report file.

This section of the report file shows the grade and tonnage of CUID, CUKRG, CUPLY and MOID values at specified cutoffs.

This section of the report file shows the tonnage and grade of CUID values at each bench. The grade is reported at whatever the minimum value specified on Panel 3


Jan 2001

Page 8—5


MPLOT Panel

Select V to view the histogram on the screen.

Plot Reference RUN122.MFR

Exercise

Page 8—6

Generate model statistics for items from IDW, polygonal and Kriging methods 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.


Jan 2001


Grade/Tonnage Plots Panel 1

Select Group Name = STATISTICS Operations Type = Plot Procedure Desc. = Grade/Tonnage Plots — pgtplt 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 or color specified.

MPLOT Panel

Select V to view the curves on the screen. (From Viewer, Click on X to Exit and go back to MPLOT Panel) Select X to Exit MPLOT Panel.


Jan 2001

Page 8—7


Plot Reference RUN122.MSG

Page 8—8


Jan 2001


Plot IDW and Kriging Histograms Together Panel 1

Select Group Name = Adv Plotting/VBM Operations Type = Plot Procedures Desc. = Plot any USERF/DATAF – anyplt.dat

Plotting panel

Enter scale and x,y limits (plotting units, not project). Plotting files are USERF. Use appropriate shift command.


Jan 2001

Page 8—9


Model Statistics At and Between Cutoffs

Page 8—10

Select Group Name = STATISTICS Operations Type = Calculation Procedures Desc. = Statistics at User Cutoffs (Model) — p60802.dat

Panel 1

File Selection

Panel 2

Item Selection


Jan 2001


Panel 3

Cutoff Specification

Check the box not to accumulate intervals.

Panel 4


Select blocks with Rock code 1 only. Enter 16.2 as multiplier for resource calculation. This is the Ktonnage/block for our project.


Jan 2001

Page 8—11


Panel 5

Mine Model Statistical Analysis

Calculate the statistics for benches 21-40.

Panel 6

Files Used

Programs Used

Page 8—12


RUN608.Ci2 RPT608.Ci2 DAT608.Ci2 HIS608.Ci2 PLT608.Ci2 RUN122.MFR M608V1


Jan 2001


This section of the report file shows the grade and tonnage of CUID values at user specified cutoffs. Note that the figures are for between the cutoffs.


Jan 2001

Page 8—13


Select Group Name = STATISTICS Operations Type = Calculation Procedure Desc. = Correlations (Model)—p61801.dat

Model Correlations Panel 1

File Selection

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.

Page 8—14


Jan 2001

Section 8—Model Statistics/Geologic Resources Panel 3

Optional Plot Parameters and Data Selection

Select benches 21-40.

Panel 4


Limit the correlation statistics to Rock Types 1 only.

Files Used

Programs Used

RUN618.CU PLT618.CU

RPT618.CU, RUN122.MSG

M608V1 M122V1


Jan 2001

Page 8—15


This section of the report file shows the summary of correlation statistics between CUID and CUKGR values.

MPLOT Panel

Page 8—16

Select V to view the scatter plot on the screen. (From Viewer, Click on X to Exit and go back to MPLOT Panel) Select X to Exit MPLOT Panel.


Jan 2001

Section 8—Model Statistics/Geologic Resources Plot Reference RUN122.MSG

Exercise

Calculate the correlations between polygonal and Kriging grades. What do you observe?


Jan 2001

Page 8—17


Probability Plots

Panel 1

Panel 2

Select Group Name = 3D DEPOSIT MODELING Operation Type= Plot Procedure Description= Probability Plots (model)-p61901.dat

File Selection

Item Selection

Select item CUKRG.

Page 8—18


Jan 2001



Panel 4

Optional Plot Files


Jan 2001

Page 8—19


Files used

Programs used

Mplot Panel

Page 8—20


RUN619.A RPT619.LA RUN122.MCP RPT122.LA PLT619.LA M619V1 M122V1

Select V to view the probability plot on the screen. (From viewer, click on X to Exit & go back to MPLOT Panel) Select X to Exit MPLOT panel.


