Drill Hole Spacing Analysis 2015
Drill Hole Spacing Analysis 2015
Drill Hole Spacing Analysis 2015
2. Peabody Energy Australia, 100 Melbourne Street, South Brisbane, Qld, 4101
Abstract
According to the recently released Australian Guidelines for the Estimation and Classification of Coal
Resources (2014), geostatistics is listed as one of the methods which can be used to assess
confidence in a coal resource estimate. In this paper, several case studies are presented in which
geostatistics has been successfully used to assess confidence for two operating coal mines and one
exploration prospect, all of which are owned and operated by Peabody Energy Australia.
The method used to apply geostatistics to the assessment of confidence and coal resource
classification is known as Drilll Hole Spacing Analysis or DHSA. An easy to use approach to DHSA,
specifically adapted to coal, is presented with reference to freely available software, thereby enabling
this methodology to be more widely used within the industry.
The results of the three DHSA studies conducted by HDR mining consultants for Peabody Energy
Australia are presented and discussed. These results clearly show that the main criteria in
determining classification distance using the DHSA method are;
Population/Global variability.
Size of the study area, which in turn is a function of working section thickness and mining
rate.
It is shown that the DHSA method represents a relatively simple way of using geostatistics to assess
confidence in coal resource estimates. The case studies presented show that DHSA can be applied to
both mature mining projects as well as early stage exploration projects.
It should be noted however that the approach to DHSA in the case of exploration projects needs to be
more conservative, recognising that data gaps potentially exist. This is illustrated in an example from
the West Burton study.
1
Introduction
One of the main aims of this paper is to present an easy to use method for the use of
geostatistics in assessing confidence in coal resource estimates. The recently updated (2014)
Australian Guidelines for the Estimation and Classification of Coal Resources (Coal
Guidelines) requires that coal resource classification be based on an assessment of the
confidence in the underlying resource estimate. A number of criteria are set out in the Coal
Guidelines that can be used in varying combinations to assess confidence, namely;
Domaining
Statistical analysis
Geostatistical analysis
Geological modelling
Many of the criteria listed above are fairly subjective and the only method able to give a truly
quantitative estimate of confidence is considered to be geostatistics. This should however not
negate the importance of the other factors; Exploratory Data Analysis (EDA) prior to
conducting an estimate in order to identify spurious data or to separate out mixed domains is
a critical step. Global or population statistics in the form of histograms, minimum, maximum
and mean values, standard deviation, coefficient of variation etc. is important for identifying
spurious data and mixed domains and it also serves to quantity global variability in variables
considered. The lack of suitable QAQC implemented during logging, sampling and analysis
will result in a low level of confidence in the resulting estimate, regardless of any subsequent
geostatistical analysis. However it is considered that only geostatistical analysis can give a
truly quantitative measure of confidence and hence it is considered to be the least subjective
method.
Not withstanding this, geostatistical methods are not without problems when applied to coal.
This paper presents a number of case studies where the DHSA method has been successfully
used as a basis for coal resource classification. Examples have been drawn from these case
studies which illustrate potential solutions to common problems encountered in the
application of geostatistics to coal.
It should be noted at the outset that the use of geostatistics to calculate estimation variance as
a basis for determining confidence in an estimate does not necessarily imply that geostatistics
has to be used as an interpolator in the estimate. It has been shown that commonly used
interpolators for coal resource estimates, such as inverse distance squared (IDW2), are quite
good at getting close to the level of precision achieved using Kriging in most cases (Williams
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et al 2010). Hence it is considered that estimation variances calculated through the method
presented in this paper can be used for estimates which employ other interpolators as long as
the attributes being estimated are not highly variable and that the drilling grids used are fairly
regular (irregular drilling patterns and highly variable attributes being estimated both result in
a significant increase in the interpolation performance of Kriging over IDW).
A thorough understanding of the coal geology and the accurate modelling thereof is also of
vital importance to any estimate. It is for this reason that this paper is being written as it
presents an easy to use method for the application of geostatistics to the assessment of
confidence in coal resource estimates. This allows the geologist, who is likely to be most
familiar with the coal geology, to do the geostatistics, rather than relying on specialist
geostatisticians who may not be as familiar with the geological characteristics of the deposit.
