Sampling Theory for Geologists: Why Your Samples Don't Represent Your Ore

Most geologists treat sampling as a field procedure: split the core, bag it, send it to the lab, get a number. The number goes into the database. The database feeds the resource estimate. Job done.

But that number — the assay result — is not the grade of your ore. It’s an estimate of the grade of a tiny fraction of your ore, obtained through a chain of physical and chemical processes, each of which introduces error. If you don’t understand sampling theory, you don’t understand where your assay numbers come from or how much you can trust them.

This post covers the fundamentals of sampling theory that every resource geologist should know, with specific application to Indonesian gold and copper deposits.

The fundamental sampling error

Every sample has error. Not measurement error — that’s the lab’s precision. Sampling error. The difference between the grade of the sample and the grade of the material it’s supposed to represent.

The Fundamental Sampling Error (FSE) is the minimum error that exists even with perfect sampling practice. It’s caused by the heterogeneous distribution of particles in the material being sampled. You can reduce it, but you can’t eliminate it.

For gold deposits, the FSE is often enormous. Gold occurs as discrete particles — nuggets — distributed unevenly through the rock. A 1kg sample might contain 3 gold particles or none. The difference in grade between these two samples is 100%, even though they came from the same material.

The Gy formula

Pierre Gy’s formula estimates the FSE:

FSE = (C × d³) / M

Where:

• C = sampling constant (depends on mineralogy, particle shape, liberation)
• d³ = cube of the maximum particle diameter (in cm)
• M = sample mass (in grams)

The key insight: FSE scales with the cube of particle diameter. If you crush the material from 10mm to 1mm before splitting, you reduce the FSE by a factor of 1,000. This is why labs crush samples before splitting — it’s not about convenience, it’s about reducing sampling error.

For a typical Indonesian gold deposit:

• C ≈ 50-200 g/cm³ (gold-rich, heterogeneous)
• d = 2mm (RC chips) or 0.1mm (pulverized)
• M = 1-3kg (assay sample)

With 2mm chips and 2kg sample:

FSE = (100 × 2³) / 2000 = 0.40 = 40%

A 40% relative error on a 2 g/t sample means the true grade could be anywhere from 1.2 to 2.8 g/t. That’s not measurement error — that’s the fundamental uncertainty of the sampling process.

With pulverized material (0.1mm) and 50g fire assay:

FSE = (100 × 0.1³) / 50 = 0.002 = 0.2%

This is why fire assay uses finely ground material — the small particle size reduces FSE to negligible levels.

The nugget effect

The “nugget effect” in geostatistics — the high variance at zero distance in the variogram — is partly caused by the FSE. When two adjacent samples have very different grades, it’s not necessarily because the geology changes dramatically — it could be because each sample captured a different set of gold particles.

For Indonesian epithermal gold deposits, the nugget effect is typically 40-60% of the total sill. This means 40-60% of the grade variability exists at scales smaller than the drillhole spacing. Some of this is geological (vein structure), but a significant portion is sampling error.

Practical implications

1. Single assay results are unreliable for high-nugget deposits. A 2 g/t result from a 1m sample might represent a 1 g/t zone with a nugget, or a 4 g/t zone with a missed nugget. Don’t make domain boundaries based on single assays.

2. Larger samples reduce the nugget effect. A 3m composite has less FSE than a 1m sample because the mass is larger. This is why compositing before variography is standard practice — it reduces sampling noise.

3. Duplicate samples don’t capture FSE. A field duplicate (split from the same sample) captures preparation error, not FSE. To estimate FSE, you need to take a second independent sample from the same interval — which for core means the other half of the split.

Sample support

“Sample support” is the volume of material that a sample represents. A 1m half-core sample at 47mm diameter has a support of about 1.8kg. A 3m composite of the same core has a support of about 5.4kg. A 50g fire assay charge has a support of 50g.