Jan 2001

Section 8—Model Statistics/Geologic Resources Plot Reference RUN122.MCP

Exercise

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


Jan 2001

Page 8—21


Page 8—22


Jan 2001

Section 9—Model Calculations

Section 9&Model Calculations

In this section you will calculate block values for item EQCU and store them in the model.

Learning Outcome


How to perform calculations using information stored in the model

Select Group Name = 3-D DEPOSIT MODELING Operations Type = Calculation Procedure Desc. = User-Calcs (Model)—p61201.dat

Model Calculations

Panel 1

Mine Model/Surface File Data Items

Specify number of levels, rows, and columns.


Jan 2001

Page 9—1


Panel 2

Mine Model/Surface File Data Items

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

Panel 3


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

Page 9—2


Jan 2001


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


Jan 2001

Page 9—3


Page 9—4


Jan 2001

Section 10—Quantifying Uncertainty

Section 10—Quantifying 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 results of the block model calculations. We will use different approaches: • • • •

Distance to the Closest Composites Calculations

Distance to the closest composite, Kriging variance, Combined Kriging variance Relative Variability Index

Assign the value of 1 to model item ZONE, when DISTP = 0 to 39 (since we used 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 to 57m, 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


Jan 2001

Page 10—1


Panel 2

Undefined values

Do not substitute undefined values

Panel 3

Page 10—2



Jan 2001

Section 10—Quantifying Uncertainty Panel 4

Define calculation

Panel 5

Store item back to model


Jan 2001

Page 10—3


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

Page 10—4

Make a model view of item ZONE.


Jan 2001


Kriging Variance

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

Combined Kriging Variance

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).


Jan 2001

Page 10—5


Relative Variability Index

Page 10—6

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?


Jan 2001

Section 11—Change of Support

Section 11—Change of Support 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.

Learning Outcome

In this section you will learn: C C C C C C C

Change of Support

What change of support means How to determine indicator cutoffs How to calculate block variance for different size blocks What is Krige’s relationship of variance How to determine change of support correction factor How to do global change of support correction Change of support methods

The term support at the sampling stage refers to the characteristics of the sampling 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 term support refers 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 to account 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.

Krige’s Relationship of Variance

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: 2 p

=

2 b

+


2 p b

January 2001

Page 11—1


Calculation of Block Variance Panel 1

Select Group Name = STATISTICS Operations Type = Calculation Procedure Desc. = Block variance - psblkv.dat Block Variance Calculation

The output report file summarizes the following:

Page 11—2


January 2001


Files Used

Programs Used

VARIO.RK1 MSBLKV.PAR MSBLKV.RPT MSBLKV

Exercise 1

Change block size to 10x10 and re-run the procedure. What change do you see in the block variance?

Exercise 2

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

Exercise 3

If you have another variogram parameter file, try running the procedure with it. What do you observe?


January 2001

Page 11—3


Change of Support on Composite Values Panel 1

Select Group Name = Statistics Operations Type = Calculation Procedure Desc. = Statistics (comps) — p40201.dat 3-D Composite Data Statistical Analysis

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

Panel 2


Make sure to check the change of support option.

Page 11—4


January 2001


Panel 3

Change of Support Parameters

Panel 4


Select Rock Type 1.


January 2001

Page 11—5


Panel 5



Panel 6



Files Used

Programs Used

Page 11—6


RPT402.CU BLOCK.DAT HIS402.CU RUN122.FRQ

M402V1

M122V1


January 2001


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.


January 2001

Page 11—7


Distribution of Theoretical Blocks Panel 1

Select Group Name = STATISTICS Operations Type = Calculation Procedure Desc. = Statistics - ASCII - p40204.dat ASCII Data Statistical Analysis

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

Panel 2

Free Format Specs

Select Column #1 to read.

