Geostatistics 2001
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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
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
Introduction to the Course
Page I—2
MineSight® Geostatistics Training Workbook
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.
MineSight® Geostatistics Training Workbook
Jan 2001
Page 1&1
Section 1&Statistics
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
Assay Data Statistical Analysis
A frequency interval of .1 will be used and all values below .0 will be ignored.
Page 1&2
MineSight® Geostatistics Training Workbook
Jan 2001
Section 1&Statistics
Panel 3
Panel 4
Optional Data Selection
Assay Data Statistical Analysis
You have the option of limiting the area of data selection.
MineSight® Geostatistics Training Workbook
Jan 2001
Page 1&3
Section 1&Statistics
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
MineSight® Geostatistics Training Workbook
Jan 2001
Section 1&Statistics
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.
MineSight® Geostatistics Training Workbook
Jan 2001
Page 1&5
Section 1&Statistics
Second report showing summary statistics and histogram
Page 1&6
MineSight® Geostatistics Training Workbook
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
MineSight® Geostatistics Training Workbook
Jan 2001
Page 1&7
Section 1&Statistics
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.
Page 1&8
MineSight® Geostatistics Training Workbook
Jan 2001
Section 1&Statistics
Panel 3
Panel 4
Optional Data Selection
3-D Coordinate Limits for Data Selection
You have the option of limiting the area of data selection.
MineSight® Geostatistics Training Workbook
Jan 2001
Page 1&9
Section 1&Statistics
Panel 5
Histogram Plot Attributes
This panel provides options for setting up your histogram display.
Files Used
Programs Used
Page 1&10
RUN402.CU DAT402.CU PLT402.CU
RPT402.CU HIS402.CU RUN122.FRQ
M402V1 M122V1
MineSight® Geostatistics Training Workbook
Jan 2001
Section 1&Statistics
Run File as it appears in the report file
The report file shows a summary of the statistics calculated.
MineSight® Geostatistics Training Workbook
Jan 2001
Page 1&11
Section 1&Statistics
The report file shows a summary by bench for the distribution of Cu Grades.
Second report with summary statistics and histogram
Page 1&12
MineSight® Geostatistics Training Workbook
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
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.
MineSight® Geostatistics Training Workbook
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Page 1&13
Section 1&Statistics
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
3-D Composite Data Statistical Analysis
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?”
Page 1&14
MineSight® Geostatistics Training Workbook
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Section 1&Statistics
Panel 3
Panel 4
Optional Data Selection
3-D Coordinate Limits for Data Selection
You have the option of limiting the area of data selection.
MineSight® Geostatistics Training Workbook
Jan 2001
Page 1&15
Section 1&Statistics
Panel 5
Histogram Plot Attributes
This panel provides options for setting up your histogram display.
Files Used
Programs Used
Page 1&16
RUN402.RCK RPT402.RCK DAT402.RCK HIS402.RCK PLT402.RCK RUN122.FRQ M402V1 M122V1
MineSight® Geostatistics Training Workbook
Jan 2001
Section 1&Statistics
The report file shows a summary of the Cu Grades at ROCK Cutoffs.
Exercise
Generate Cu statistics within ALTR codes.
MineSight® Geostatistics Training Workbook
Jan 2001
Page 1&17
Section 1&Statistics
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.
Page 1&18
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Section 1&Statistics
Panel 3
Optional Data Selection
Select Rock Types 1 and 2 for plotting.
Panel 4
Optional Plot Files
MineSight® Geostatistics Training Workbook
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Page 1&19
Section 1&Statistics
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
MineSight® Geostatistics Training Workbook
Jan 2001
Section 1&Statistics
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
MineSight® Geostatistics Training Workbook
Jan 2001
Page 1&21
Section 1&Statistics
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.
Page 1&22
MineSight® Geostatistics Training Workbook
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Section 1&Statistics
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.
MineSight® Geostatistics Training Workbook
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Page 1&23
Section 1&Statistics
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
Section 1&Statistics
Run file as it appears in the report file
The report file shows a summary of the statistics calculated in each grid cell.
MineSight® Geostatistics Training Workbook
Jan 2001
Page 1&25
Section 1&Statistics
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.
MineSight® Geostatistics Training Workbook
Jan 2001
Section 1&Statistics
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.
