71
mineral controls are digitized in plan for each level, following the circular grade contours
of an isotropic model of Cu and Au. The polylines are converted to quaternions and interpolated into each block, creating the LVA field. The LVA variogram program calculates the
SPD between all points and embeds the points in multidimensional space, and an exponential variogram model is fit to the output. LVA kriging is performed in the multidimensional
space which has taken into account the SPD following mineral controls. Parameter files
for the programs are batched together into a script file to simplify the process. Estimation
parameters are optimized by iterating various parameters and running k-fold validation.
Standard model validation techniques such as swath plots, comparison with other estimation techniques and visual inspection are completed prior to inserting the LVA results into
the final resource model.
3.4 LVA field evolution
Defining the LVA field is the most critical aspect of the workflow, as the multi-dimensional
scaling and calculation of the isotropic variogram are all dependent on the SPD specified
by the LVA field. Several methods have been proposed for inferring the LVA field, including
from drill hole data, image processing, structural models, simulations, gradients, or from
geologic interpretation (Lillah and Boisvert, 2015). The vast number of assays and advanced
nature of the geologic interpretation of the Grasberg led FCX to choose to define the LVA
field from the Cu and Au grade distribution. In this context, improvements to the LVA field
for estimation in the GIC has been the focus of improvements to the estimation workflow.
It has evolved from a simple circular geometry applied for all three metals to more complex
geometries that better reflect local mineral controls for each metal.
3.4.1 2012–2014
FCX began exploring the LVA method in 2012 after discussions with academics from the
Centre for Computational Geostatistics (CCG) at University of Alberta at APCOM in Wollongong, Australia in 2011. In order to prove that the method could be effective, a simplified,
perfectly circular LVA field was constructed. The center of the circle was defined and the
LVA field was created by finding the perpendicular vector for each block from the circle’s
centroid location. Each block’s perpendicular vector to the centroid forms its strike angle (or
“angle1” in GSLIB parlance), the rotation around the z-axis (Fig. 5a). During this exploratory stage of the method application at Grasberg, the same LVA field was applied for all three
metals, Cu, Au and Ag. Applying the circular LVA field for kriging showed that the circular
grade continuity was far better replicated with LVA kriging then by the traditionally applied
linear ordinary kriging, and the proof-of-concept study was positive enough to warrant additional work on the method.
3.4.2 2014–2017
Prior to using the LVA kriging model to develop mine plans, more effort was devoted to creating an LVA field that would reflect local mineral controls in more detail. The decision was
made to use the grade contours of the existing models to guide the anisotropy paths for the
LVA field. Two polylines were digitized on each level: 1) an inner polyline of generally elliptical shape that followed the Au grade contours, and 2) an outer polyline of irregular, circular
shape that followed the Cu contours. Importantly, the post-mineralization barren Kali dike
was treated as though it did not exist; the polylines pass smoothly through the Kali, connecting up the matching parts of the grade contours in the Dalam and MGI (Fig. 5b).
The two anisotropy-guiding polylines were digitized for all 15 m high levels from 2,387.5 m
to 4,322.5 m elevation, then input into a semi-automatic LVA field generation program called
SPFIT, developed by researchers at the Center for Computational Geostatistics at the University
of Alberta (Dr. Jeff Boisvert and his student, Maksuda Lillah). SPFIT computes the azimuths
or strikes for each block in a 2D grid, guided by one or more user-supplied polylines that mimic
the anisotropic geometry of the variable under consideration. The azimuth grids for each level
were collated into a single 3D LVA field file for input into GAMV_LVA and KT3D_LVA.
mineral controls are digitized in plan for each level, following the circular grade contours
of an isotropic model of Cu and Au. The polylines are converted to quaternions and interpolated into each block, creating the LVA field. The LVA variogram program calculates the
SPD between all points and embeds the points in multidimensional space, and an exponential variogram model is fit to the output. LVA kriging is performed in the multidimensional
space which has taken into account the SPD following mineral controls. Parameter files
for the programs are batched together into a script file to simplify the process. Estimation
parameters are optimized by iterating various parameters and running k-fold validation.
Standard model validation techniques such as swath plots, comparison with other estimation techniques and visual inspection are completed prior to inserting the LVA results into
the final resource model.
3.4 LVA field evolution
Defining the LVA field is the most critical aspect of the workflow, as the multi-dimensional
scaling and calculation of the isotropic variogram are all dependent on the SPD specified
by the LVA field. Several methods have been proposed for inferring the LVA field, including
from drill hole data, image processing, structural models, simulations, gradients, or from
geologic interpretation (Lillah and Boisvert, 2015). The vast number of assays and advanced
nature of the geologic interpretation of the Grasberg led FCX to choose to define the LVA
field from the Cu and Au grade distribution. In this context, improvements to the LVA field
for estimation in the GIC has been the focus of improvements to the estimation workflow.
It has evolved from a simple circular geometry applied for all three metals to more complex
geometries that better reflect local mineral controls for each metal.
3.4.1 2012–2014
FCX began exploring the LVA method in 2012 after discussions with academics from the
Centre for Computational Geostatistics (CCG) at University of Alberta at APCOM in Wollongong, Australia in 2011. In order to prove that the method could be effective, a simplified,
perfectly circular LVA field was constructed. The center of the circle was defined and the
LVA field was created by finding the perpendicular vector for each block from the circle’s
centroid location. Each block’s perpendicular vector to the centroid forms its strike angle (or
“angle1” in GSLIB parlance), the rotation around the z-axis (Fig. 5a). During this exploratory stage of the method application at Grasberg, the same LVA field was applied for all three
metals, Cu, Au and Ag. Applying the circular LVA field for kriging showed that the circular
grade continuity was far better replicated with LVA kriging then by the traditionally applied
linear ordinary kriging, and the proof-of-concept study was positive enough to warrant additional work on the method.
3.4.2 2014–2017
Prior to using the LVA kriging model to develop mine plans, more effort was devoted to creating an LVA field that would reflect local mineral controls in more detail. The decision was
made to use the grade contours of the existing models to guide the anisotropy paths for the
LVA field. Two polylines were digitized on each level: 1) an inner polyline of generally elliptical shape that followed the Au grade contours, and 2) an outer polyline of irregular, circular
shape that followed the Cu contours. Importantly, the post-mineralization barren Kali dike
was treated as though it did not exist; the polylines pass smoothly through the Kali, connecting up the matching parts of the grade contours in the Dalam and MGI (Fig. 5b).
The two anisotropy-guiding polylines were digitized for all 15 m high levels from 2,387.5 m
to 4,322.5 m elevation, then input into a semi-automatic LVA field generation program called
SPFIT, developed by researchers at the Center for Computational Geostatistics at the University
of Alberta (Dr. Jeff Boisvert and his student, Maksuda Lillah). SPFIT computes the azimuths
or strikes for each block in a 2D grid, guided by one or more user-supplied polylines that mimic
the anisotropic geometry of the variable under consideration. The azimuth grids for each level
were collated into a single 3D LVA field file for input into GAMV_LVA and KT3D_LVA.