geostatistics

Geostatistics in
Surpac 6.0
August 2007

www.gemcomsoftware.com


Copyright © 2007 Gemcom Software International Inc. (Gemcom).
This software and documentation is proprietary to Gemcom and, except where expressly provided
otherwise, does not form part of any contract. Changes may be made in products or services at any time
without notice.
Gemcom publishes this documentation for the sole use of Gemcom licensees. Without written permission
you may not sell, reproduce, store in a retrieval system, or transmit any part of the documentation. For
such permission, or to obtain extra copies please contact your local Gemcom office or visit
www.gemcomsoftware.com.

While every precaution has been taken in the preparation of this manual, we assume no responsibility for
errors or omissions. Neither is any liability assumed for damage resulting from the use of the information
contained herein.
Gemcom Software International Inc. Gemcom, the Gemcom logo, combinations thereof, and
Whittle, Surpac, GEMS, Minex, Gemcom InSite and PCBC are trademarks of Gemcom Software
International Inc. or its wholly-owned subsidiaries.

Contributors
Rowdy Bristol
Peter Esdale
Phil Jackson
Kiran Kumar
Product
Gemcom Surpac 6.0

Table of Contents
Introduction ................................................................................................................................................... 5
Requirements ........................................................................................................................................... 5
Objectives ................................................................................................................................................. 5
Workflow ................................................................................................................................................... 5
Required Files ............................................................................................................................................... 6
Tutorial profile ........................................................................................................................................... 7
Important Concepts....................................................................................................................................... 9
Understand the Domains .......................................................................................................................... 9
Check the Input Data ................................................................................................................................ 9
Understand the Estimation Method and Parameters ............................................................................. 10
Check the Output Model ......................................................................................................................... 10
Domains ...................................................................................................................................................... 11
A Simple Example .................................................................................................................................. 12
Viewing Domains in Surpac.................................................................................................................... 14
Extracting Data with a Domain in Surpac ............................................................................................... 16
Basic Statistics ............................................................................................................................................ 19
The Histogram ........................................................................................................................................ 20
Bimodal Distributions .............................................................................................................................. 22
Outliers ................................................................................................................................................... 23
Displaying Histograms in Surpac ........................................................................................................... 24
Removing Outliers in Surpac .................................................................................................................. 27
Anisotropy ................................................................................................................................................... 31
Isotropy vs. Anisotropy ........................................................................................................................... 32
Geostatistical Estimation Using Isotropy ................................................................................................ 34
Geostatistical Estimation Using Anisotropy ............................................................................................ 38
Ellipsoid Visualiser .................................................................................................................................. 43
Variograms .................................................................................................................................................. 53
Introduction to the Variogram ................................................................................................................. 54

Calculating a Variogram ......................................................................................................................... 56
Modifying the Lag Distance .................................................................................................................... 60
Omnidirectional Variograms ................................................................................................................... 63
Directional Variograms ........................................................................................................................... 64
Calculating an Omnidirectional Variogram in Surpac ............................................................................. 66
Modelling Variograms in Surpac............................................................................................................. 73
Variogram Maps.......................................................................................................................................... 85
Primary Variogram Map.......................................................................................................................... 86
Secondary Variogram Map ..................................................................................................................... 94
Anisotropy Ellipsoid Parameters ............................................................................................................ 96
Steps for Using Variogram Maps to Create Anisotropy Ellipsoid Parameters ..................................... 103
Inverse Distance Estimation ..................................................................................................................... 106
Isotropic vs Anisotropic Inverse Distance Estimation ........................................................................... 107
Steps to Performing Inverse Distance Estimation ................................................................................ 108
The Impact of Inverse Distance Power ................................................................................................ 113
Ordinary Kriging ........................................................................................................................................ 115
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Table of Contents

Impact of the Nugget Effect .................................................................................................................. 116
Impact of the Range ............................................................................................................................. 117
Block Size Analysis ................................................................................................................................... 123
Debug Output from Ordinary Kriging .................................................................................................... 124
Using Kriging Efficiency and Conditional Bias Slope ........................................................................... 125
Block Site Selection .............................................................................................................................. 127
Model Validation ....................................................................................................................................... 128
Comparing Cross-sectional data with Model ........................................................................................ 129
Grade-Tonnage Curves ........................................................................................................................ 131