Figure 1 Calculation of estimation variance into a regular square region V, of increasing size V2 and V3
Estimation Variance
The estimation variance or extension variance is defined as the variance associated with using
the known average grade for a small volume v, to estimate the grade for a much larger
region V. The first step in the DHSA process is to calculate the estimation variance for a
given block size. The equation for the calculation of the estimation variance, 2E , is shown
below;
( , ) = 2 ( , ) ( , ) ( , ). . . . . . . . . . . . . 1
3
The equation is based on the average variagram value , where the sample pairs for the
calculation of the semi-variogram value, , are between the central sample and a series of
random positions within the larger region V for the first term (v,V), between random
positions within the smaller volume v for the second term (v,v) and between random
positions within the larger region V for the third term (V,V).
Charts which provide the solution to the above equation for spherical and exponential
isotropic (omnidirectional) variogram models are provided by Journel and Huijbregts (1978),
pp 131-148. The chart for the spherical variogram model, estimating a central sample into a
square region (pp 131) shows that the estimation variance increases linearly as you increase
the block side length from V through V2, V3 etc., until it reaches about 80% of the sill semi-
variogram value, at a block side length equal to twice the variogram range. After this the
estimation variance increases much more slowly as the block side length increases, reaching
the sill semi-variogram value at a block side length equal to 10 times the variogram range.
When conducting a DHSA, the increase in estimation variance as block size increases is
determined by calculating the estimation variance for a number of test block sizes as shown
in Figure 1.
= .............2
N is the number of blocks at the specific test block size that would fit into the area of interest.
The above approximation is based on the direct combination of independent elementary
errors and assumes all blocks are roughly square. This approximation is less effective when
the number of blocks N is small, which becomes a problem when we want to determine 2EST
over an area using very large blocks.
The final step in the DHSA process is to convert the global estimation variance into a
standard deviation by taking the square root and then determining the relative error at the 95
percent confidence interval around the mean, expressed as a percentage of the mean value,
using the following equation;
95 % 100%. . . . . . . . . . . . . 3
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Limitations of Global Estimation Variance and DHSA
The DHSA method is normally only used to determine percentage errors for larger study
areas, typically at least equivalent to one years mining. Smaller areas than this also suffer
from the problem with the low N in the equation for 2EST. For smaller study areas,
conditional simulation is considered to be a better geostatistical method to use.
For larger areas, benchmarking conducted by Bertoli et al (2013) has shown that results
obtained from DHSA are very similar to those obtained from conditional simulation.
EDA
The first step in the process is the Exploratory Data Analysis or EDA. It has been found that a
combination of histograms and colour ramped spatial plots of the composited seam
intersections for each variable, for each seam, are useful tools when conducting the EDA.
This is done in conjunction with the tabulated global statistics which present the mean,
variance, standard deviation and the coefficient of variation for each seam/domain.
In the case of coal exploration data sets, drilling grids are normally fairly evenly distributed
and there is no need for declustering prior to generation of global statistics and histograms.
However, in cases where clustering of holes is a problem, it is suggested that declustering
should be performed prior to generation of global statistics.
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Figure 2 Seam thickness histogram and colour ramped plot showing distribution of points for the E12E22 seam
In Figure 2, the seam thickness histogram for the E12E22 seam at Wilpinjong shows a thin
seam tail to the histogram. Closer inspection shows that all thin seam composites below
1.2 m involve intersections truncated by weathering. The colour ramped plot shows that the
thin seam intersections (blue) are not grouped spatially and are therefore not part of a
separate domain. These samples were therefore excluded prior to conducting the variogram
analysis.
Figure 3 Seam thickness histogram and colour ramped plot showing distribution of points for the D2 seam
In Figure 3, the seam thickness for the D2 seam at Wilpinjong shows a wide range of values
and examination of the colour ramp plot shows that there is a possibility that two domains
may be present, a thin seam domain in the south and a thick seam domain in the north.
However the variogram for D2 seam thickness in Figure 4 shows significant trend in the data,
which importantly only starts at a lag distance beyond the sill of the variogram. As a result it
was possible to successfully model the variogram for D2 thickness without the need for
domaining.