MineSight® Geostatistics Training Workbook
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Page 1&27
Section 1&Statistics Panel 3
Optional Plot Parameters
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
MineSight® Geostatistics Training Workbook
Jan 2001
Section 1&Statistics
Run File as it appears in the report file
The report file shows a summary of correlation statistics for Cu and Mo grades.
MineSight® Geostatistics Training Workbook
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Page 1&29
Section 1&Statistics MPLOT Panel
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
Page 1&30
MineSight® Geostatistics Training Workbook
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Section 1&Statistics
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.
MineSight® Geostatistics Training Workbook
Jan 2001
Page 1&31
Section 1&Statistics
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.
MineSight® Geostatistics Training Workbook
Jan 2001
Section 1&Statistics
Panel 5
Files Used
Programs Used
Parameters for plotting
RUN403.CU PLT403.CU
RPT403.CU RUN122.STU
DAT403.CU
M403V1 M122V1 M607V4
MineSight® Geostatistics Training Workbook
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Page 1&33
Section 1&Statistics
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
Page 1&34
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Section 1&Statistics
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
MineSight® Geostatistics Training Workbook
Jan 2001
Page 1&35
Section 1&Statistics
Page 1&36
MineSight® Geostatistics Training Workbook
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.
MineSight® Geostatistics Training Workbook
Jan 2001
Page 2—1
Section 2—Variograms
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
Page 2—2
Optional Plot Parameters
MineSight® Geostatistics Training Workbook
Jan 2001
Section 2—Variograms
Panel 3
Optional Data Selection
Use Rock Type 1 data only.
Panel 4
Coordinate Limits
MineSight® Geostatistics Training Workbook
Jan 2001
Page 2—3
Section 2—Variograms
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
Run File as it appears in the report file
Page 2—4
MineSight® Geostatistics Training Workbook
Jan 2001
Section 2—Variograms
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.
MineSight® Geostatistics Training Workbook
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.
MineSight® Geostatistics Training Workbook
Jan 2001
Section 2—Variograms
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
MineSight® Geostatistics Training Workbook
Jan 2001
Page 2—7
Section 2—Variograms
Panel 3
Optional Data Selection
Limit the data input to Rock Type 1 only.
Panel 4
Optional Coordinate Limits
You have the option of limiting the area of data selection.
Page 2—8
MineSight® Geostatistics Training Workbook
Jan 2001
Section 2—Variograms
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
MineSight® Geostatistics Training Workbook
Jan 2001
Page 2—9
Section 2—Variograms
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
MineSight® Geostatistics Training Workbook
Jan 2001
Section 2—Variograms
Select Group Name = STATISTICS Operations Type = Calculation Procedures Desc. = Variogram Modeling — p30002.dat
Modeling Variograms
Panel 1
Variogram File Input
MineSight® Geostatistics Training Workbook
Jan 2001
Page 2—11
Section 2—Variograms
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
MineSight® Geostatistics Training Workbook
Jan 2001
Section 2—Variograms
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.
MineSight® Geostatistics Training Workbook
Jan 2001
Page 2—13
Section 2—Variograms
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
MineSight® Geostatistics Training Workbook
Jan 2001
Section 2—Variograms
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.
MineSight® Geostatistics Training Workbook
Jan 2001
Page 2—15
Section 2—Variograms
Panel 3
Panel 4
Optional Variogram Parameters
Optional Data Selections
Limit input data to Rock Type 1 and 2 only.
Page 2—16
MineSight® Geostatistics Training Workbook
Jan 2001
Section 2—Variograms
Panel 5
Optional Coordinate Limits
You have the option of limiting the area of data selection.
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
MineSight® Geostatistics Training Workbook
Jan 2001
Page 2—17
Section 2—Variograms
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
MineSight® Geostatistics Training Workbook
Jan 2001
Section 2—Variograms
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.
MineSight® Geostatistics Training Workbook
Jan 2001
Page 2—19
Section 2—Variograms
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
MineSight® Geostatistics Training Workbook
Jan 2001
Section 2—Variograms
Panel 3
Variogram Contour Parameters
Panel 4
Optional User Plot Files
MineSight® Geostatistics Training Workbook
Jan 2001
Page 2—21
Section 2—Variograms
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.
MineSight® Geostatistics Training Workbook
Jan 2001
Section 2—Variograms
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.
MineSight® Geostatistics Training Workbook
Jan 2001
Page 2—23
Section 2—Variograms
Exercise 2
Page 2—24
Repeat for rock type 2.
MineSight® Geostatistics Training Workbook
Jan 2001
Section 2—Variograms
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.
