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![Page 1: Using Statistical Interpolation to Build Block Models – Part III (Using Pintrp.dat to project sample values to blocks) Using MineSight® ©2007 Dr. B. C.](https://reader035.fdocuments.us/reader035/viewer/2022062804/56649ebd5503460f94bc6a7c/html5/thumbnails/1.jpg)
Using Statistical Interpolation to Build Block Models – Part III(Using Pintrp.dat to project sample values to blocks)
Using MineSight®©2007 Dr. B. C. Paul(Note – The Screenshots contained in this show are operating views of the MineSight® computer programs and the steps suggested for operating include ideas taken from Minetec operating manuals, courses, publications, or technical support advice)
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To Put Ore Grades Into The Block Model, You Need Samples
Most of samples today are from core drilling and assays. Because this has been the major
method for 60 years Many ore deposits are reviewed more
than once before being developed Most deposits may have drilling and
assay data in a variety of formats. We have to get this data into MineSight
to use it.
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Reading in a Readying Data
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Interpolation is done with the Pintrp routine – We need to Activate Compass to get it.
Pull downThe menuUnderCompass
Select OpenCompass
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Compass is a Large Collection of Programs – We can simplify our life by filtering which ones we look at.
On group –Push theDown arrowTo get theMenu
Then select3D modeling
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Under Operations – Click Calculation
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Pintrp is the Model Interpolation Routine – Click on it to select it
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The Routine Starts – For Method of Interpolation Select Ordinary Kriging
There areManySpecializedKrigingTechniquesThat areBeyond theScope of thisCourse.
Click theForwardArrow to moveTo the nextscreen
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We Can Accept the Defaults for the Files and Data Sources to be Used
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We Have to Decide on How Far to Search for Samples
My selectionsWill resultIn samplesFrom a 300X 300 meterSquare onThe sameLevel andRequire atLeast 2 Samples toInterpolateAnd limit toNo more than30.
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Searching Ranges
Pintrp lets you use a variety of interpolation techniques Even without semivariograms and ranges of
influence people have understood that distant samples may not be relevant
Allowed people to impose a sort of influence range. (Semivariograms will automatically weight for that)
In Kriging most of the weight will go the best positioned closer samples Since you may be Kriging 1,000,000 blocks lets
you go for faster computation by eliminating samples that will get little weight anyways
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Next Screen Wants to Know if I will Limit samples by the Quadrant they come from
I am choosingNot to limit.
If my samplesAre allClusteredKriging willAdjust sampleWeights forThat.
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Why Quadrant Limits
Pintrp allows many types of interpolation Old methods don’t consider how the samples
may be related to each other Allowed people to try to prevent all the weight
from coming from just one direction In Kriging sample inter-relationships are
considered. If you have 7 samples in one quadrant and 1 in
the other 3 each quadrant may get about 25% and the seven samples will share the weight for their quadrant
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It Needs to Know What Variables I Will Store my Data in.
Note that if ICreate placesFor the dataIn my blockModel I canStore whatData I usedFor eachInterpolation.
I’m notStoring that inMy example
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Asks Whether I Want to Use an Extra Weight Factor for Samples
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Why Extra Weight Factors
Some samples may be longer than others
Some methods that try to adjust by instinct feel that larger samples should get more weight Kriging considers the amount of
variance averaged out in a sample or if they are small considers them point samples
We composited our samples to bench height so not really an issue for us.
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Screen For Ellipsoidal Search Parameters
We are notGoing toHave any.
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Why Ellipsoidal Search
Pintrp allows a lot of techniques Old techniques understood continuity
was greater in some direction than others but had no regular way to accommodate
Kriging of course build geometric anisotropy into semivariogram
Alternative approach was to search further in some directions than other and then alter distance estimates by direction.
Obviously we don’t need it here.
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Outlier and Low Grade Cut-OffCan let youUse a differentDistance limitIf the sampleHas an extremeGrade.
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This was important for non-geostatistical techniques
Remember the issue that large blocks are much less variable than little samples
Problem is that we evaluate block by weighting samples that are far more variable than the blocks they will predict Old timers found that when they used
COVs they expected to get a bigger grade boost than they really had.
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The Problem
COV
Distribution of blocks
Distribution of samples
The old routines overpredictedWidth of distribution. TheyWould expect to mine only the best70% and instead mine the best95% so they over-estimated theirgrades
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The Old Timer Solution
Create arbitrary ways of screening out high or low grade values to try to force a narrower distribution
Kriging automatically compensates for distribution width differences between samples and blocks.
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The Practical Problem of Dilution
Allows youTo includeOre dilutionIn block model
We won’t.