Page 11—8


January 2001


Panel 3


Panel 4


Files Used

Programs Used

RUN402.D RPT402.BLK DAT402.BLK HIS402.BLK PIT402.BLK RUN122.FRQ BLOCK.DAT M402V1

M122V1


January 2001

Page 11—9


MPLOT Panel

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


Page 11—10


January 2001


Volume-Variance Correction on Composite Data Panel 1

Panel 2

Select Group Name = STATISTICS Operations Type = Calculation Procedure Desc. = Volume-variance (comps) - pcmpvc.dat

Select the File to Use

Volume-Variance Correction in Composite grades

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


January 2001

Page 11—11


Panel 3


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

Page 11—12

RUN508.A RPT508.LVC


January 2001


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 extension AFF.

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)


January 2001

Page 11—13


Select Group Name = Adv Plotting/VBM Operations Type = Plot Procedure Desc. = Plot any USERF/DATAF - anyplt.dat

Plotting Panel

Page 11—14

Enter scale and x,y limits (plotting units, not project). Plotting files are USERF. Use appropriate shift command.


January 2001


Volume Variance Correction on Model Data Panel 1

Select Group Name = STATISTICS Operations Type = Calculation Procedure Desc. = Volume-variance - pmodvc.dat Select the File to Use

Enter benches 21-30.

Panel 2

Select Items to be Used

Select indirect lognormal correction option.


January 2001

Page 11—15


Panel 3


Select Rock Type 1.

Panel 4

Files Used

Page 11—16

Volume-Variance Correction Parameters

RUN612.A RPT612.LVC


January 2001


RPT612.LVC

Summary of the results from Volume-Variance correction is displayed.

Exercise 1

Run stats on item CUKGG to look at the new distribution.

Exercise 2

Plot grade-tonnage curves of CUKRG and CUKGG items to compare the original and corrected grade distributions.


January 2001

Page 11—17


Page 11—18


January 2001

Section 12—Indicator Kriging

Section 12—Indicator Kriging to Define Geologic Boundary above a Cutoff Prior to this section you should have the composite and 3-D model initialized and loaded.

Learning Outcome

In this section you will learn: C C C

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 each block having a grade value above the cutoff.

Assign Indicators

Select Group Name = COMPOSITES Operation Type = Calculations Procedure Desc. = User-Calcs (comps) - p50801.dat

Panel 1

Labels of Composite Items to use

Use item altrx as the item to store the indicators.


Jan 2001

Page 12—1


Panel 2


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

Panel 3

Page 12—2

Limits for Data Selection


Jan 2001


Panel 4

Special Project Calculations

Assign an initial code of 0 to item altrx.

Files Used

Program used

RUN508.A RPT508.LA M508RP Repeat the procedure, but this time enter a range for cu from 0.3 to 99, and use altrx =1.


Jan 2001

Page 12—3


Variogram of Indicators Panel 1

Select Group = COMPOSITES Operation types = Calculation Procedure Desc. = Variograms (comp)- p30302.dat Experimental Variograms for 3-D Composites

Enter ALTRX as the item to use.

Panel 2

Page 12—4



Jan 2001


Panel 3


Use both rock types.

Panel 4



Jan 2001

Page 12—5


Panel 5

Files used

Programs used

Parameters for Multi-Directional Variograms

RUN303.ALT DAT303.ALT RPT303.ALT M303V2 Select Group = COMPOSITES Operation Type = Calculations Procedure Desc. = Variogram Modeling - p30002.dat

Model the Indicator Variogram Panel 1

Variogram File Input

Enter output from previous exercise.

Page 12—6


Jan 2001


Pick the 3-D global variogram from the list and exit panel. Make a new model. (nugget = .068, sill = .234, range = 370).

Files used

Programs used

RUN300.A DAT303.ALT M300V1


Jan 2001

Page 12—7


Krige Indicators

Page 12—8

Select Group = 3D DEPOSIT MODELING Operations Type = Calculations Procedure Desc. = Ordinary Kriging - p62401.dat

Panel 1

Files and Model Specification Area

Panel 2

Krige Search Parameters


Jan 2001


Panel 3

Interpolation Control Items

Use composite item ALTRX to interpolate item CUIND.

Panel 4

Optional Input Parameters


Jan 2001

Page 12—9


Panel 5


Use figures from previous exercise.

Leave the rest of the panels blank.

