69
Kriging is performed in the q-dimensional space, and the space is then back-transformed
to the original grid coordinates. The LVA kriging programs used by FCX at Grasberg were
built by Boisvert (2010), who modified GSLIB (Deutsch and Journel, 1992) open-source
software. Specifically, the GSLIB programs modified are GAM3, a variogram calculation
program and KT3D, a three-dimensional kriging program. GAM3 was modified to GAM3_
LVA and performs the multidimensional scaling and then calculates the resulting isotropic
omni-dimensional variogram. KT3D was modified to KT3D_LVA and reads in the hyper
dimensional rescaled coordinates and performs the kriging.
3 GRASBERG RESOURCE ESTIMATION
3.1 Motivation for adopting LVA
The motivation for adopting LVA for estimation at Grasberg derives from the complex, nonlinear geometry of grade continuity in the ore zone, which is a direct reflection of the geologic
evolution of the deposit. There are also mine planning considerations. In 2019, mining at
Grasberg will transition from open pit operations, where blasthole assays are available prior
to mining, to underground block caving where only the long term resource model will guide
production grade forecasting. Not only is it important to calculate the correct grade-tonnage
curve for long term planning, it is critical to produce the most accurate and realistic spatial
distribution of grades in the resource model. Linear ordinary kriging cannot sufficiently
reproduce the circular grade continuity of the primary mineralized domain in the deposit.
LVA kriging is far more effective for replicating the curved nature of mineralization.
3.2 Geology of the Grasberg deposit
The Grasberg Cu-Au-Ag deposit, located in the central highlands of Papua, Indonesia, is
one of the largest porphyry Cu-Au deposits in the world, containing over 5 billion metric
tonnes of material at around 0.6% Cu and 0.5 ppm Au for an estimated 32 million metric tonnes of copper and 96 million troy ounces of gold (Leys et al., 2012). Mineralization
at Grasberg is hosted primarily by Pliocene intrusive rocks that were emplaced in a tightly
folded and faulted sequence of Tertiary carbonate rocks. These carbonate rocks also host
substantial skarn deposits within the Ertsberg-Grasberg District (Fig. 2; Leys, et al., 2012).
The Grasberg intrusive rocks were emplaced in three main stages collectively referred to as
the Grasberg Intrusive Complex (GIC) (MacDonald and Arnold, 1994). The first stage, the
Dalam, makes up the bulk of the GIC and forms an upward flaring, funnel shaped package of
monzodioritic intrusions, subvolcanic breccias and volcanic rocks. An early stage of alteration,
veining and Cu-Mo mineralization is associated with a deep porphyry intrusion of Dalam age
known as the Gajah Tidur porphyry. The second stage, the Main Grasberg Intrusion (MGI),
is a pipe-like diorite plug positioned just north of the central axis of the Dalam phase rocks.
The bulk of the Cu-Au mineralization in the Grasberg deposit is associated in time and space
with the MGI. The third and final stage, the Kali, is a barren, wedge-shaped intrusion thickening from the center of the GIC to the southeast, truncating older mineralization.
High grade Cu-Au mineralization is hosted in a quartz-magnetite vein stockwork centered on
the MGI with Cu-Au-Ag grade contours decreasing outward in a concentric pattern that reflects
the temperature gradient at the time of mineralization (Fig. 3). The MGI stage of mineralization
produced an ore column approximately 1,500 m in vertical extent. Mineralization also extends
along radial structures that locally disrupt the relatively stable concentric grade contours.
3.3 Process summary
Figure 4 illustrates the LVA kriging workflow developed for the Grasberg deposit. Individual aspects of the process will be described in more detail in the following sections. The
LVA process at FCX begins by defining mineralization controls. Polylines outlining the
Kriging is performed in the q-dimensional space, and the space is then back-transformed
to the original grid coordinates. The LVA kriging programs used by FCX at Grasberg were
built by Boisvert (2010), who modified GSLIB (Deutsch and Journel, 1992) open-source
software. Specifically, the GSLIB programs modified are GAM3, a variogram calculation
program and KT3D, a three-dimensional kriging program. GAM3 was modified to GAM3_
LVA and performs the multidimensional scaling and then calculates the resulting isotropic
omni-dimensional variogram. KT3D was modified to KT3D_LVA and reads in the hyper
dimensional rescaled coordinates and performs the kriging.
3 GRASBERG RESOURCE ESTIMATION
3.1 Motivation for adopting LVA
The motivation for adopting LVA for estimation at Grasberg derives from the complex, nonlinear geometry of grade continuity in the ore zone, which is a direct reflection of the geologic
evolution of the deposit. There are also mine planning considerations. In 2019, mining at
Grasberg will transition from open pit operations, where blasthole assays are available prior
to mining, to underground block caving where only the long term resource model will guide
production grade forecasting. Not only is it important to calculate the correct grade-tonnage
curve for long term planning, it is critical to produce the most accurate and realistic spatial
distribution of grades in the resource model. Linear ordinary kriging cannot sufficiently
reproduce the circular grade continuity of the primary mineralized domain in the deposit.
LVA kriging is far more effective for replicating the curved nature of mineralization.
3.2 Geology of the Grasberg deposit
The Grasberg Cu-Au-Ag deposit, located in the central highlands of Papua, Indonesia, is
one of the largest porphyry Cu-Au deposits in the world, containing over 5 billion metric
tonnes of material at around 0.6% Cu and 0.5 ppm Au for an estimated 32 million metric tonnes of copper and 96 million troy ounces of gold (Leys et al., 2012). Mineralization
at Grasberg is hosted primarily by Pliocene intrusive rocks that were emplaced in a tightly
folded and faulted sequence of Tertiary carbonate rocks. These carbonate rocks also host
substantial skarn deposits within the Ertsberg-Grasberg District (Fig. 2; Leys, et al., 2012).
The Grasberg intrusive rocks were emplaced in three main stages collectively referred to as
the Grasberg Intrusive Complex (GIC) (MacDonald and Arnold, 1994). The first stage, the
Dalam, makes up the bulk of the GIC and forms an upward flaring, funnel shaped package of
monzodioritic intrusions, subvolcanic breccias and volcanic rocks. An early stage of alteration,
veining and Cu-Mo mineralization is associated with a deep porphyry intrusion of Dalam age
known as the Gajah Tidur porphyry. The second stage, the Main Grasberg Intrusion (MGI),
is a pipe-like diorite plug positioned just north of the central axis of the Dalam phase rocks.
The bulk of the Cu-Au mineralization in the Grasberg deposit is associated in time and space
with the MGI. The third and final stage, the Kali, is a barren, wedge-shaped intrusion thickening from the center of the GIC to the southeast, truncating older mineralization.
High grade Cu-Au mineralization is hosted in a quartz-magnetite vein stockwork centered on
the MGI with Cu-Au-Ag grade contours decreasing outward in a concentric pattern that reflects
the temperature gradient at the time of mineralization (Fig. 3). The MGI stage of mineralization
produced an ore column approximately 1,500 m in vertical extent. Mineralization also extends
along radial structures that locally disrupt the relatively stable concentric grade contours.
3.3 Process summary
Figure 4 illustrates the LVA kriging workflow developed for the Grasberg deposit. Individual aspects of the process will be described in more detail in the following sections. The
LVA process at FCX begins by defining mineralization controls. Polylines outlining the