24-MMP-A4 Mine Valuation and Mineral Resource Estimation · May 2016
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
EGBC National Exam — Mining and Mineral Processing Engineering, 09-Mmp-A4 Mine Valuation and Mineral Resource Estimation, 2016-May. 3 hours duration; one handwritten 8.5×11 in reference sheet permitted (not an open-book exam); only approved Sharp or Casio calculators allowed. Question 1 is compulsory (40 marks, parts 1.1–1.6); candidates then select THREE of the six optional Questions 2–7 (20 marks each) to complete the paper.
Reference texts: Isaaks & Srivastava, An Introduction to Applied Geostatistics (variogram modelling, kriging estimators, volume–variance relations); Hustrulid, Kuchta & Martin, Open Pit Mine Planning and Design (mine valuation, NPV and cut-off grade methodology, mineable reserves); Gentry & O'Neil, Mine Investment Analysis (Canadian mining taxation, inflation and financing effects on DCF yield, smelter/refining contract terms, net smelter return); SME Mining Engineering Handbook, 3rd ed. (mineral exploration/evaluation stages, ore reserve classification, ore deposit models); CIM Best Practice Guidelines and NI 43-101 (Canadian Securities Administrators).
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
Simple kriging (SK) does NOT impose the Σλi=1 constraint that ordinary kriging does, because SK is derived assuming the population mean m is already KNOWN (stationary and given, not estimated from the local data). The SK estimator is instead $$Z^*_{SK} = m + \sum_i \lambda_i\big(Z(x_i)-m\big)$$ so any "missing" weight (1 − Σλi) is implicitly applied to the KNOWN mean m itself, not left unaccounted for. Because the estimator is built this way, it is unbiased BY CONSTRUCTION regardless of whether Σλi happens to equal 1 – the deviation term Σλi(Z(xi)−m) correctly reverts toward the known mean m wherever local data is sparse or far away, rather than systematically over- or under-shooting. No separate correction is needed; the "problem" is only apparent, not real, once the estimator's own structure is understood.