Files used

Programs used

Page 12—10

RUN624.ALT RPT624.ALT M624V1


Jan 2001


View Results in MineSight®

Create a view of item CUIND. Set up intervals of 0 to 1 with an increment of 0.1. Black out all cutoffs except 0.5. What you will see is a probabilistic boundary of model values above 0.3.


Jan 2001

Page 12—11


Page 12—12


Jan 2001

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

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

Learning Outcome

In this section you will learn: C C C C C C C C C

How to determine indicator cutoffs How to calculate indicator variograms How to model indicator variograms How to determine indicator class means How to assign indicators to composite data How to setup indicator variogram parameter files How to calculate affine correction How to do multiple indicator Kriging run How to calculate indicator Kriging reserves

M.I.K.

Multiple Indicator Kriging (M.I.K.) is a technique developed to overcome the problems with estimating local recoverable reserves. The basis of the technique is the indicator function which transforms the grades at each sampled location into a [0,1] random variable. The indicator variograms of these variables are estimated at various cutoff grades. The technique consists of estimating the distribution of composite data. The distribution is then corrected to account for the actual selective mining unit (SMU) size. This yields the distribution of SMU grades within each block. From that distribution, recoverable reserves within the block can be retrieved. Accumulation of recoverable reserves for these blocks over a volume gives the global recoverable reserves for that volume.

Uses of Indicators

Indicators can be used to: C C C C C

deal with outliers model multiple populations estimate categories (descriptive or qualitative variables) estimate distributions estimate confidence intervals


Jan 2001

Page 13—1


Select Group Name = STATISTICS Operations Type = Calculation Procedure Desc. = Statistics (Composites) - p40201.dat

Incremental Statistics Panel 1

Composite Data Statistical Analysis

Enter CU as both the first and the second item. This is because we will use an option in the second panel for not accumulating the intervals.

Panel 2


Enter a frequency interval of 0.02 and set the number of frequency intervals to 100 (maximum). Here you need to check the option not to report the first item and not to accumulate the intervals.

Page 13—2


Jan 2001


Panel 3


Limit the data to Rock Types 1.

Panel 4

Coordinate Limits for Data Selection


Jan 2001

Page 13—3


Panel 5



Files Used

Programs Used

RUN402.IK1 DAT402.IK1 PLT402.IK1

RPT402.IK1 HIS402.IK1 RUN122.FRQ

M402V1 M122V1

The report file shows this summary for each indicator class.

Page 13—4


Jan 2001


MPLOT Panel

Select V to view the histogram on the screen. (From Viewer, click on X to Exit & go back to MPLOT Panel.) Select X to Exit MPLOT Panel.



Jan 2001

Page 13—5


Determine M.I.K. Cutoffs

Select Group Name = MIK Operations Type = Calculation Procedure Desc. = MIK Cutoff Analysis - pikcut.dat This procedure is used to analyze where the M.I.K. cutoffs should be for a given grade distribution and the number of M.I.K. cutoffs specified. The basis of analysis is the metal contained in each indicator class. It is possible that the user may try this procedure several times until he or she is satisfied with the results.

Panel 1

M.I.K. Cutoff Grade Determination

Enter the histogram file output from M402V1 for composites. This file must have been generated using statistics within cutoff option. Enter 10 as the number of M.I.K. cutoffs desired.

Files Used

Programs Used

Page 13—6

MIKCUT.INP MIKCUT.RPT MIKCUT.PAR DAT402.IK1 MIKCUT.OUT MIKCUT


Jan 2001


The report file shows a summary of the statistics calculated at specified increments.


Jan 2001

Page 13—7


Select Group Name = MIK Operations Type = Calculation Procedure Desc. = Statistics for IK — p40202.dat

Statistics for M.I.K.

Panel 1


Enter Cu as the base assay for cutoffs.

Panel 2


Enter the indicator cutoffs.

Page 13—8


Jan 2001


Panel 3


Select Rock Type 1 composites.

