# Using Statistical Interpolation to Build Block Models – Part III (Using

```Using Statistical Interpolation to
Build Block Models – Part III
(Using Pintrp.dat to project sample values to blocks)
Using MineSight&reg;
&copy;2007 Dr. B. C. Paul
(Note – The Screenshots contained in this show are operating views of the
MineSight&reg; computer programs and the steps suggested for operating include
ideas taken from Minetec operating manuals, courses, publications, or
To Put Ore Grades Into The Block
Model, You Need Samples

Most of samples today are from
core drilling and assays.
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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.
Interpolation is done with the Pintrp
routine – We need to Activate Compass
to get it.
Pull down
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
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

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
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
Weights for
That.

Pintrp allows many types of interpolation

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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
and the seven samples will share the weight
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

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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.
Can let you
Use a different
Distance limit
If the sample
Has an extreme
This was important for nongeostatistical 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
The Problem
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
Distribution of samples
Distribution of blocks
COV
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

inplace rock – but sometimes we
don’t mine in place rock.
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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
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
What Are Negative Weights


Interpolation schemes assign blocks a
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
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

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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
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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

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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
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&reg;


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

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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&reg;
does not have code for this option)
My Suggestion

Use MineSight’s&reg; 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
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
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