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)

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.

Reading in a Readying Data

Interpolation is done with the Pintrp routine – We need to Activate Compass to get it.

Pull downThe menuUnderCompass

Select OpenCompass

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

Under Operations – Click Calculation

Pintrp is the Model Interpolation Routine – Click on it to select it

The Routine Starts – For Method of Interpolation Select Ordinary Kriging

There areManySpecializedKrigingTechniquesThat areBeyond theScope of thisCourse.

Click theForwardArrow to moveTo the nextscreen

We Can Accept the Defaults for the Files and Data Sources to be Used

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.

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

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.

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

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

Asks Whether I Want to Use an Extra Weight Factor for Samples

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.

Screen For Ellipsoidal Search Parameters

We are notGoing toHave any.

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.

Outlier and Low Grade Cut-OffCan let youUse a differentDistance limitIf the sampleHas an extremeGrade.

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.

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

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.

The Practical Problem of Dilution

Allows youTo includeOre dilutionIn block model

We won’t.

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.

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.

Screen Also Deals with Block Discretization

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

Variogram Rock Unit Limits

Allows you toImpose rockType limits toWhich theSemivariogramApplies.(RememberThe StationarityAssumption)

Also Allows You To Decide What To Do About Negative Weights

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

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

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

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

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

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

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

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)

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”)

Time To Enter the Semivariogram!

Pick the modelType(Sph = spherical,The only one youKnow about)

Model can beSingle or containA nestedStructure.

Nugget and Cill Entries

Can also put inRanges inDifferentDirections

Have System for Rotating Coordinates Also

Have the Option to Store Kriging Variance and Well As Grade

ThisExampleIs notGoing toStore theKrigingVariance.

Can Limit Blocks that Get Coded

Useful inAvoidingCoding blocksOf a differentRock type withThe wrongSemivariogram.

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.

The Routine Runs

We Can Set the Model View to Display Our Copper Grades