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Variography
The second step in the process is variography on a cleaned data set where outlier values due
to sampling or database/laboratory issues have been identified and fixed/removed and mixed
domains separated. In the three case studies presented, variography was conducted using
omnidirectional variograms for a number of reasons;
Firstly it can be shown that the range of an omnidirectional variogram is the same as
the average range of the maximum and minimum axis of continuity in a deposit that
exhibits directional anisotropy (Table 7.2 and 7.4 in Isaaks and Srivastava, 1989). As
a result, whether a single omnidirectional or two anisotropic variograms are used, the
estimation variance calculated for a square block is the same.
Secondly, in coal deposits, there is often a shortage of valid data points for variogram
analysis, particularly in the down dip direction which often corresponds to the
direction of minimum continuity. Use of an omnidirectional variagram allows for
pairs to be identified in all directions, there bye making maximum use of available
data.
When modelling variograms, it is important to do this in conjunction with the final (clean
data set) histogram for the attribute being modelled as the population variance for the
attribute gives a guide to which semi-variogram value to set the sill of the variogram model at
(the population variance should be similar to the variogram model sill).
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Apart from the common problem of lack of sufficient data points to allow for a robust
variogram to be constructed, discussed above with reference to the use of omnidirectional
variograms, other commonly encountered difficulties associated with variogram modelling of
coal deposits are;
In the case of trend in the data, normally a sill to the experimental variogram is seen before
the trend sets in, as shown in Figure 4, in which case the trend does not impact on the
variogram modelling. If this is not the case then trend in the data must be removed by
correcting for the drift in the data.
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Figure 6 Variogram for the B23 seam thickness at Wilpinjong using a 50 m lag
Once the test parameters have been set up, the variogram model parameters can be used to
calculate the estimation variance for that attribute for each test block size. Charts which
provide the solution to Equation 1 for spherical and exponential isotropic (omnidirectional)
variogram models, provided in Journel and Huijbregts (1978), were used for this purpose.
Care should be taken to add the nugget effect semi-variogram value to that calculated from
the estimation variance equation (Equation 1) for each variogram model structure, to arrive at
a total estimation variance for each attribute at each test block size.
The higher value of N, the lower the global estimation variance for the study area. A high
value for N can be achieved by reducing the block size (in other words reducing the drill
spacing, which makes intuitive sense) or by increasing the test size area. This makes less
intuitive sense and a standardized study area of 5 years mining is recommended as a result.
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This will allow for direct comparison with other DHSA studies published in the literature
such as Bertoli et al (2013) which in turn will allow for benchmarking of results (as was done
in each of the three case studies).
Calculation of the study area size can be done using Equation 4 which incorporates the
mining period, the likely mining rate, the total thickness of seams to be mined and the
estimated average raw coal density;
Study area = years mining x mining rate / estimated total thickness of seams too be mined x
estimated average density4
Global estimation variances at each test block size then need to be converted into relative
errors expressed as a percentage of the mean value by applying Equation 3. Relative
percentage errors can then be plotted against the test block/drilling grid size and the distances
at which the 10%, 20% and 50% relative percentage error thresholds are reached can be used
as resource classification distances for Measured, Indicated and Inferred Resources
respectively.
Two common problems with determining the Inferred distance are illustrated in Figure 7 and
Figure 8. In Figure 7, the 50% relative error is not reached at the maximum test grid spacing.
In this instance the trend of increasing error with grid spacing is extended until the 50% error
threshold is intersected and the associated Inferred classification distance is read off the
x-axis by projecting the 50% percentage error intersection point onto the x-axis.
In Figure 8, there is a marked inflection in the trend line of relative percentage error against
increasing grid spacing associated with the point where N values of 1 are reached. When the
block size matches or exceeds the test area size, N = 1 for all remaining test block sizes,
resulting in the increase in global estimation variance with increasing block size levelling off.
In this case, the trend line is projected from immediately before the inflection point and then
the Inferred classification distance is read off the x-axis in the same way as described
previously.
It should be noted in the first example that it is possible in some cases that a 50% error will
never be reached for attributes with a low population variance. In such cases there should
theoretically be no limit to Inferred Resources within the tenement (apart from the limit
imposed by the margin of the drilling) and projecting the trend to reach a 50% error is
therefore seen as a conservative approach.
In the second example, the study area is too small to allow for a 50% error to be reached. In
this case the projection to a 50% error is purely a theoretical exercise to get a maximum
distance for Inferred Resources as Inferred Resources will fill the entire study area anyway, at
any test grid size above the one at which N = 1 first occurred.
