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24-MMP-A4 Mine Valuation and Mineral Resource Estimation · May 2016

Question 27 of 29: 3: Ordinary vs. Simple Kriging for Gold Block Estimation

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

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 6.1.3: Ordinary vs. Simple Kriging for Gold Block Estimation (2 marks)

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.

Ordinary kriging (OK). Assumes only LOCAL stationarity of the mean within the search neighbourhood – it does not require the global population mean to be known and instead estimates it implicitly through the Σλi=1 constraint (Question 1.6). This makes OK robust to a mean that drifts slowly across the deposit (e.g. broad zonation in a large epithermal system), and it is the default, standard method for routine resource-block-model estimation.

Simple kriging (SK). Requires the population mean m to be known/assumed constant (globally stationary) everywhere. Where that assumption genuinely holds (e.g. within an already-defined, homogeneous geological/grade domain), SK is provably MORE efficient (lower estimation variance) than OK for the same data configuration, because it does not "spend" any of its degrees of freedom re-estimating a mean it is told is already known. SK is therefore favoured within well-defined single-population domains and is the building block underlying indicator/probability kriging (Question 6.2), where the "mean" being kriged is itself a known probability (the global proportion below a cutoff).

Comparison for gold block estimation. For a typical epithermal gold deposit – often exhibiting real broad-scale grade zonation (e.g. higher grade toward a feeder structure) – OK's local-mean flexibility is usually preferred for the PRIMARY grade estimate; SK is reserved for sub-applications where the relevant "mean" (e.g. a cutoff-grade probability) genuinely is known and constant within a domain, such as the indicator-kriging framework discussed next.