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technical > isatis geostatistical
software
Geostatistics is now widely recognized by the mining industry
as being a particularly effective tool at all stages from initial
feasibility studies to production control. Quantitative Group
(QG) are users of the leading commercial geostatistical software
system Isatis. Our familiarity with this product allows
us to provide tailored training solutions for mining industry
clients.
Training using Isatis: tailored to your operational needs
QG's principals are serious industrial users of this software
and can provide excellent practical (hand-on) training. This
can be provided in conjunction with classroom style geostatistical
training or "stand alone". To obtain more information
about Isatis, contact the developers Geovariances.
Geostatistical software: UNIX and Win 2000/XP/NT
Isatis is a specialist geostatistical package which offers all
the geostatistical techniques within a user-friendly, windows-mouse-icon
interface. It offers geologists and mining engineers a wide
range of tools for mining data analysis, estimation and simulations
of deposits. Import/Export facilities exist to allow Isatis
to "talk" to any mining or geological software. Isatis
is available to run in native Unix or using Hummingbird on Windows
platforms.
Powerful graphics
Graphical features have been included so that users can quickly
visualize their data and results . Moreover graphical tools
are essential in some statistical tasks such as the exploratory
data analysis or variogram modelling. The initial graphical
outputs generated by Isatis are produced using sensible default
values. If the user is satisfied with the graphic, it can be
printed directly. If the user wishes to modify the graphic the
figure can be saved as a Metafile and the Isatis module Mfedit
used to conveniently modify any graphic parameter.
Exploratory Data Analysis (EDA) for geostatistics
Classical statistics as well as geostatistical analysis are
available simultaneously in the same exploratory module. The
various applications and tools used for spatial and non-spatial
data analysis include a large variety of univariate or multivariate
statistics in linked graphical displays. They allow the user
to check the impact of selecting or discarding some data, for
example.
Statistics for earth scientists
A wide range of statistics are computed by Isatis. They describe:
- the location of the data distribution with the number
of defined samples, the minimum and the maximum values,
the mean and the quantities;
- the variability of the data with the variance and the
standard deviation;
- the shape of the distribution with the coefficient of
skewness, the kurtosis and the coefficient of variation;
In the multivariate analysis, the correlation matrix between
the variables is also provided.
Isatis can create histograms, QQ plots, scattergrams, cumulative
frequency plots.
Principal components analysis [PCA] for geochemical and other
data
Multivariate statistical analysis can be handled by Isatis,
specifically PCA.
This widely used statistical method for multivariate data analysis
enables a quick analysis of several variables at a time. The
orthogonal factors and different types of graphical outputs
are computed: basemaps, scatter plots, spin plots (representation
of samples where three variables are defined - these can be
three factors), circle of correlations (unit circle representing
the coefficients of correlation according to the factors, and
thus the 'affinities' and 'antagonisms' between variables) and
scree graph (this graph shows the evolution of the different
eigen values related to the factors and how they replicate the
global variability).
Spatial data analysis and variography
A wide range of statistical values are computed by Isatis, including:
Base map to make proportional "post plots" of data:
see where the highs and lows are... and how they are linked
The samples are represented by a symbol, the dimension of which
is proportional to the value of the variable. When the data
is collected on a regular grid, the base map is displayed in
raster mode. Other representations are also available such as
literal maps (each sample location is plotted with the value
of the data), contour maps (to visualise the general trend of
the data), symbolic maps (the data is classified into classes
which are represented by a symbol or a color - this can produce
indicator maps if only two classes are defined) or gradient
maps (represented as proportional and directional arrows).
H-scatterplots: a complement to variograms to assess spatial
continuity
This X-Y representation of two variables is meant to analyze
the spatial continuity of the data and display all the pairs
of samples which are separated by a certain distance along a
given direction. If you like, it 'explodes' each point plotted
on a variogram. The coordinates correspond to the value of the
first variable at the first sample location versus the value
of the second variable (which can be identical to the first
one) at the second sample location. The shape of the cloud of
points spreads out as the spatial correlation between the two
samples decreases or the relationship between the two variables
weakens. This tool is complementary to the variogram approach.
