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

Question 3 of 29: 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, 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 1.3: The Semi-Variogram – Components and Sketch (6 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. 1.3 – Empirical semi-variogram (blue points) with fitted spherical model (red), showing nugget, sill and range. Axes: X = lag distance h (m); Y = γ(h), squared-assay units (e.g. %² or (g/t)²).

Random component. The nugget-like, spatially unstructured part of a sample's grade variability – short-scale noise from sampling/assay error and true grade variation at a scale finer than the closest sample spacing, which appears as an apparently random scatter with no spatial correlation to nearby samples.

Regional component. The spatially structured part of grade variability – the systematic increase of γ(h) with separation distance h that reflects genuine geological continuity (mineralizing controls, zoning, structural trends); it is this component the variogram is built to capture and that kriging exploits to weight nearby samples more than distant ones.

Nugget, C0. The y-intercept of the fitted model – the value γ(h) jumps to as h → 0+, quantifying the random component (micro-scale variability plus sampling/assay error) that exists even between arbitrarily close samples.

Sill. The plateau value C0 + C that γ(h) rises to and then flattens at; it represents the total variance of the (stationary) grade population and equals the a-priori sample variance when the model is well fitted.

Range, a. The lag distance at which γ(h) first reaches the sill – beyond this separation, samples are no longer spatially correlated ("no memory" of each other), and the range defines the practical search radius/anisotropy ellipsoid used in kriging.

Axis units. X-axis (h) carries the units of physical separation between samples (m); Y-axis (γ(h)) carries the squared units of the grade variable itself (e.g. %² Cu, (g/t)² Au), since γ(h) is half the expected squared difference between paired sample grades.