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24-MMP-A4 Mine Valuation and Mineral Resource Estimation · May 2017

Question 2 of 18: The Semi-Variogram – Components and Sketch

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, 2017-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 five optional Questions 2–6 (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, smelter/refining contract terms, net smelter return, transportation logistics); SME Mining Engineering Handbook, 3rd ed. (cost-estimating relationships, mineral exploration/evaluation stages, ore reserve classification); Evans, An Introduction to Ore Geology and Guilbert & Park, The Geology of Ore Deposits (ore deposit models); CIM Best Practice Guidelines and NI 43-101 (Canadian Securities Administrators).

Question 1.2: The Semi-Variogram – Components and Sketch (7 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.

Lag distance hγ(h)Sill C₀ + CNugget C₀Range a
Fig. 1.2 – Experimental variogram (blue points) and fitted spherical model (red curve). X axis: lag distance h, in metres (m) – the separation distance between sample pairs. Y axis: γ(h), in the squared units of the grade variable (e.g. %Cu², g/t Au²) – half the expected squared difference in grade between two points separated by h.

(a) Random component. The apparent scatter of experimental γ(h) points around the fitted model curve – short-range, essentially unpredictable grade variation (micro-scale mineralogical/sampling noise) that a variogram model cannot resolve below its own nugget and sampling spacing. It is captured numerically by the nugget effect.

(b) Regional component. The smooth, structured rise of γ(h) with increasing lag – the spatially continuous, geologically controlled part of the grade field (e.g. mineralization trends, alteration zoning) that IS predictable and is exactly what ordinary/simple kriging exploits to interpolate block grades.

(c) Nugget, C0. The value of γ(h) extrapolated back to h=0 – representing sampling/analytical error plus true short-range (sub-sample-spacing) grade variability that the sampling grid cannot resolve. A large nugget relative to the sill means poor local predictability, i.e. the deposit is "spotty" at the scale sampled.

(d) Sill, C0+C. The value γ(h) rises to and levels off at once spatial correlation is exhausted – equal to the a priori (stationary) variance of the grade population σ². Beyond the range, samples carry no more information about each other than any two randomly chosen samples in the deposit.

(e) Range, a. The lag distance at which γ(h) reaches the sill – the maximum distance over which two samples remain spatially correlated. It directly sets the kriging search-neighbourhood radius: pairs separated by more than the range contribute no useful information to a block estimate.

(f) Axis units (shown on the sketch above). X axis: lag distance h in metres. Y axis: γ(h) in the squared units of the grade variable being modelled (e.g. %Cu² for a copper deposit, (g/t Au)² for a gold deposit) – the variogram is a variance, so its units are always the grade unit squared.