Variograms: the fundamental tool of geostatistics - Isatis has
many types
Variograms are the fundamental tools of geostatistics. They
characterise the correlation between samples and between variables
as a function of the distance. In Isatis, the variogram may
be calculated in various directions or specifically along lines
(e.g. down-the-hole). The cloud of pairs from which the curves
are derived can also be displayed and used for exploration.
The variogram can be replaced by a large variety of representations
of the spatial variability (in total, 18 representations or
"types of variogram" are available, among them the
covariance, general and pair-wise relative variograms, the correlogram,
the madogram, the rodogram...etc. etc.).
Variograms of normal Gaussian scores: efficient detection of
anisotropy and structure
Isatis can make Gaussian transforms (among many others, such
a logs). The resulting data can be assessed with variogram tools
to allow variography of noisy, high nugget situations more feasible.
This is very useful in many mining (gold, uranium, precious
metals) and environmental (trace element pollution) situations.
Variograms of Indicators: Indicator variograms have many practical
uses
Isatis can make indicator transforms. Again, the resulting data
can be assessed with variogram tools to allow variography of
noisy, high nugget situations more feasible. As for Gaussian
cases, this is very suited to many mining (gold, uranium, precious
metals) and environmental (trace element pollution) variables.
Indicators also allow the spatial analysis of behaviour at variable
cut offs to be characterised.
Variogram surface: or variogram "maps"
This representation of the variogram in all directions is a
good visual tool to identify possible anisotropy in the data.
The principle is to define a grid such that the origin of the
space is located at the center of this grid. Each pair of samples
corresponds to a distance and a direction, which can be converted
into a grid cell to which is associated a measure of spartial
variability or correlation.
Linear and non-linear, stationary and non-stationary geostatistics
Isatis can handle both stationary and non-stationary techniques,
and will provide both kriging
and non-linear estimators (lognormal kriging, disjunctive kriging,
uniform conditioning, service variables, etc.), not to mention
grade or indicator conditional simulations.
Linear methods
Isatis can perform a wide range of geostatistical and non-geostatistical
linear estimations for points and blocks, including:
- Inverse (power of the) distance
- Nearest neighbour
- Least square fit (order 2)
- Moving average (moving window mean)
- Moving median
- Moving projected slope
- Discrete spline
- Ordinary Kriging
- Simple Kriging
- Cokriging
- Kriging with a spline generalised covariance
and more...
Kriging neighbourhood testing: quantified search analysis
Isatis can perform a quantified search analysis. This is a critical
step in the kriging process
and also in setting up the conditioning of simulations.
The analysis is graphical and interactive and provides a range
of statistics for assessing the quality of kriging given a specified
variogram, block size, search, data geometry etc. These statistics
include:
- estimation variance
- weight of the mean in a simple kriging
- slope of the regression of true on estimated values
- kriging weights (graphical display/map)
etc...
Non-Linear estimation: beyond ordinary kriging
Many advanced non-linear estimation methods are available, including:
- Uniform Conditioning for recoverable reserves
- Disjunctive Kriging for non linear problems
- Lognormal Kriging for highly skeewed distributions
- Indicator Kriging for the estimation of discrete variables
- Factorial Kriging Analysis to extract components of a
model
Grade tonnage curve tools
Coherent geostatistical models provide solutions to problems
such as: the formulation of grade tonnage relationships, the
determination of cut-off grades, sampling pattern optimization,
selectivity studies and the evaluation of the support effect
on ore reserves.Grade distributions can be modelled using Gaussian
anamorphosis techniques. The discrete Gaussian model of change
of support allows the influence of the size of the selective
mining units (SMU) on grade tonnage curves to be studied. The
same model can be used to obtain local grade tonnage relationships
(uniform conditioning). |
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Scott Jackson (left), Scott Dunham (centre), and John Vann (right) are the Directors of Quantitative Group
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