Panel 4

Coordinate Limits



Jan 2001

Page 13—9


Panel 5



Files Used

Programs Used

Page 13—10

RUN402.MIK RPT402.MIK DAT402.MIK HIS402.MIK PLT402.MIK RUN122.FRQ

M402V1 M122V1


Jan 2001


This report file (DAT402.MIK) summarizes the indicator class statistics


Jan 2001

Page 13—11


Calculating Indicator Variograms

Select Group Name = MIK Operations Type = Calculation Procedures Desc = Indicator Variograms — p30303.dat Panel 1

Compute Indicator Variograms

Use Composite item CU to compute the variograms.

Panel 2


Specify the cutoffs at which indicator variograms are to be computed.

Page 13—12


Jan 2001


Panel 3


Limit the data input to Rock Type 1 only.

Panel 4




Jan 2001

Page 13—13


Panel 5

Parameters for Multi-Directional Composite Variograms

Compute 2 indicator variograms (2x1), starting at horizontal angle 0.0 with 90 degree increments and a t vertical angle 0.0. Use 10 intervals with 50m lag distance. There will be a set of indicator variograms for each of the 10 cutoffs. There will also be a set of variograms for the grade item. This is the last set.

Files Used

Programs Used

Page 13—14

RUN303.B RPT303.MIK DAT303.MIK M303V2


Jan 2001


In the report file, a summary appears for each variogram calculated. This is a 3-D omni-directional variogram for the first indicator cutoff (IND1).


Jan 2001

Page 13—15


Modeling Indicator Variograms Panel 1

Select Group Name = MIK Operations Type = Calculation Procedures Desc. = Variogram Modeling— p30002.dat Variogram File Input

Program M300V1 will display on the screen a list of the 2 directional variograms plus the 2-D Global variogram and the 3-D Global variogram for each indicator. Click on 3-D Global on each of the 10 indicators and then on Exit Panel.

Page 13—16


Jan 2001


Variogram Parameter File

Panel 1

Select Group Name = MIK Operations Type = Edit Procedure Desc. = MIK Variogram Parameter File — pvgmik.dat Output and Description File

Variogram parameters will be written to the output file specified. Affine correction factor must be equal to or greater than 1.

Panel 2


Enter the parameters for the first cutoff.


Jan 2001

Page 13—17


Variogram parameter file VARIO.MIK setup

Note

Page 13—18

Continue to set up the variogram parameters for the other indicator cutoffs. You can use the figures from the table.


Jan 2001


Multiple Indicator Kriging Panel 1

Panel 2

Select Group Name = MIK Operations Type = Calculation Procedure Desc. = Multiple Indicator Kriging — p62402.dat Select Files / Area

M24IK Search Parameters

Specify a 3-D search to find all composites within 400m horizontally and 50m vertically of a block. Use a maximum of 16 composites.


Jan 2001

Page 13—19


Panel 3

MIK Interpolation Control Items

The program computes the grade and the percent of ore above the specified cutoff for each block and stores them into the 3-D block model.

Panel 4

MIK Input Parameters

MIK variogram parameters file must be specified.

Page 13—20


Jan 2001

Section 13—Multiple Indicator Kriging (M.I.K.) Panel 5



Panel 6

Optional Search Parameters


Jan 2001

Page 13—21


Panel 7


Kriging will be done in Rock Type 1 blocks only.

Files Used

Programs Used

Page 13—22

RUN624.IK0 RUN624.IK0 VARIO.MIK M624IK


Jan 2001


MIK Reserves

Panel 1

Panel 2

Select Group = MIK Operations = Calculation Procedure Desc. = Statistics (model) — p60801.dat 3-D Model Data Statistical Analysis

Model Data Statistical Analysis

Since MIK computes ore percent in each block, a second weighting item is necessary for MIK cutoffs greater than 0.


Jan 2001

Page 13—23


Panel 3

Panel 4

Model Data Statistical Analysis


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

Page 13—24


Jan 2001


Panel 5

Mine Model Statistical Analysis

Calculate the statistics for the specified benches.

Panel 6

Files Used

Programs Used


RUN608.IK0 DAT608.IK0 PLT608.IK0

RPT608.IK0 HIS608.IK0 RUN122.MFR

M608V1


Jan 2001

Page 13—25


This report file summarizes the MIK reserves.

MPLOT Panel

Page 13—26

Select V to view the histogram on the screen.


Jan 2001

Geostatistics 2001

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