The grade of a sample depends on its support. Larger support = less variability = more representative. This is called the “support effect” — the variance of grades decreases as sample support increases.

Why this matters for resource estimation

Your block model estimates grades at the block scale — typically 5m × 5m × 5m, or about 500 tonnes. But your data is at the sample scale — 1-3kg. The variance of your data is higher than the variance of your blocks. If you kriging without accounting for this, your model will be too variable — too many high-grade blocks and too many low-grade blocks.

The correction is called “volume-variance correction” or “support adjustment.” It reduces the variance of the kriged estimates to match the block support. Most estimation software does this automatically, but you need to verify that the correction is applied and that the parameters are correct.

For Indonesian deposits, the support effect is particularly important because of the high nugget effect. Without proper support adjustment, your model will overstate the proportion of high-grade material — and your mine will underperform.

The sampling chain

The total error in an assay result is the sum of errors at each stage of the sampling chain:

1. Primary sampling — taking the original sample (core split, RC chip sample)
2. Sample preparation — drying, crushing, splitting, pulverizing
3. Sub-sampling — taking the assay charge from the pulp
4. Analysis — the lab measurement (fire assay, ICP, etc.)

Each stage adds error. The total error is:

Total Error = √(FSE² + GSE² + PE² + AE²)

Where:

• FSE = Fundamental Sampling Error
• GSE = Grouping and Segregation Error (particles separate by size/density)
• PE = Preparation Error (contamination, loss, incorrect drying)
• AE = Analytical Error (lab precision and bias)

For well-run labs, AE is typically 1-5%. For well-run sampling, PE is 2-10%. GSE can be 5-15% if not controlled. But FSE dominates — 20-40% for gold in rock chips, reduced to <1% for pulverized pulp.

The critical insight: Most of the error is introduced BEFORE the sample reaches the lab. No amount of lab QA/QC can fix a badly sampled interval. The field sampling protocol — core diameter, sample length, splitting method — determines the maximum accuracy of your data.

Practical recommendations for Indonesian projects

1. Use the largest practical core diameter

NQ (47.6mm) is standard, but HQ (63.5mm) gives 78% more mass per meter. For high-nugget gold deposits, the reduced FSE justifies the higher drilling cost.

2. Crush and split before assaying

Never send whole core to the lab. Split it on site using a riffle splitter or rotary splitter — not by grabbing handfuls. The split should be representative of the whole.

3. Use screen fire assay for coarse gold

If your deposit has visible gold or a history of coarse gold, standard 50g fire assay will under-report grade. Use screen fire assay (SFA): sieve at 75 microns, assay the coarse fraction separately, and combine. This captures the coarse gold that standard fire assay misses.

4. Monitor FSE through duplicates

Take field duplicates at 5-10% rate. If the duplicates agree within 10-15%, your sampling protocol is adequate. If they don’t, your FSE is too high — increase sample mass or reduce particle size before splitting.

5. Document your sampling protocol

JORC Table 1 Section 1 requires you to describe your sampling methodology. “Core was split and sent to the lab” is not adequate. Document:

• Core diameter
• Sample length and method
• Splitting method (diamond saw, riffle splitter)
• Sample mass
• Lab preparation protocol (crush, split, pulverize)
• Assay method and charge size

The bottom line

Your assay database is not a set of facts. It’s a set of estimates, each with an error band that depends on the sampling protocol. Understanding sampling theory — the fundamental sampling error, the nugget effect, sample support, the sampling chain — is what separates a geologist who trusts their data blindly from one who knows its limitations.

The best resource estimates I’ve seen come from geologists who understand that a 2 g/t assay doesn’t mean “the grade is 2 g/t.” It means “the grade of this 1.8kg sample, which has a 30% relative error, is 2 g/t — and the grade of the 500-tonne block it represents could be anywhere from 1 to 3 g/t.” That understanding changes how you interpret data, how you build domains, and how you report resources.