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Advances in Data Spacing and Uncertainty Open Access


Other title
Data Spacing
Conditional Simulation
Drillhole Spacing
Type of item
Degree grantor
University of Alberta
Author or creator
Cabral Pinto, Felipe A
Supervisor and department
Deutsch, Clayton (Civil & Environmental Engineering)
Examining committee member and department
Boisvert, Jeff (Civil & Environmental Engineering)
Askari-Nasab, Hooman (Civil & Environmental Engineering)
Department of Civil and Environmental Engineering
Mining Engineering
Date accepted
Graduation date
2016-06:Fall 2016
Master of Science
Degree level
Collecting information is of vital importance for the development of a mineral project. The capital costs of mining projects are high and there is significant risk due to the available data. At all stages of a project, from exploration to mine closure, decisions need to be made that are based off of the data available. Some of the important sources of data include field work, outcrops, geophysical and geochemical measurements, and drilling. The information gathered can be either quantitative or qualitative, and the specific data available depends on each individual project. Of the data typically available, the information gathered from drilling is the most direct approach to understanding the subsurface mineral deposit. This thesis addresses two important decisions companies face regarding drilling, (1) What is the data spacing needed to achieve an acceptable level of uncertainty for a relevant scale? and (2) What is the rate that uncertainty changes when more data is collected? There is a level of uncertainty for drillhole spacing in any scale. The level of uncertainty can be shown as a measurement such as the probability of the grade to be within a percentage of the mean, which can be calculated for a relevant production scale. This may suggest a drillhole spacing, that is on average, associated to a desired level of precision. For example, the estimated grade of monthly production volumes falling within ±15% of the mean 80% of the times. With a specific level of precision, the drillhole spacing associated with it increases as the production scale increases. In certain circumstances, the uncertainty versus data spacing can be established analytically. A "Learning Curve" is established to gain a deeper understanding of how uncertainty relates to data spacing for different spatial structure. The Learning Curve summarizes the rate at which the scale of variability is resolved for additional drilling. This work also addresses the influence of important explanatory factors on the total variability. Explanatory factors are mostly economic, geologic and geometric factors that explain the variability in a variable. Uncertainty does not depend solely on data spacing (geometric factor), local uncertainty is also influenced by conditional mean, conditional variance (economic factors) and entropy (geologic factor). The influence of these factors explaining uncertainty is modelled by statistical regression techniques. A comprehensive case study is presented that includes geological and grade modelling. This full data spacing study is practically important to present the concepts reviewed in this thesis and to demonstrate new concepts regarding uncertainty versus drillhole spacing.
This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for the purpose of private, scholarly or scientific research. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
Citation for previous publication
Pinto, F.A.C. and Deutsch, V.C. (2015) Expected Uncertainty as a Function of the Variogram, Data Spacing and Other Factors, presented at 37th International Symposium on Application of Computers and Operations Research in the Mineral Industry (APCOM ) in Fairbanks, Alaska, USA, 1149 pp.

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