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The example shown in Figure 9 is of the LCU1 seam in the East Domain at Coppabella Mine.
Note firstly the much steeper trend in the thickness relative percentage error curve which
reaches a 10% error at only 175 m, whereas in the 5 year case at Wilpinjong Mine for the M4
seam thickness, 10% error is reached at 1250 m. This reflects the much more complex
geology and variable seam thickness at Coppabella as compared to Wilpinjong. The problem
encountered in this example is that thickness relative percentage errors are greater than that
for coal quality (raw ash%) and the convention adopted in such instances is to use the
attribute with the highest errors for classification distance determination (which in this case
would be thickness).
Figure 7 Wilpinjong M4 seam, relative percentage errors for LOM
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Figure 9 Coppabella LCU1 seam, relative percentage error for 5 years mining
Commonly, quantity points of observation (Pobs) are more numerous than quality Pobs and
there has been a tendency in the past to use confidence limits based on only quality Pobs for
resource classification. There are however deposits in which there is greater quantity
variability than quality variability, in which case the drill hole spacings determined from a
DHSA study can be applied to both quality and quantity points of observation (Pobs) to
determine resource outlines. Again the final confidence limits should be the more
constrained of the two.
An example of this is shown below for Coppabella in Figure 10, where a spacing of 350 m is
used for quantity points to define the Indicated area. The corresponding spacing for quality
points for Indicated Resources would be 600 m (Figure 9) and although not used as the
primary classification distance, a polygon using this spacing is constructed around quality
points of observation. The area of Indicated Resource is then the intersection between these
two polygons.
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Figure 10 Intersection of Indicated polygons for quantity and quality points for the LCU1 seam at Coppabella
It should also be noted that DHSA spacings relate to global estimation variances (and
associated relative errors) over the study area considered, at a given average drill hole
spacing. It therefore follows that isolated pockets of drill holes, away from the main body of
drilling at any given spacing, are associated with higher relative errors within the local
isolated polygon. Care should therefore exercised in this regard when using spacings obtained
using DHSA in coal resource classification, not to use isolated resource mask polygons.
Coppabella determine the drill spacing for a 10% relative error over 1 year and 5
years.
West Burton determine drill spacings for classification and further infill drilling
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Figure 11 Total coal thickness distribution at Coppabella Mine and three domain areas (Creek, Central and East)
In the case of Coppabella, it was important to determine the confidence limits to the estimate
as variation in ROM ash% at the mine was being studied in order to determine whether this
was due to the geological model being less accurate in places or due to increased mining
dilution.
The first step in each of the studies was EDA and domaining of the data. At Coppabella the
mine was divided into three domains, namely East Domain, Central Domain and Creek
Domain, based on variation in total coal thickness across the deposit and the presence of
faulting and intrusives (Figure 11). East Domain contains intrusive sills which increase
thickness variability in this area compared to the other two domains. Central Domain has a
more consistent total coal thickness of around 10 m which drops to a total coal thickness of
around 6 m for Creek Domain.
At Wilpinjong it was not necessary to domain any of the seams. Although significant trend is
present in thickness for some seams this did not prevent suitable variograms from being
modelled in each case.
In the case of West Burton, a relatively small localised area of higher raw ash% was found
for the GM seam, however it was decided not to domain this out and to rather consider this as
part of the variability in the single domain. This is because this is an exploration tenement
with relatively wide spaced drilling in places. If the high ash area were to be domained out,
this would reduce the population variance for the two resulting domains and increase the
classification spacings as a result. It is possible that further infill drilling may find other
localised high ash areas within the larger domain currently deemed to be low ash. This would
result in the larger drill spacings determined previously due to domaining being incorrect. It
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was therefore decided to err on the side of caution and to consider the GM seam to have
higher ash variability from the outset.
After completing the EDA and variography on the two critical variables selected for each
study, namely thickness and raw ash%, the estimation variances for a range of block sizes
and global estimation variances were determined (a selected set of variograms for critical
variables are shown in Figures 12 to 14). Test block sizes were smaller for Coppabella due to
the shorter ranges exhibited by the variogams.
Input parameters used to determine the study area size for 5 years mining for each study are
shown in Table 1. It is important to note that the total coal thickness used in the calculation of
study area size is not a straight summation of average coal thickness for all seams in the
resource. It is based on an assessment of average coal thickness and interburdens in order to
determine the number of potential simultaneous mining faces. This in turn allows for an
estimate of the potential average total working section thickness per annum.