Basic Statistics of Model Values........................................................................................................... 133
Trend Analysis ...................................................................................................................................... 134

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Introduction
Geostatistics is used in fields such as mining, forestry, hydrology, and meteorology in order to understand
how data values change over distance. Probably the most common use of geostatistics is to make
estimations, such as the specific gravity of rock for an area where there are only a few known sample
values. This is often done in three-dimensional space. A set of estimated points in space is known as a
“model”. As George Box, a professor of Statistics at the University of Wisconsin in the United States,
once said, “All models are wrong. Some are useful.”

Requirements
Prior to proceeding with this tutorial, you will need to have installed Surpac 6.0 or later from a CD.
Additionally, you should have a good understanding of the following concepts in Surpac:

1.
2.
3.
4.

Geological Database
Solid modelling
Block modelling (how to create and constrain a model)
Tcl scripts

If you do not have a good background in these subjects, many parts of this tutorial may be difficult to
follow.

Objectives
The primary objective of this tutorial is to help you become familiar with the methods for performing
geostatistical operations with Surpac. Also, this tutorial will introduce you to some general geostatistical
concepts, and provide some guidance on making geostatistical decisions. Ultimately, the models you
create are your responsibility. There are often more methods than those described here to obtain a
model.

Workflow
The process described in this tutorial is outlined below:

1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.

Introduction
Required Files
Important geostatistical concepts
Domains
Basic statistics
Anisotropy

Variograms
Variogram maps
Inverse distance estimation
Ordinary kriging
Block size analysis
Model validation

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Required Files

Workflow

Required Files
Overview

This chapter will identify where you will find the files required for this tutorial.

Requirements

Prior to performing the exercises in this chapter, you should have installed Surpac 6.0 or later from a CD.

The files and directory structure for each tutorial will only be present if you have installed the software
from the CD.

If you have not installed the software from a CD:

1. Create the following directory:

c:/surpacminex/surpac_60/demo_data/tutorials/geostatistics

2. Download the geostatistics tutorial/data (contained in a single zip file) from:

/>
3. Unzip the file geostatistics.zip into the directory you created.

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Required Files

Tutorial profile

Tutorial profile
Profiles are a collection of menubars and toolbars. The tutorial profile contains a set of menus that assist
you with learning various aspects of the software.
To display the tutorials profile:
1.
2.

Right click in the blank area to the right of the menus.
From this popup menu, choose Profiles > tutorials.

A new menubar will be displayed, listing all available tutorials.

3.

Choose Geostatistics > CD to geostatistics folder.

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Required Files

Tutorial profile

This should set your working directory to:

C:/surpacminex/surpac_60/demo_data/tutorials/geostatistics

This directory contains all of the files required to perform the steps in this tutorial.

Summary

The files you will need for the remainder of the tutorial should now be present in your work directory.

Refer to the Introduction to Surpac manual for more information on profiles.

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Important Concepts

Understand the Domains

Important Concepts
Overview
Although geostatistics is not an exact science, there are some important concepts which can reduce
estimation errors. These concepts can be divided into four regions:

1.
2.
3.
4.

Domains
Validation of input data
Understanding estimation methods and parameters
Validating the output model

Requirements
There are no requirements for reading this chapter, but you may find some of the principles easier to
understand if you:

•

have some understanding of basic statistics.

•

know what a geostatistical model is, or

•

have previously performed a geostatistical estimation.

Understand the Domains
It is important to recognise separate “regions” or “domains” within a model. Once you have identified the
domains, it is important to group all sample data contained within each domain into distinct subsets. After

that, you can analyse each subset individually, and use data from each separate domain to make
estimations within that domain.

Check the Input Data
The saying “Garbage in = Garbage out” is certainly true in geostatistics. Although sampling theory and
laboratory quality control practices are important concepts which impact the quality of any estimation
made using a set of data values, these subjects are outside the scope of this tutorial.

