140
To simplify the planning and mining engineering studies, the Uniform Conditioning estimates have been ‘localized’. This estimation approach is an addition to the conventional
Uniform Conditioning process. The Grade-Tonnage relationships inside each panel are discretized into a set of SMU grades that respects the estimated Uniform Conditioning Grade
Tonnage relationships. These SMU grades are then located within each panel using a linear
estimate of the SMU grades to reveal the likely locations of the highest-grade SMUs and
lowest grade SMU’s. This approach has been described by Abzalov 2006.
The panel grade estimate, using co-kriging was performed in the panel level in order to
minimize the conditional bias while retaining some local variability, the panel size is similar to the long-term sample space. The discretization and the neighborhood definition were
chosen using quantitative kriging neighborhood analysis QKNA, (Vann, et al., 2003). The
UC conditioning was performed using the panel model and the DGM, for the main variable
was chosen 61 regular cut-off grades (0 to 6) were chosen. The UC post-process (LUC) was
carried to localize the grades using the SMU model which was estimated using the same
approach used for the panel estimate.
9 TURNING BAND UNIVARIATE SIMULATION
Geostatistical simulation produces a model of uncertainty that is represented by multiple
sets of possible values distributed in a space; one set of possible outcomes is referred to as a
realization (McLennan and Deutsch, 2004). In this study, the fluctuation of 100 realizations
is used to check the localized uniform conditioning estimate.
The Turning Bands algorithm, used in this study, consists in drawing many lines in space,
with random or, preferably, quasi-regular orientations, and simulating a one-dimensional
random field along each line (Lantuéjoul, 1994, 2002). By adequately choosing the covariance function of such one-dimensional random fields, their superposition provides a multidimensional random field with the target covariance function, the distribution of which is
practically Gaussian by virtue of the central limit theorem. The application of the method is
therefore controlled by the number of lines used and by the method used to simulate the basic
one-dimensional random fields
For Nb 2 O 5 Turning Bands simulation, 400 bands were chosen to create a multidimensional
simulation, it was performed in a node level using the same neighborhood strategy defined
by QKNA and applied in the UC workflow. Finally, the normal scores simulated results were
retro-calculated to raw and averaged in order to calculate simulations to the SMU grades.
The quality of the turning band simulation was checked using the Minimum Acceptance
Criteria for Geostatistical Realizations (Leuangthong, et al., 2004), in a nutshell, it consists
in the fact that the simulation must reproduce the those following steps:
• data values at their location,
• distribution of the attribute of interest, and
• the spatial continuity characterized by the variogram model.
10 DISCUSSION
The performance of two popular algorithms: 1) – Multivariate Uniformed Conditioning
(and the add-on localized) that estimates the conditional distribution of metal and tonnage
above a cut-off within a mining panel and; 2) – Turning Bands which performs simulations
in a multi-dimensional space through a series of one-dimensional simulations were tested in
this study through a real case.
The set of 100 realizations obtained via TB were plotted in a grade tonnage curve and
then compared with the UC and the LUC. It demonstrates that the UC and the LUC were
able to correctly predict the recoverable tonnage of the deposit, since those curves match in
every cut-off grade (from 0 to 3% Nb 2 O 5 ) with the fluctuation curves derived as a result of
the simulation, see Figure 8.
To simplify the planning and mining engineering studies, the Uniform Conditioning estimates have been ‘localized’. This estimation approach is an addition to the conventional
Uniform Conditioning process. The Grade-Tonnage relationships inside each panel are discretized into a set of SMU grades that respects the estimated Uniform Conditioning Grade
Tonnage relationships. These SMU grades are then located within each panel using a linear
estimate of the SMU grades to reveal the likely locations of the highest-grade SMUs and
lowest grade SMU’s. This approach has been described by Abzalov 2006.
The panel grade estimate, using co-kriging was performed in the panel level in order to
minimize the conditional bias while retaining some local variability, the panel size is similar to the long-term sample space. The discretization and the neighborhood definition were
chosen using quantitative kriging neighborhood analysis QKNA, (Vann, et al., 2003). The
UC conditioning was performed using the panel model and the DGM, for the main variable
was chosen 61 regular cut-off grades (0 to 6) were chosen. The UC post-process (LUC) was
carried to localize the grades using the SMU model which was estimated using the same
approach used for the panel estimate.
9 TURNING BAND UNIVARIATE SIMULATION
Geostatistical simulation produces a model of uncertainty that is represented by multiple
sets of possible values distributed in a space; one set of possible outcomes is referred to as a
realization (McLennan and Deutsch, 2004). In this study, the fluctuation of 100 realizations
is used to check the localized uniform conditioning estimate.
The Turning Bands algorithm, used in this study, consists in drawing many lines in space,
with random or, preferably, quasi-regular orientations, and simulating a one-dimensional
random field along each line (Lantuéjoul, 1994, 2002). By adequately choosing the covariance function of such one-dimensional random fields, their superposition provides a multidimensional random field with the target covariance function, the distribution of which is
practically Gaussian by virtue of the central limit theorem. The application of the method is
therefore controlled by the number of lines used and by the method used to simulate the basic
one-dimensional random fields
For Nb 2 O 5 Turning Bands simulation, 400 bands were chosen to create a multidimensional
simulation, it was performed in a node level using the same neighborhood strategy defined
by QKNA and applied in the UC workflow. Finally, the normal scores simulated results were
retro-calculated to raw and averaged in order to calculate simulations to the SMU grades.
The quality of the turning band simulation was checked using the Minimum Acceptance
Criteria for Geostatistical Realizations (Leuangthong, et al., 2004), in a nutshell, it consists
in the fact that the simulation must reproduce the those following steps:
• data values at their location,
• distribution of the attribute of interest, and
• the spatial continuity characterized by the variogram model.
10 DISCUSSION
The performance of two popular algorithms: 1) – Multivariate Uniformed Conditioning
(and the add-on localized) that estimates the conditional distribution of metal and tonnage
above a cut-off within a mining panel and; 2) – Turning Bands which performs simulations
in a multi-dimensional space through a series of one-dimensional simulations were tested in
this study through a real case.
The set of 100 realizations obtained via TB were plotted in a grade tonnage curve and
then compared with the UC and the LUC. It demonstrates that the UC and the LUC were
able to correctly predict the recoverable tonnage of the deposit, since those curves match in
every cut-off grade (from 0 to 3% Nb 2 O 5 ) with the fluctuation curves derived as a result of
the simulation, see Figure 8.