Table 1 Input parameters to determine study area size for 5 years mining
Results from the three studies for some key seams are presented in Table 2. In Table 2, a
measure of population variability, the coefficient of variation, is shown for each critical
variable for each seam, together with the variogram range for each variable and classification
distances determined through DHSA.
In the case of Wilpinjong, the M4 seam has greater classification distances than the A12
seam, mainly due to the much higher CV for ash for the A12 seam. The other two main
contributing factors to the classification distance, namely study area size and variogram range
are similar.
For Coppabella, The LCU1 seam in the Central Domain has larger classification distances
than for the same seam in the East Domain. This is due to the higher variability of the LCU1
seam thickness in the East Domain as evidenced by the higher CV for thickness of 0.4 and
shorter variogram ranges, which results in shorter classification distances. This higher
variability is due to the presence of intrusive sills in this domain.
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Table 2 Selected results from the three DHSA studies
The Coppabella LCU1 seam in the East Domain has a similar CV for thickness to the A12
seam ash CV at Wilpinjong; however classification distances for LCU1 East Domain are
much shorter. This is partly a function of the much smaller Coppabella study area size, which
in turn is a function of the lower mining rate due to the complexity of the deposit. Secondly
the variogram ranges for LCU1 East Domain are much shorter.
In the case of West Burton, the study area size is larger than at Wilpinjong and the CV for ash
for the GM seam is similar to that of the M4 seam. Despite this, the classification distances
for the GM seam are less than that of the M4 seam, especially for Measured and Indicated.
This is the result of the much longer variogram range (more than double) for the M4 seam
ash as compared to the GM seam ash variogram range.
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Figure 12 Wilpinjong A12 seam raw ash variogram
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Figure 13 Coppabella LCU1 seam, East Domain, thickness variogram
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Figure 14 Coppabella LCU1 seam, Central Domain, thickness variogram
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Discussion
The DHSA method is presented as an easy to use process which includes examples from case
studies which illustrate solutions to commonly encountered problems in coal. The use of
SGeMS geostatistical software and a reference to charts for solving the estimation variance
equation, published in Journel and Huijbregts (1978), are mentioned so as to enable
geologists without access to sophisticated (and expensive) geostatistical software to conduct
their own DHSA studies.
The results of the three DHSA studies conducted by HDR mining consultants for Peabody
Energy Australia are presented and discussed. These results clearly show that the main
criteria in determining classification distance using the DHSA method are;
Population variability.
Size of the study area, which in turn is a function of working section thickness and
mining rate.
The results from the three studies are consistent with each other and differences in
classification distance between seams at the three sites can be explained by variation in the
three main criteria listed above.
It is considered that this paper shows that the DHSA method, as presented in this paper with
specific reference to its application to coal, represents a relatively simple way of using
geostatistics to assess confidence in coal resource estimates. The case studies presented show
that DHSA can be applied to both mature mining projects as well as early stage exploration
projects.
It should be noted however that the approach to DHSA in the case of exploration projects
needs to be more conservative, recognising that data gaps potentially exist. An example of
this is the decision not to domain out a localised high ash area in the GM seam when
conducting the West Burton DHSA study. DHSA determined spacings should also not be
used in isolation to other factors that may affect confidence in a coal resource estimate, such
as degree of faulting for example.
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References
BERTOLI, O., PAUL, A., CASLEY, Z., & DUNN, D., 2013: Geostatistical drillhole spacing
analysis for coal resource classification in the Bowen Basin, Queensland, International
Journal of Coal Geology, 112, pp 107-113.
ISAAKS, H.I., & SRIVASTAVA, R.M., 1989: Applied Geostatistics, Oxford University
Press, New York, New York.
JOURNEL, A.G., & HUIJBREGTS, CH, J., 1978: Mining Geostatistics, The Blackburn
Press, Caldwell, New Jersey.
WILLIAMS, C.M., NOPPE, M., & CARPENTER, J., 2010: Coal Quality estimation error
Ordinary Kriging challenges inverse distance, Bowen Basin Symposium 2010 Back in (the)
Black, Geological Society of Australia Inc. Coal Group and the Bowen Basin Geologists
Group, Mackay, October 2010, 77-87.
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