MineSight® Geostatistics Training Workbook
Jan 2001
Page 2—25
Section 2—Variograms
Panel 2
Variogram Parameters
The variogram file will be printed on the screen.
Page 2—26
MineSight® Geostatistics Training Workbook
Jan 2001
Section 2—Variograms
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.)
MineSight® Geostatistics Training Workbook
Jan 2001
Page 2—27
Section 2—Variograms
Page 2—28
MineSight® Geostatistics Training Workbook
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.
MineSight® Geostatistics Training Workbook
Jan 2001
Page 3—1
Section 3—Point Validation/Cross Validation (for variogram evaluation)
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
MineSight® Geostatistics Training Workbook
Jan 2001
Section 3—Point Validation/Cross Validation (for variogram evaluation)
Panel 3
Ellipsoidal Search Parameters
Ellipsoidal Search and use of anisotropic distances are optional.
Panel 4
Angle definition for Ellipsoidal Search
MineSight® Geostatistics Training Workbook
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
MineSight® Geostatistics Training Workbook
Jan 2001
Section 3—Point Validation/Cross Validation (for variogram evaluation)
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
MineSight® Geostatistics Training Workbook
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
MineSight® Geostatistics Training Workbook
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).
MineSight® Geostatistics Training Workbook
Jan 2001
Page 3—7
Section 3—Point Validation/Cross Validation (for variogram evaluation)
Page 3—8
MineSight® Geostatistics Training Workbook
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.
MineSight® Geostatistics Training Workbook
Jan 2001
Page 4—1
Section 4—Declustering
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
Optional Data Selection
Use all the values of Cu.
Page 4—2
MineSight® Geostatistics Training Workbook
Jan 2001
Section 4—Declustering
Panel 3
Files Used Programs Used
Area limits and Cell Size
RUN523.50
RPT523.50
M523V1
Run File as it appears in the report file
MineSight® Geostatistics Training Workbook
Jan 2001
Page 4—3
Section 4—Declustering
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
MineSight® Geostatistics Training Workbook
Jan 2001
Section 4—Declustering
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
ASCII Data Statistical Analysis
Enter column number for item to analyze from ascii file.
MineSight® Geostatistics Training Workbook
Jan 2001
Page 4—5
Section 4—Declustering
Panel 3
ASCII Data Statistical Analysis
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.
MineSight® Geostatistics Training Workbook
Jan 2001
Section 4—Declustering Plot Reference RUN122.FRQ
MineSight® Geostatistics Training Workbook
Jan 2001
Page 4—7
Section 4—Declustering
Page 4—8
MineSight® Geostatistics Training Workbook
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
Interpolation Controls
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.
Search distance N-S, E-W, and by elevation
Minimum and maximum number of composites to use for a block
Maximum distance to the nearest composite
Use or omit geologic control
In the following example, inverse distance weighting is used without the octant search.
MineSight® Geostatistics Training Workbook
Jan 2001
Page 5—1
Section 5—Model Interpolation
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.
MineSight® Geostatistics Training Workbook
Jan 2001
Section 5—Model Interpolation
Panel 3
Interpolation Control Items Interpolate the Cu and Mo grades.
Panel 4
Store Local Error
MineSight® Geostatistics Training Workbook
Jan 2001
Page 5—3
Section 5—Model Interpolation
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
MineSight® Geostatistics Training Workbook
Jan 2001
Section 5—Model Interpolation
Panel 7
Optional Geologic Codes Use only Rock Type 1.
Panel 8
Optional Data Selection Include Rock Type 1 and 2 data only.
MineSight® Geostatistics Training Workbook
Jan 2001
Page 5—5
Section 5—Model Interpolation
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
MineSight® Geostatistics Training Workbook
Jan 2001
Section 5—Model Interpolation
MineSight® Geostatistics Training Workbook
Jan 2001
Page 5—7
Section 5—Model Interpolation
Page 5—8
MineSight® Geostatistics Training Workbook
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
MineSight® Geostatistics Training Workbook
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
MineSight® Geostatistics Training Workbook
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.
MineSight® Geostatistics Training Workbook
Jan 2001
Page 6—3
Section 6—Kriging
Panel 5
Variogram Parameters
Enter the variogram parameters used in Kriging.
Panel 6
Page 6—4
Optional Sear Parameters
MineSight® Geostatistics Training Workbook
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
Optional Geologic Codes
Use Rock Type 1.
