Mining Goes Digital – Mueller et al. (Eds)
© 2019 Taylor & Francis Group, London, ISBN 978-0-367-33604-2
67
Application of Locally Varying Anisotropy (LVA) kriging at the
Grasberg porphyry Cu-Au-Ag deposit, Papua, Indonesia
Andrew Issel, Adam Schwarz, Ken Moss & Rick Rossi†
Freeport-McMoRan, Inc. Phoenix, Arizona, USA
ABSTRACT: The Grasberg porphyry Cu-Au-Ag deposit in Papua, Indonesia is primarily
hosted by a funnel shaped body of Pliocene intrusive rocks known as the Grasberg Intrusive
Complex (GIC). Cu-Au-Ag mineralization exhibits concentric grade contours in plan view
and extends over a vertical depth of 1,500 m. Traditional geostatistical tools measure the spatial continuity between sample locations as a function of Euclidean distance and direction.
Complex geometries often violate first- and second-order stationarity assumptions. The circular pattern of grade continuity at Grasberg challenges traditional linear estimation methods
limited by a fixed anisotropy for a domain of interest. Locally Varying Anisotropy (LVA)
kriging overcomes this limitation, removing anisotropy by multidimensional scaling according to a defined anisotropy grid. Implementation of LVA kriging to estimate block grades at
the Grasberg porphyry Cu-Au-Ag deposit began in 2013 and continuous improvement efforts
have focused on correctly modeling the anisotropy grid, known as the LVA field. The LVA
field is the most important input to the LVA estimation process, as it defines the direction
and magnitude of continuity of the attribute under consideration. The LVA field for Grasberg evolved from a perfect circle used for all three metals to a grid interpolated from guiding
polylines on each level that are individualized for each metal. Progress is substantiated by cross
validation techniques. The resulting models display grade distributions that better reflect field
observations, and have improved the reliability of resource estimates for this complex domain.
1 INTRODUCTION
Traditional geostatistical tools such as the variogram, covariance, and correlogram measure
the spatial continuity between sample locations as a function of both distance and direction.
However, distance and direction are straight-line or vector or Euclidean measures. Nonlinear
geologic features (e.g. anticlines, folded strata, fluvial reservoir channels, porphyry deposits
with concentric grade contours) present formidable challenges for geostatistical estimation
because of the curvilinear features. In geostatistical terms, complex geometries often violate
first-order stationarity (the mean is invariant of location in the estimation domain) and the
second-order stationarity (the covariance is invariant of location in the estimation domain)
assumptions. Locally varying anisotropy (LVA) kriging offers an alternative.
LVA kriging was adopted by Freeport-McMoRan (FCX) to model block grades of Cu,
Au, and Ag at the supergiant Grasberg porphyry deposit in Papua, Indonesia in 2013. In the
subsequent years, several improvements to the estimation framework and workflow have been
implemented. This paper describes the evolution of the LVA estimation workflow applied at
the Grasberg deposit.
2 LOCALLY VARYING ANISOTROPY KRIGING
The LVA kriging methodology, developed by Boisvert (2010) and employed by FCX for
resource estimation at the Grasberg deposit, starts with the construction of a 3D LVA field.
© 2019 Taylor & Francis Group, London, ISBN 978-0-367-33604-2
67
Application of Locally Varying Anisotropy (LVA) kriging at the
Grasberg porphyry Cu-Au-Ag deposit, Papua, Indonesia
Andrew Issel, Adam Schwarz, Ken Moss & Rick Rossi†
Freeport-McMoRan, Inc. Phoenix, Arizona, USA
ABSTRACT: The Grasberg porphyry Cu-Au-Ag deposit in Papua, Indonesia is primarily
hosted by a funnel shaped body of Pliocene intrusive rocks known as the Grasberg Intrusive
Complex (GIC). Cu-Au-Ag mineralization exhibits concentric grade contours in plan view
and extends over a vertical depth of 1,500 m. Traditional geostatistical tools measure the spatial continuity between sample locations as a function of Euclidean distance and direction.
Complex geometries often violate first- and second-order stationarity assumptions. The circular pattern of grade continuity at Grasberg challenges traditional linear estimation methods
limited by a fixed anisotropy for a domain of interest. Locally Varying Anisotropy (LVA)
kriging overcomes this limitation, removing anisotropy by multidimensional scaling according to a defined anisotropy grid. Implementation of LVA kriging to estimate block grades at
the Grasberg porphyry Cu-Au-Ag deposit began in 2013 and continuous improvement efforts
have focused on correctly modeling the anisotropy grid, known as the LVA field. The LVA
field is the most important input to the LVA estimation process, as it defines the direction
and magnitude of continuity of the attribute under consideration. The LVA field for Grasberg evolved from a perfect circle used for all three metals to a grid interpolated from guiding
polylines on each level that are individualized for each metal. Progress is substantiated by cross
validation techniques. The resulting models display grade distributions that better reflect field
observations, and have improved the reliability of resource estimates for this complex domain.
1 INTRODUCTION
Traditional geostatistical tools such as the variogram, covariance, and correlogram measure
the spatial continuity between sample locations as a function of both distance and direction.
However, distance and direction are straight-line or vector or Euclidean measures. Nonlinear
geologic features (e.g. anticlines, folded strata, fluvial reservoir channels, porphyry deposits
with concentric grade contours) present formidable challenges for geostatistical estimation
because of the curvilinear features. In geostatistical terms, complex geometries often violate
first-order stationarity (the mean is invariant of location in the estimation domain) and the
second-order stationarity (the covariance is invariant of location in the estimation domain)
assumptions. Locally varying anisotropy (LVA) kriging offers an alternative.
LVA kriging was adopted by Freeport-McMoRan (FCX) to model block grades of Cu,
Au, and Ag at the supergiant Grasberg porphyry deposit in Papua, Indonesia in 2013. In the
subsequent years, several improvements to the estimation framework and workflow have been
implemented. This paper describes the evolution of the LVA estimation workflow applied at
the Grasberg deposit.
2 LOCALLY VARYING ANISOTROPY KRIGING
The LVA kriging methodology, developed by Boisvert (2010) and employed by FCX for
resource estimation at the Grasberg deposit, starts with the construction of a 3D LVA field.