Stochastic Distance Based Geological Boundary Modeling with Curvilinear Features
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Stochastic Distance Based Geological Boundary Modeling with Curvilinear Features Maksuda Lillah · Jeff B. Boisvert
Received: 13 July 2011 / Accepted: 28 September 2012 / Published online: 20 October 2012 © International Association for Mathematical Geosciences 2012
Abstract Obtaining accurate geological boundaries and assessing the uncertainty in these limits are critical for effective ore resource and reserve estimation. The uncertainty in the extent of an ore body can be the largest source of uncertainty in ore resource estimation when drilling is sparse. These limits are traditionally interpreted deterministically and it can be difficult to quantify uncertainty in the boundary and its impact on ore tonnage. The proposed methodology is to consider stochastic modeling of the ore boundary with a distance function recoding of the available data. This technique is modified to incorporate non-stationarities in the form of a locally varying anisotropy field used in kriging and sequential Gaussian simulation. Implementing locally varying anisotropy kriging retains the geologically realistic features of a deterministic model while allowing for a stochastic assessment of uncertainty. A case study of a gold deposit in Northern Canada is used to demonstrate the methodology. The proposed technique generates realistic, curvilinear geological boundary models and allows for an assessment of the uncertainty in the model. Keywords Geostatistics · Resource · Estimation · Rock type · Stationarity · Locally varying · Lithology 1 Introduction When considering resource estimation with a standard geostatistical block model, there are two main sources of uncertainty due to sparse sampling: (1) the uncertainty M. Lillah · J.B. Boisvert Centre for Computational Geostatistics, Department of Civil and Environmental Engineering, 3-133 Markin/CNRL Natural Resources Facility, University of Alberta, Edmonton, AB, Canada, T6G 2W2 J.B. Boisvert () Centre for Computational Geostatistics, Department of Civil and Environmental Engineering, 3-133 Markin/CNRL Natural Resources Facility, University of Alberta, Edmonton, AB, Canada, T6G 2G4 e-mail: [email protected]
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Math Geosci (2013) 45:651–665
in the mineral grade distribution which controls the quality of ore found within each block of the model, and (2) identifying which blocks in the model are considered to belong to the ore deposit and which are unmineralized waste. The boundaries between rock types define the stationary zones within which the data are considered to come from the same distribution (i.e. same mean, variance and spatial statistics). The grade distributions are modeled within each independent domain using kriging, inverse distance or change of support-based strategies. The determination of the boundary separating ore and waste is a critical aspect in ore reserve estimation because incorrect assumptions of stationarity can lead to a significant bias in the final resource estimation model. Normally, it is not sufficient to model grades first and assume waste is determined by cut
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