MineSight® Geostatistics Training Workbook
Jan 2001
Page 6—5
Section 6—Kriging Panel 9
Optional Data Selection
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.
MineSight® Geostatistics Training Workbook
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
Interpolation Controls
In this section you will learn: •
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.
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.
MineSight® Geostatistics Training Workbook
Jan 2001
Page 7—1
Section 7—Point Validation/Cross Validation
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
MineSight® Geostatistics Training Workbook
Jan 2001
Section 7—Point Validation/Cross Validation
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
MineSight® Geostatistics Training Workbook
Jan 2001
Page 7—3
Section 7—Point Validation/Cross Validation Panel 5
Panel 6
Variogram Parameters
Optional Geologic Codes
Include Rock Type 1 data only.
Page 7—4
MineSight® Geostatistics Training Workbook
Jan 2001
Section 7—Point Validation/Cross Validation
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
MineSight® Geostatistics Training Workbook
Jan 2001
Page 7—5
Section 7—Point Validation/Cross Validation
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
MineSight® Geostatistics Training Workbook
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?
MineSight® Geostatistics Training Workbook
Jan 2001
Page 7—7
Section 7—Point Validation/Cross Validation
Page 7—8
MineSight® Geostatistics Training Workbook
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.
MineSight® Geostatistics Training Workbook
Jan 2001
Page 8—1
Section 8—Model Statistics/Geologic Resources
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
MineSight® Geostatistics Training Workbook
Jan 2001
Section 8—Model Statistics/Geologic Resources
Panel 4
Optional Data Selection
Enter 16.2 as multiplier for resource calculation. This is the Ktonnage/block for our project.
MineSight® Geostatistics Training Workbook
Jan 2001
Page 8—3
Section 8—Model Statistics/Geologic Resources
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
Histogram Plot Attributes
MineSight® Geostatistics Training Workbook
Jan 2001
Section 8—Model Statistics/Geologic Resources
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
MineSight® Geostatistics Training Workbook
Jan 2001
Page 8—5
Section 8—Model Statistics/Geologic Resources
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.
MineSight® Geostatistics Training Workbook
Jan 2001
Section 8—Model Statistics/Geologic Resources
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.
MineSight® Geostatistics Training Workbook
Jan 2001
Page 8—7
Section 8—Model Statistics/Geologic Resources
Plot Reference RUN122.MSG
Page 8—8
MineSight® Geostatistics Training Workbook
Jan 2001
Section 8—Model Statistics/Geologic Resources
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.
MineSight® Geostatistics Training Workbook
Jan 2001
Page 8—9
Section 8—Model Statistics/Geologic Resources
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
MineSight® Geostatistics Training Workbook
Jan 2001
Section 8—Model Statistics/Geologic Resources
Panel 3
Cutoff Specification
Check the box not to accumulate intervals.
Panel 4
Optional Data Selection
Select blocks with Rock code 1 only. Enter 16.2 as multiplier for resource calculation. This is the Ktonnage/block for our project.
MineSight® Geostatistics Training Workbook
Jan 2001
Page 8—11
Section 8—Model Statistics/Geologic Resources
Panel 5
Mine Model Statistical Analysis
Calculate the statistics for benches 21-40.
Panel 6
Files Used
Programs Used
Page 8—12
Histogram Plot Attributes
RUN608.Ci2 RPT608.Ci2 DAT608.Ci2 HIS608.Ci2 PLT608.Ci2 RUN122.MFR M608V1
MineSight® Geostatistics Training Workbook
Jan 2001
Section 8—Model Statistics/Geologic Resources
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.
MineSight® Geostatistics Training Workbook
Jan 2001
Page 8—13
Section 8—Model Statistics/Geologic Resources
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
MineSight® Geostatistics Training Workbook
Jan 2001
Section 8—Model Statistics/Geologic Resources Panel 3
Optional Plot Parameters and Data Selection
Select benches 21-40.
Panel 4
Optional Data Selection
Limit the correlation statistics to Rock Types 1 only.
Files Used
Programs Used
RUN618.CU PLT618.CU
RPT618.CU, RUN122.MSG
M608V1 M122V1
MineSight® Geostatistics Training Workbook
Jan 2001
Page 8—15
Section 8—Model Statistics/Geologic Resources
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.
MineSight® Geostatistics Training Workbook
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?