Assuming that the quality of the data is as good as you’re going to get, there are a couple of potentially
hazardous characteristics of the data which you should look for: “bimodalism” and “outliers”. You can
look for both of these features with a histogram. A data set is said to be “unimodal” if the histogram
shows a single peak. If there are two peaks, the data is said to be “bimodal”. If you use some of the
more common estimation techniques to create a model based on a bimodal distribution, it is likely to
contain more estimation errors than a model created from a unimodal data set. Additionally, “outliers”, or
values which are significantly distant from the majority of the data, can cause estimation errors.

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Important Concepts

Understand the Estimation Method and Parameters

Understand the Estimation Method and Parameters
There are a large number of estimation methods, and a large number of parameters within each method.
Before using a particular estimation method, you should have a good background in basic statistics, as
well as basic geostatistical principles.

Using geostatistics can be likened to flying a jet plane. Although there are “autopilot” modes, where you
just press a few buttons and something happens, it is important that the pilot understand the theory of

aerodynamics to understand what impact a particular control has upon the end result.

Check the Output Model
A final method you should use to check the quality of estimation is to take time to examine the output.
Histograms of estimated values, contours of plans, cross sections of block models, colour coded and
rotated in three-dimensional space are all methods which can be used to verify the output values.

Summary

Geostatistics is the study of how data varies in space. It is an inexact science which is used to make
estimations at locations where no data exists. It is important to recognise that validation of input and
output data are as important as understanding geostatistical theory and the estimation method being
used.

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Domains

Check the Output Model

Domains
Overview

One of the most important aspects of geostatistics is to ensure that any data set is correctly classified into
a set of homogenous “domains”. A domain is either a 2D or 3D region within which all data is related.
Mixing data from more than one domain, or not classifying data into correct domains, can often be the
source of estimation errors.

The following concepts will be presented in this chapter:

1.
2.

Estimation without domains
The impact of domains on estimated values

Requirements

Prior to proceeding with this chapter, you should:

•

understand what Surpac string and DTM files are.

•

know how to display string and DTM files.

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Domains

A Simple Example

A Simple Example
Imagine that you are a meteorologist, and you are given three air temperatures measured at locations A,
B, and C, as displayed below. Based on the values shown, what would you guess the temperature is at
location X? Would you guess that the temperature at location X was greater than 25?

What is the temperature at location X?

Using the information above, you may have the following thoughts:

1.
2.
3.
4.

Since location A is relatively distant from X, the value at A may have little or no influence on the
estimated temperature at X.
Since locations B and C are about the same distance from X, they will probably have equal
influence on the estimated temperature.
Given the previous two points, the temperature at X would probably be the average of the
temperatures at B and C: (18 + 32) / 2 = 25 degrees
Since the influence of A has not been accounted for at all, and the estimate is exactly 25 degrees,
it is difficult to say with certainty if the temperature at X is above 25 degrees.

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Domains

A Simple Example

Now consider the following: Imagine that you want to go to your favourite beach, but only if the
temperature is 25 degrees or more. You have three friends who live near the beach you want to go to,
and you call them up and ask each one what the temperature is at each of their homes. You draw the
map below, with the locations of each friend (A, B, and C) and the temperatures they give you. Your

favourite beach is at location X. Note that the friend at location B lives high up in the mountains, while
friends at A and C live near the beach.

Would you go to the beach?

Using the information above, you may have the following thoughts:

1. The data from B can be ignored, because temperatures high up in the mountains are usually not
good estimates of temperatures on the beach.
2. A and C are on the beach, so they can be used to guess the temperature at X.
3. Since X is between A and C on the map, the temperature at X will probably be somewhere
between the temperature at A and the temperature at C.
4. Therefore, the temperature at X will be somewhere between 28 and 32 degrees
5. Since the temperature range of 28 to 32 degrees is greater than the minimum value of 25
degrees, you would probably decide “Yes, I’m going to the beach!”

Compare this example with the first one. In both cases, all of the locations and temperatures are exactly
the same. However, in the second case, when you took account of the domain which the data is
contained within, you came up with a considerably different result. The point is that separating data into
similar regions, or domains is a very important part of making any geostatistical estimation.

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Domains

Viewing Domains in Surpac

Viewing Domains in Surpac
1.

