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 down The menu Under Compass Select Open Compass

Compass is a Large Collection of Programs – We can simplify our life by filtering which ones we look at. On group – Push the Down arrow To get the Menu Then select 3D 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 are Many Specialized Kriging Techniques That are Beyond the Scope of this Course. Click the Forward Arrow to move To the next screen

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 selections Will result In samples From a 300 X 300 meter Square on The same Level and Require at Least 2 Samples to Interpolate And limit to No more than 30.

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 choosing Not to limit. If my samples Are all Clustered Kriging will Adjust sample Weights for That.

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 I Create places For the data In my block Model I can Store what Data I used For each Interpolation. I’m not Storing that in My 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 not Going to Have 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-Off Can let you Use a different Distance limit If the sample Has an extreme Grade.

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 overpredicted Width of distribution. They Would expect to mine only the best 70% and instead mine the best 95% so they over-estimated their grades

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 you To include Ore dilution In 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 enter Our variogram Interactively We will also Assume we Don’t need To rotate Coordinates.

Screen Also Deals with Block Discretization

What is Discretization Kriging will require the Average value of gamma Between each sample and The block This is calculated with a Mathematical approximation. Block is divided into blocks And then gamma between The sample and each one of The points is averaged to get The average gamma. MineSight’s default is 4X4. I changed it cause I like 5X5

Variogram Rock Unit Limits Allows you to Impose rock Type limits to Which the Semivariogram Applies. (Remember The Stationarity Assumption)

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 model Type (Sph = spherical, The only one you Know about) Model can be Single or contain A nested Structure.

Nugget and Cill Entries Can also put in Ranges in Different Directions

Have System for Rotating Coordinates Also

Have the Option to Store Kriging Variance and Well As Grade This Example Is not Going to Store the Kriging Variance.

Can Limit Blocks that Get Coded Useful in Avoiding Coding blocks Of a different Rock type with The wrong Semivariogram.

Handling Blocks that Don’t Have Samples Close Enough to Interpolate Default is to Set the value To missing. There is A difference Between a Zero grade And an I don’t Know.

The Routine Runs

We Can Set the Model View to Display Our Copper Grades