MineSight® Geostatistics Training Workbook
Jan 2001
Page 8—17
Section 8—Model Statistics/Geologic Resources
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
MineSight® Geostatistics Training Workbook
Jan 2001
Section 8—Model Statistics/Geologic Resources Panel 3
Optional Data Selection
Panel 4
Optional Plot Files
MineSight® Geostatistics Training Workbook
Jan 2001
Page 8—19
Section 8—Model Statistics/Geologic Resources Panel 5
Files used
Programs used
Mplot Panel
Page 8—20
Optional Plot Parameters
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.
MineSight® Geostatistics Training Workbook
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.
MineSight® Geostatistics Training Workbook
Jan 2001
Page 8—21
Section 8—Model Statistics/Geologic Resources
Page 8—22
MineSight® Geostatistics Training Workbook
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
In this section you will learn: •
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.
MineSight® Geostatistics Training Workbook
Jan 2001
Page 9—1
Section 9—Model Calculations
Panel 2
Mine Model/Surface File Data Items
We will calculate EQCU values from values stored for CUID and MOID.
Panel 3
Optional Data Selection
Restrict EQCU calculations to blocks in Rock Types 1 and 2 only.
Page 9—2
MineSight® Geostatistics Training Workbook
Jan 2001
Section 9—Model Calculations
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
MineSight® Geostatistics Training Workbook
Jan 2001
Page 9—3
Section 9—Model Calculations
Page 9—4
MineSight® Geostatistics Training Workbook
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
MineSight® Geostatistics Training Workbook
Jan 2001
Page 10—1
Section 10—Quantifying Uncertainty
Panel 2
Undefined values
Do not substitute undefined values
Panel 3
Page 10—2
Optional Data Selection
MineSight® Geostatistics Training Workbook
Jan 2001
Section 10—Quantifying Uncertainty Panel 4
Define calculation
Panel 5
Store item back to model
MineSight® Geostatistics Training Workbook
Jan 2001
Page 10—3
Section 10—Quantifying Uncertainty
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.
MineSight® Geostatistics Training Workbook
Jan 2001
Section 10—Quantifying Uncertainty
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).
MineSight® Geostatistics Training Workbook
Jan 2001
Page 10—5
Section 10—Quantifying Uncertainty
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?
MineSight® Geostatistics Training Workbook
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
+
MineSight® Geostatistics Training Workbook
2 p b
January 2001
Page 11—1
Section 11—Change of Support
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
MineSight® Geostatistics Training Workbook
January 2001
Section 11—Change of Support
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?
MineSight® Geostatistics Training Workbook
January 2001
Page 11—3
Section 11—Change of Support
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
3-D Composite Data Statistical Analysis
Make sure to check the change of support option.
Page 11—4
MineSight® Geostatistics Training Workbook
January 2001
Section 11—Change of Support
Panel 3
Change of Support Parameters
Panel 4
Optional Data Selection
Select Rock Type 1.
MineSight® Geostatistics Training Workbook
January 2001
Page 11—5
Section 11—Change of Support
Panel 5
3-D Coordinate Limits for Data Selection
You have the option of limiting the area of data selection.
Panel 6
Histogram Plot Attributes
This panel provides options for setting up your histogram display.
Files Used
Programs Used
Page 11—6
RUN402.CU DAT402.CU PLT402.CU
RPT402.CU BLOCK.DAT HIS402.CU RUN122.FRQ
M402V1
M122V1
MineSight® Geostatistics Training Workbook
January 2001
Section 11—Change of Support
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.
MineSight® Geostatistics Training Workbook
January 2001
Page 11—7
Section 11—Change of Support
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
MineSight® Geostatistics Training Workbook
January 2001
Section 11—Change of Support
Panel 3
ASCII Data Statistical Analysis
Panel 4
Histogram Plot Attributes
Files Used
Programs Used
RUN402.D RPT402.BLK DAT402.BLK HIS402.BLK PIT402.BLK RUN122.FRQ BLOCK.DAT M402V1
M122V1
MineSight® Geostatistics Training Workbook
January 2001
Page 11—9
Section 11—Change of Support
MPLOT Panel
Click on the Preview/Create Metafile (M122MF) Button.
Plot Reference RUN122.FRQ
Page 11—10
MineSight® Geostatistics Training Workbook
January 2001
Section 11—Change of Support
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).