2.
3.
4.

Open all_composites2.str.
Choose Display > Hide everything.
Choose Display > Point > Markers.
Enter the information as shown, and then click Apply.

5.
6.

Choose Display > 3D grid.
Enter the information as shown, and then click Apply.

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Domains

Viewing Domains in Surpac

You will see an image as shown.

all_composites2.str

The points in this string file represent 2 metre downhole composites. The D1 field contains the
composited value for gold. The D1 values have been used to classify the points into different strings:

String

D1

1

< 1.000

2

1 – 1.999

3

2 – 2.999

4

3 –3.999

5

4 – 4.999

6

5 – 5.999

7

>= 6.000

As in the first example above, any estimation that you would make with only this file would be based only
on the distances between the sample points and the estimated location.

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Domains

7.

Extracting Data with a Domain in Surpac

With all_composites2.str still displayed on the screen, open ore_solid1.dtm.

ore_solid1.dtm

This solid represents a single domain, as interpreted by a geologist. Only composites which fall inside
this domain should be used to estimate points inside the domain.

Extracting Data with a Domain in Surpac
The domain ore_solid1.dtm represents an ore zone known as the QV1 zone. You will now go through
the process of extracting composites only inside the QV1 domain.

1.
2.

Run the macro 01_create_downhole_composites.tcl.
After reading the text below on the first form, click Apply.

A geostatistical analysis of data in a drillhole database generally starts with compositing a
sample value within a given geological zone.

In this example, you will be creating 2 metre downhole composites within the QV1 geological
code.

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Domains

Extracting Data with a Domain in Surpac

The function COMPOSITE DOWNHOLE is invoked using Database > Composite > Downhole.
Note that a composite length of 2 metres has been selected. The selection of a composite length is
important, but is beyond the scope of this tutorial. You may want to consider the opinion of a
geostatistical consultant to determine the optimal composite length for your data set.

3.

After viewing the form below, click Apply.

On the next form, notice that the character field rock has been set up in the geology table, which is an
interval table. The text “QV1” has been inserted into the field rock for every interval of a drillhole which is
inside ore_solid1.dtm.

4.

After viewing the form, click Apply.

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Domains

5.

Extracting Data with a Domain in Surpac

After reading the text on the next form, click Apply.

2 metre downhole composites have been created within the QV1 rock type, and are stored in
the D1 field in gold_comp2.str.

String 1 contains composites where 50% to 100% of the 2m length contained a gold value.
String 2 contains composites where less than 50% of the 2m length contained a gold value.

Either or both of these strings may be used for further geostatistical analysis. In this example,
you will use both strings.

You will see an east-west section of the database and the composites which were created.

2metre composites inside QV1 zone
Summary
You should now understand the impact which domains have upon geostatistical estimations, and how to
use Surpac to extract data within a domain.

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Basic Statistics

Extracting Data with a Domain in Surpac

Basic Statistics
Overview

One of the important preliminary steps in performing a geostatistical evaluation is to have a good
understanding of the raw data. Two characteristics which can potentially reduce the quality of your
estimations are bimodalism and outliers. A histogram can be used to identify both of these.

The following concepts will be presented in this chapter:

1.
2.
3.

Using a histogram to identify a bimodal distribution.
Using a histogram to identify outliers.
Selection of a cutoff value.

Requirements

Prior to proceeding with this chapter, you should:
•

be familiar with Surpac string files

•

know how to run a Surpac macro

Page 19 of 137


Basic Statistics

The Histogram

The Histogram
A histogram is a statistical term which refers to a graph of frequency vs. value. A histogram is the
graphical version of a table which shows what proportion of cases fall into each of several nonoverlapping intervals of some variable.
For example, a distribution of gold grades could be represented by the following table:

Gold (g/t)

Number of samples
(frequency)

0.0 - 0.5

0

0.5 – 1.0

40

1.0 - 1.5

58

1.5 – 2.0

82

2.0 - 2.5

40

2.5 – 3.0

29

3.0 - 3.5

18

3.5 – 4.0

10

4.0 – 4.5

12

4.5 – 5.0

5

5.5 – 6.0

5

6.0 – 6.5

5

6.5 – 7.0

5

7.0 – 7.5

8

7.5 – 8.0

5

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Basic Statistics

The Histogram

This same data can be displayed in a histogram as shown:

