D2 · Publication Volume 18

Statistics, Geostatistics, Resource Estimation and Classification

Connects data support, spatial continuity, estimation and classification in an auditable resource workflow.

Purpose and boundary of this book

A resource estimate is a decision-bounded numerical interpretation of geological evidence. It combines validated samples, geological domains, measurement support, spatial continuity, density, geometry, estimation rules and economic context. It is not a count of all sampled mineralisation, and it is not made reliable by a smooth block display or a familiar software setting. Every estimate is conditional on the data available, the scale represented, the assumptions adopted and the purpose for which the result will be used.

This book develops an auditable workflow from data readiness through exploratory analysis, compositing, declustering, treatment of extreme values, variography, neighbourhood design, estimation, block-model construction, validation, grade–tonnage analysis, classification and uncertainty. The recurring questions are: what does each value represent, which population may it belong to, how far may its information be extended, how does support change variability, which assumptions control metal or material quantity, and what evidence is required before a confidence category is assigned?

The book does not certify a mineral resource, prepare a public disclosure, determine legal compliance, approve an investment, select a mining method, or replace the judgement of appropriately qualified geoscience, mining, processing, economic, environmental and reporting professionals. A classroom estimate can illustrate a workflow but cannot establish reasonable prospects for extraction in a real setting. Applicable law, reporting codes, professional duties and project-specific modifying factors must be assessed independently.

General and institution-neutral scope

This is a general, institution-neutral tutorial. It has no relationship to, affiliation with, sponsorship by, endorsement from or curriculum dependency on any company or individual. It is not written for a named owner, operator, consultancy, university, regulator, software product, property, deposit, mine or private database. Every unnamed collar, interval, assay, density value, domain, variogram, block, grade, cost, scenario and classification example is synthetic teaching material.

Names of standards bodies, public agencies, researchers and technical publications occur only in source notes when they are needed to identify evidence. A citation does not make a named person or organisation the author, publisher, sponsor, provider, partner, endorser, scientific authority or subject of this tutorial. The website carrying these pages is only a hosting and delivery surface. It is not the tutorial's author, publisher, sponsor, provider, owner, scientific authority or curriculum subject, and it asserts no institutional ownership of the curriculum.

Institutional neutrality is also a quality control. A recognised name cannot repair mixed supports, biased sampling, an invalid variogram, an untested top cut, a block model with the wrong rotation or a confidence category defined by one convenient metric. Credibility must come from traceable data, geological coherence, explicit assumptions, reproducible calculations, sensitivity analysis and evidence proportionate to the decision.

The estimation contract

Before calculation begins, write an estimation contract with eight linked statements:

  1. Purpose: which decision, review or communication task will use the estimate?
  2. Target material: which variable, unit, material state and reference point are represented?
  3. Model extent: what horizontal extent, vertical range, domains and time state are included?
  4. Data support: what physical volume, mass or interval does each observation represent?
  5. Selectivity: what block or selective unit is relevant to the intended use?
  6. Continuity model: which assumptions describe spatial dependence inside each domain?
  7. Acceptance tests: which global, local, visual and sensitivity checks must pass?
  8. Reporting boundary: which result is an inventory, an estimate, a classified resource or merely an exploration hypothesis?

The contract prevents the workflow from becoming a sequence of software operations. It also creates a review structure: every transformation and parameter must answer one of these statements, and every output must retain a route back to its evidence.

Learning outcomes

After completing the book, the learner should be able to:

  • distinguish data quality, sampling support, spatial representativity and geological domaining;
  • use exploratory statistics without confusing a sample distribution with a spatial population;
  • composite irregular intervals while preserving mass, boundaries, gaps and residual-length decisions;
  • diagnose preferential sampling and apply declustering as a sensitivity rather than a cosmetic correction;
  • investigate extreme values and document the consequences of capping or restricted influence;
  • calculate and interpret experimental variograms, anisotropy, nugget, sill and range;
  • design search neighbourhoods from geology, data geometry, support and validation evidence;
  • explain nearest-neighbour, inverse-distance and kriging estimates and their assumptions;
  • design a block model with explicit origin, rotation, dimensions, support and coding rules;
  • validate an estimate globally, locally, spatially and against alternative methods;
  • construct grade–tonnage sensitivities without presenting an unconstrained inventory as a resource;
  • assign confidence categories using convergent geological, data and estimation evidence; and
  • represent uncertainty with scenarios, realizations, envelopes and decision consequences.

Prerequisites and notation

The book assumes familiarity with quantities, probability, descriptive statistics, geological domains, drillhole data and three-dimensional models. A sample value is written z(\mathbf{u}_i) at location \mathbf{u}_i with support v_i. A target block centred at \mathbf{u}_0 has volume V. A weighted estimate is


z^*(\mathbf{u}_0)=\sum_{i=1}^{n}\lambda_i z(\mathbf{u}_i),

where the weights \lambda_i depend on the chosen method. A semivariogram is written \gamma(\mathbf{h}), where \mathbf{h} is a separation vector. Tonnage in a block is T_b=V_b\rho_b, and contained quantity for a mass-fraction grade g_b is Q_b=T_bg_b after compatible units and reference points have been confirmed.

Symbols are deliberately method-neutral. A formula is not permission to use data outside a valid domain or beyond defensible continuity. All coordinates, units, density bases, missing-value conventions, detection limits and transformations must be declared with the model.

Workflow and evidence artefacts

An auditable estimate is a chain of artefacts rather than a single block file. The minimum chain contains a source register, validation report, domain version, support table, exploratory analysis, compositing specification, declustering study, extreme-value decision, variogram models, neighbourhood tests, estimation configuration, block definition, validation package, sensitivity tables, classification criteria and release manifest.

Every artefact should record inputs, filters, parameters, code or calculation version, reviewer, date, outputs and limitations. Preserve the pre-transformation values. A composite must retain its contributing intervals; a capped value must retain the uncapped grade; a classified block must retain the criteria it satisfied. This lineage allows a reviewer to distinguish a geological change from a calculation change.

Synthetic study volume used in examples

Worked examples use a fictional folded lens inside a rectangular volume 1{,}400\,\mathrm{m} long, 800\,\mathrm{m} wide and 520\,\mathrm{m} vertically. The synthetic dataset contains 58 drillholes, 2,460 assay intervals, 410 density measurements and three mineralisation domains. Drilling is deliberately clustered in the central sector. Sample lengths vary, several intervals are unsampled, the upper tail is strongly skewed and one domain has uncertain continuity across a synthetic fault.

The teaching block model uses a fictional local coordinate system and contains parent cells with optional subcells for geometry. All values were invented and do not correspond to any real property or organisation. Contradictions are intentional: one duplicate assay differs from its source, some composites cross a proposed boundary, a variogram direction is weakly informed, and alternative cut-off assumptions change the reported inventory. The purpose is to expose review decisions, not to imitate a real estimate.

Assessment and completion standard

Completion requires an estimation review package, not merely a coloured block model. For every chapter, the learner should preserve the input subset, calculation or rule, diagnostic output, sensitivity and decision note. A satisfactory final package includes:

  • a signed-off data-readiness and support register;
  • domain-specific exploratory and spatial statistics;
  • reproducible composite, declustering and extreme-value studies;
  • directional experimental variograms and adopted models;
  • neighbourhood and block-support sensitivity tests;
  • estimates from at least two methods used for comparison rather than voting;
  • global, local, swath, visual and boundary validation;
  • grade–tonnage and assumption sensitivities;
  • a classification matrix with geological and data evidence; and
  • an uncertainty statement that separates measurement, domain, parameter, spatial and economic sources.

Core sources