MineSight® Geostatistics Training Workbook
January 2001
Page 11—11
Section 11—Change of Support
Panel 3
Optional Data Selection
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
MineSight® Geostatistics Training Workbook
January 2001
Section 11—Change of Support
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)
MineSight® Geostatistics Training Workbook
January 2001
Page 11—13
Section 11—Change of Support
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.
MineSight® Geostatistics Training Workbook
January 2001
Section 11—Change of Support
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.
MineSight® Geostatistics Training Workbook
January 2001
Page 11—15
Section 11—Change of Support
Panel 3
Optional Data Selection
Select Rock Type 1.
Panel 4
Files Used
Page 11—16
Volume-Variance Correction Parameters
RUN612.A RPT612.LVC
MineSight® Geostatistics Training Workbook
January 2001
Section 11—Change of Support
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.
MineSight® Geostatistics Training Workbook
January 2001
Page 11—17
Section 11—Change of Support
Page 11—18
MineSight® Geostatistics Training Workbook
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.
MineSight® Geostatistics Training Workbook
Jan 2001
Page 12—1
Section 12—Indicator Kriging
Panel 2
Optional Data Selection
Use RANGE for the calculation on rock type and cu grade.
Panel 3
Page 12—2
Limits for Data Selection
MineSight® Geostatistics Training Workbook
Jan 2001
Section 12—Indicator Kriging
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.
MineSight® Geostatistics Training Workbook
Jan 2001
Page 12—3
Section 12—Indicator Kriging
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
Optional Variogram Parameters
MineSight® Geostatistics Training Workbook
Jan 2001
Section 12—Indicator Kriging
Panel 3
Optional Data Selection
Use both rock types.
Panel 4
3-D Coordinate Limits for Data Selection
MineSight® Geostatistics Training Workbook
Jan 2001
Page 12—5
Section 12—Indicator Kriging
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
MineSight® Geostatistics Training Workbook
Jan 2001
Section 12—Indicator Kriging
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
MineSight® Geostatistics Training Workbook
Jan 2001
Page 12—7
Section 12—Indicator Kriging
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
MineSight® Geostatistics Training Workbook
Jan 2001
Section 12—Indicator Kriging
Panel 3
Interpolation Control Items
Use composite item ALTRX to interpolate item CUIND.
Panel 4
Optional Input Parameters
MineSight® Geostatistics Training Workbook
Jan 2001
Page 12—9
Section 12—Indicator Kriging
Panel 5
Variogram Parameters
Use figures from previous exercise.
Leave the rest of the panels blank.
Files used
Programs used
Page 12—10
RUN624.ALT RPT624.ALT M624V1
MineSight® Geostatistics Training Workbook
Jan 2001
Section 12—Indicator Kriging
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.
MineSight® Geostatistics Training Workbook
Jan 2001
Page 12—11
Section 12—Indicator Kriging
Page 12—12
MineSight® Geostatistics Training Workbook
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
MineSight® Geostatistics Training Workbook
Jan 2001
Page 13—1
Section 13—Multiple Indicator Kriging (M.I.K.)
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
Composite Data Statistical Analysis
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
MineSight® Geostatistics Training Workbook
Jan 2001
Section 13—Multiple Indicator Kriging (M.I.K.)
Panel 3
Optional Data Selection
Limit the data to Rock Types 1.
Panel 4
Coordinate Limits for Data Selection
MineSight® Geostatistics Training Workbook
Jan 2001
Page 13—3
Section 13—Multiple Indicator Kriging (M.I.K.)
Panel 5
Histogram Plot Attributes
This panel provides options for setting up your histogram display.
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
MineSight® Geostatistics Training Workbook
Jan 2001
Section 13—Multiple Indicator Kriging (M.I.K.)
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
MineSight® Geostatistics Training Workbook
Jan 2001
Page 13—5
Section 13—Multiple Indicator Kriging (M.I.K.)
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
MineSight® Geostatistics Training Workbook
Jan 2001
Section 13—Multiple Indicator Kriging (M.I.K.)
The report file shows a summary of the statistics calculated at specified increments.
MineSight® Geostatistics Training Workbook
Jan 2001
Page 13—7
Section 13—Multiple Indicator Kriging (M.I.K.)
Select Group Name = MIK Operations Type = Calculation Procedure Desc. = Statistics for IK — p40202.dat
Statistics for M.I.K.
Panel 1
Composite Data Statistical Analysis
Enter Cu as the base assay for cutoffs.
Panel 2
Assay Data Statistical Analysis
Enter the indicator cutoffs.