Histogram of gold grades

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Basic Statistics

Bimodal Distributions

Bimodal Distributions
The “mode” is the most commonly occurring value in a data set. For example, in the following data set,
the number 8 is the mode:

1 3 5 5 8 8 8 9

“Bimodal” means that there are two relatively “most common” values which are not adjacent to one
another. In the following data set, the numbers 2 and 8 are equally common, and the distribution is said
to be “bimodal”:

1 2 2 2 3 5 5 8 8 8 9

Imagine that you are studying the average specific gravity, or density of rocks in a coal deposit. A
histogram of all rock samples might look like this:

Specific Gravity

Any histogram which displays two humps, as in the example above, is said to be “bimodal”. The bimodal
distribution in the example above can be explained by the fact that the data set is comprised of coal
samples as well as intervening sandstone and mudstone bands. The specific gravity values between 1
and 2 are representative of the coal, while specific gravity values between 2 and 3 represent the
intervening rock.

Often the source of a bimodal distribution can be two domains being mixed into a single data set. In
order to minimise estimation errors, you should make every attempt to separate any data set which has a
bimodal distribution. In the example above, merely segregating the data based on rock type would result
in two separate normal distributions.
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Basic Statistics

Outliers

Outliers
An “outlier” is a statistical term for a data value which is relatively distant from the majority of all other
values in the data set. For example, in the following data set, the number 236 would be considered to be
an outlier:

1 3 5 5 8 8 8 236

Outliers can cause problems with the calculation of variograms. Additionally, if used in an estimation,
outliers can result in unrealistic results. One technique used to reduce the impact of outliers is to apply a
“cutoff” to them. In the example above, the value of 236 could be “cut”, or changed to a value of 9:

1 3 5 5 8 8 8 9

Another alternative is to remove the outlier value(s).

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Basic Statistics

Displaying Histograms in Surpac

Displaying Histograms in Surpac
1.
2.

Run the macro 02_basic_statistics.tcl.
After reading the text below on the first form, click Apply.

Basic statistics should be performed before variogram modelling for a couple of reasons:

1. The shape of the histogram can be used to determine if a distribution is bimodal (has two
humps).
If the histogram shows a bimodal distribution, the data should be analysed graphically to see
if it can be physically segregated into two separate zones. If so, each zone should be
modelled separately.

2. The quality of experimental variograms and subsequent block model estimations are
sensitive to outliers (relatively large values).

Outlier values should be cut or removed prior to variogram modelling or block model
estimation. The value used to cut or remove outliers can be calculated from information in the
basic statistics report.

The Basic Statistics window is opened by selecting Geostatistics > Basic statistics.
Next, File > Load data from string files is selected, and the form below is displayed.

Basic Statistics on gold_comp2.str

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Basic Statistics

Displaying Histograms in Surpac

You will use strings 1 and 2 from the file gold_comp2.str as the basis of our study. The columns
labelled “Minimum value” and “Maximum value” allow you to exclude data which is below a given
minimum value or above a given maximum value.
On the Advanced tab, you can exclude data which is greater or less than any Y, X, or Z coordinate
values.
The D1 field contains values of gold in grams per tonne. The “Name” field is optional. The name value
will appear on the output report.

Also, note that it is possible to view the histogram based on a number of bins or on a bin width. The “bin
width” method is more commonly used.
3.

After reviewing the form, click Apply.

Next, a histogram and a line representing the cumulative frequency is displayed. The cumulative
frequency is an accumulation of the values of all previous histogram bins.

After this, Report was selected from the Statistics menu. This form prompts you to enter the name of an
output report, the report format, and a range of percentiles which will be written to the report.
4.

When you have completed viewing the form, click Apply.

Basic statistics histogram and report

5.

After reading the text displayed on the next form, click Apply.

As you can see from the histogram, this distribution is not bimodal.
The basic statistics report will be displayed next.
Note the values of the mean, standard deviation, and percentiles.

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