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The Dilution Problem
Interpolation predicts the grade of inplace rock – but sometimes we don’t mine in place rock. Underground Caving Methods lots of
outside rock mixes in as ore is drawn to draw points
Surface Mining Blasting May stir the layers of rock together
This is a mining method dependent problem not addressed by Kriging.
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Screen to Allow Variogram Parameters to be in a file or a rotation of coordinates with respect to project coordinates
We will enterOur variogramInteractively
We will alsoAssume weDon’t needTo rotateCoordinates.
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Screen Also Deals with Block Discretization
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What is Discretization
Kriging will require theAverage value of gammaBetween each sample andThe block
This is calculated with aMathematical approximation.Block is divided into blocksAnd then gamma betweenThe sample and each one ofThe points is averaged to getThe average gamma.
MineSight’s default is 4X4.I changed it cause I like 5X5
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Variogram Rock Unit Limits
Allows you toImpose rockType limits toWhich theSemivariogramApplies.(RememberThe StationarityAssumption)
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Also Allows You To Decide What To Do About Negative Weights
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What Are Negative Weights
Interpolation schemes assign blocks a weighted average grade of the surrounding samples
The Minimization of Error Variance Scheme of Kriging can result in some samples being assigned negative weights Sample Weights must add up to one But sometimes one sample may be a better
predictor than another by more than one unit Practical result is that samples can be
assigned negative weights
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Emotional Comfort
I have no problem understanding but some people feel no real sample could ever have a negative influence on something. That’s not an issue if you look at
weights as relative influence to each other
Sometimes its more than emotional if a block gets assigned a negative ore grade
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A Real Life Story
There was a channel cutting through a coal seam with good reserves on the other side and some sampling
One attempt to go through the channel had run into problems with pinching out in a lense
Geologists drew different projections into the reserve Used geostatistics to appraise the reserve
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Results
The reserve contained only 70% of the coal reserves projected by the most pessimistic geologist But some of the coal blocks came out
with negative thickness Those blocks had assigned a negative
weight greater than -1 to a thick coal seam sample
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What Was Done and What Did it Mean
Semivariogram model used was Gaussian Gaussian assumes that samples don’t loose much
influence for the first little bit Remember Stationarity
The area on the other side of the channel had little wash out pockets
It was a separate geologic process Semivariogram fit the original thinning and thickening of
the coal The washouts were very short range local events They were not Stationary in their localized area Drill grid was 500 feet and could not pick up the
washouts Negative thickness coal blocks picked up a big
positive weight in a washout and a negative weight in an undisturbed coal
Semivariogram could not account for the local loss of stationarity
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What Happened
We Switched to a Spherical Semivariogram More forgiving of the local difference in stationarity Does not result in large negative weights Over-all reserve appraisal stayed the same but the
negative thickness blocks went away. Company was warned that available reserves
were less than they had hoped (even on a bad day) They would either have to do a drill grid in the 100
ft center range (tough given the rough terrain and 1200 ft depth) or mine flexible enough to keep running into the washout lenses
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Negative Weight Alternatives In MineSight®
Option 0 – Do nothing – if the weight is negative so be it.
Option 1 – Check the predicted block value If it is below a user specified minimum
then turn all negative weights to 0 and normalize the remaining weights to equal 1.
No that is not a true Kriging approach
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More Choices
Option 2 – Without regard to the predicted value, zero all negative weights and normalize the remaining to 1.
Option 3 – Drop samples with negative weights and re-Krig with the remaining samples till there are no more negative weights
Literature Contains a means to add a no negative weights equation and then find the minimum error variance subject to a no negative weights allowed (MineSight® does not have code for this option)
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My Suggestion
Use MineSight’s® default 0 option and allow negative weights Spherical models are robust, they seldom
assign large enough negative weights to make a difference
Negative weights will only bite you if you have a stationarity problem
MineSight only allows exponential, spherical, or linear models all of which are naturally robust
They don’t have the Gaussian model (which is a great model for normally distributed sedimentation events with good stationarity – but a real touchy model if you can’t say “stationarity”)
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Time To Enter the Semivariogram!
Pick the modelType(Sph = spherical,The only one youKnow about)
Model can beSingle or containA nestedStructure.
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Nugget and Cill Entries
Can also put inRanges inDifferentDirections
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Have System for Rotating Coordinates Also
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Have the Option to Store Kriging Variance and Well As Grade
ThisExampleIs notGoing toStore theKrigingVariance.
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Can Limit Blocks that Get Coded
Useful inAvoidingCoding blocksOf a differentRock type withThe wrongSemivariogram.
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Handling Blocks that Don’t Have Samples Close Enough to Interpolate
Default is toSet the valueTo missing.
There isA differenceBetween a Zero gradeAnd an I don’tKnow.
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The Routine Runs
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We Can Set the Model View to Display Our Copper Grades