Page 13—8
MineSight® Geostatistics Training Workbook
Jan 2001
Section 13—Multiple Indicator Kriging (M.I.K.)
Panel 3
Optional Data Selection
Select Rock Type 1 composites.
Panel 4
Coordinate Limits
You have the option of limiting the area of data selection.
MineSight® Geostatistics Training Workbook
Jan 2001
Page 13—9
Section 13—Multiple Indicator Kriging (M.I.K.)
Panel 5
Histogram Plot Attributes
This panel provides options for setting up your histogram display.
Files Used
Programs Used
Page 13—10
RUN402.MIK RPT402.MIK DAT402.MIK HIS402.MIK PLT402.MIK RUN122.FRQ
M402V1 M122V1
MineSight® Geostatistics Training Workbook
Jan 2001
Section 13—Multiple Indicator Kriging (M.I.K.)
This report file (DAT402.MIK) summarizes the indicator class statistics
MineSight® Geostatistics Training Workbook
Jan 2001
Page 13—11
Section 13—Multiple Indicator Kriging (M.I.K.)
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
Optional Variogram Parameters
Specify the cutoffs at which indicator variograms are to be computed.
Page 13—12
MineSight® Geostatistics Training Workbook
Jan 2001
Section 13—Multiple Indicator Kriging (M.I.K.)
Panel 3
Optional Data Selection
Limit the data input to Rock Type 1 only.
Panel 4
Optional Coordinate Limits
You have the option of limiting the area of data selection.
MineSight® Geostatistics Training Workbook
Jan 2001
Page 13—13
Section 13—Multiple Indicator Kriging (M.I.K.)
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
MineSight® Geostatistics Training Workbook
Jan 2001
Section 13—Multiple Indicator Kriging (M.I.K.)
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).
MineSight® Geostatistics Training Workbook
Jan 2001
Page 13—15
Section 13—Multiple Indicator Kriging (M.I.K.)
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
MineSight® Geostatistics Training Workbook
Jan 2001
Section 13—Multiple Indicator Kriging (M.I.K.)
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
Variogram Parameters
Enter the parameters for the first cutoff.
MineSight® Geostatistics Training Workbook
Jan 2001
Page 13—17
Section 13—Multiple Indicator Kriging (M.I.K.)
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.
MineSight® Geostatistics Training Workbook
Jan 2001
Section 13—Multiple Indicator Kriging (M.I.K.)
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.
MineSight® Geostatistics Training Workbook
Jan 2001
Page 13—19
Section 13—Multiple Indicator Kriging (M.I.K.)
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
MineSight® Geostatistics Training Workbook
Jan 2001
Section 13—Multiple Indicator Kriging (M.I.K.) Panel 5
Optional Data Selection
Include Rock Type 1 data only.
Panel 6
Optional Search Parameters
MineSight® Geostatistics Training Workbook
Jan 2001
Page 13—21
Section 13—Multiple Indicator Kriging (M.I.K.)
Panel 7
Optional Geologic Codes
Kriging will be done in Rock Type 1 blocks only.
Files Used
Programs Used
Page 13—22
RUN624.IK0 RUN624.IK0 VARIO.MIK M624IK
MineSight® Geostatistics Training Workbook
Jan 2001
Section 13—Multiple Indicator Kriging (M.I.K.)
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.
MineSight® Geostatistics Training Workbook
Jan 2001
Page 13—23
Section 13—Multiple Indicator Kriging (M.I.K.)
Panel 3
Panel 4
Model Data Statistical Analysis
Optional Data Selection
Enter 16.2 as multiplier for resource calculation. This is the Ktonnage/block for our project.
Page 13—24
MineSight® Geostatistics Training Workbook
Jan 2001
Section 13—Multiple Indicator Kriging (M.I.K.)
Panel 5
Mine Model Statistical Analysis
Calculate the statistics for the specified benches.
Panel 6
Files Used
Programs Used
Histogram Plot Attributes
RUN608.IK0 DAT608.IK0 PLT608.IK0
RPT608.IK0 HIS608.IK0 RUN122.MFR
M608V1
MineSight® Geostatistics Training Workbook
Jan 2001
Page 13—25
Section 13—Multiple Indicator Kriging (M.I.K.)
This report file summarizes the MIK reserves.
MPLOT Panel
Page 13—26
Select V to view the histogram on the screen.
MineSight® Geostatistics Training Workbook
Jan 2001
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