Chapter 04

The language

The vocabulary, and then the schema. If you learn one thing from this chapter, learn the drillhole data model — nearly every downstream bug in exploration analytics is a violation of it.

Core vocabulary

The drillhole data model

A drill hole is a 1-D transect sampled through a 3-D field. That single sentence explains most of the awkwardness. The data arrives in four related tables, and they are related in ways that break naive joins.

1 · Collar — one row per hole

hole_id      TEXT   PK    -- 'BAB-0417'
easting      FLOAT        -- projected X (metres, in a stated CRS)
northing     FLOAT        -- projected Y
elevation    FLOAT        -- collar height, "RL" (reduced level)
total_depth  FLOAT        -- final depth along the hole
azimuth      FLOAT        -- initial bearing, degrees from grid north
dip          FLOAT        -- initial inclination, usually NEGATIVE (downward)

2 · Survey — many rows per hole

hole_id      TEXT   FK
depth        FLOAT        -- measured depth ALONG the hole ("downhole")
azimuth      FLOAT
dip          FLOAT

Holes bend. A hole collared at −60° can be −52° at 400 m; deep holes wander tens of metres from where a straight-line projection would put them. The survey table records the actual trajectory at intervals.

3 · Lithology and 4 · Assay — interval tables

hole_id      TEXT   FK
from_depth   FLOAT        -- downhole start
to_depth     FLOAT        -- downhole end
-- lithology:  rock_code TEXT
-- assay:      element TEXT, value FLOAT, unit TEXT,
--             method TEXT, detection_limit FLOAT

Desurveying: turning the tables into geometry

To put an assay interval in 3-D space you must integrate the hole trajectory. The standard method is minimum curvature, which fits a circular arc between consecutive survey stations rather than assuming a straight segment.

Let two stations have inclinations I₁, I₂ measured from vertical and azimuths A₁, A₂, separated by measured depth ΔMD. The dogleg angle β and the ratio factor RF are:

β = arccos[ cos(I₂ − I₁) − sin(I₁)·sin(I₂)·(1 − cos(A₂ − A₁)) ]

RF = (2 / β) · tan(β / 2)          → 1 as β → 0

ΔN = (ΔMD / 2) · (sin I₁ cos A₁ + sin I₂ cos A₂) · RF
ΔE = (ΔMD / 2) · (sin I₁ sin A₁ + sin I₂ sin A₂) · RF
ΔZ = (ΔMD / 2) · (cos I₁        + cos I₂       ) · RF
Accumulate ΔN, ΔE, ΔZ from the collar to get the trajectory. Subtract ΔZ from collar elevation for true elevation; TVD (true vertical depth) is the accumulated ΔZ.

Compositing

Raw assay intervals have varying lengths, and you cannot average them naively — a 0.3 m sample and a 3 m sample do not carry equal weight. Grades are combined length-weighted:

ḡ = Σᵢ (gᵢ · ℓᵢ) / Σᵢ ℓᵢ
gᵢ = grade of interval i, ℓᵢ = its length. For a proper metal accounting you also weight by bulk density ρᵢ, since metal mass ∝ g · ℓ · ρ · area.

This is the support problem in miniature: a measurement is an average over a physical volume, and statistics computed on one support do not transfer to another. Chapter 8 makes this precise; it is the reason you cannot treat grades as point samples of a smooth field.

Resources, reserves, and why the words are legal

Public disclosure of mineral inventories is regulated — NI 43-101 in Canada, the JORC Code in Australia, S-K 1300 in the US, all broadly aligned to CRIRSCO templates. The classification encodes geological confidence, and it is one-directional: economics can demote a reserve, but only more data can promote a resource.

Deposit types you will hear about

Rosetta stone

Most of what geostatistics does, you already know under another name. Keep this table; Chapter 8 proves the top half of it.

Sources for this chapter

• CIM — NI 43-101 and the CIM Definition Standards, and the JORC Code. The actual regulatory texts behind the resource/reserve classification. Read the definitions sections; they are short and they are what the words legally mean.
• CRIRSCO — the international template that NI 43-101, JORC, SAMREC and the rest are all aligned to. Useful when you need to compare disclosures across jurisdictions.
• Marjoribanks, Geological Methods in Mineral Exploration and Mining (Springer, 2nd ed. 2010) — logging conventions, sampling practice, and where the interval tables actually come from.
• Bourgoyne et al., Applied Drilling Engineering (SPE Textbook Series). The reference derivation of directional survey calculations, including minimum curvature. Petroleum-focused, but the geometry is identical — and it is where the ratio-factor formula comes from.
• Rossi & Deutsch, Mineral Resource Estimation (Springer, 2014) — compositing, support, and how the classification categories are applied in practice.