D1 · Publication Volume 17

3D Geological Modelling, Domains and Uncertainty

Builds purpose-driven 3D geological models with explicit domains, topology, scenarios and confidence.

Purpose and boundary of this book

A three-dimensional geological model is a structured interpretation of the subsurface. It joins observations, inferred contacts, structural relations, geometric rules and chosen representations inside a stated volume. It is not the ground itself, and visual smoothness does not turn an interpretation into an observation. Every model answers a purpose at a scale. A model suitable for regional groundwater screening may be unsuitable for a narrow excavation, and a detailed mineralisation envelope may be irrelevant to a basin-scale question.

This book develops a purpose-driven workflow from the decision question to a reviewable, versioned geological interpretation. It covers data preparation, geological domains, explicit and implicit surface construction, fault frameworks, surfaces and solids, topology, lithological and mineralisation domains, structural scenarios, validation, uncertainty, confidence and change review. The emphasis is on what a model claims, what constrains it, which assumptions create its geometry and how a reviewer can distinguish supported structure from extrapolation.

The book does not certify a geological interpretation, approve a resource estimate, prescribe a commercial modelling package, replace competent structural or resource-geology judgement, or authorise engineering, investment, environmental or safety decisions. A model can support those decisions only after the relevant disciplines have checked its purpose, evidence, scale, uncertainty and downstream consequences.

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, public agency, software product, property, deposit, mine or private database. Every unnamed coordinate, drillhole, contact, unit, fault, domain, volume, scenario and decision in the examples is synthetic teaching material.

Names of public bodies, standards organisations, research teams and technical documents occur only in source notes when 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 modelling control. A recognised brand cannot repair an inverted stratigraphic order, an open solid, an unexplained fault termination, a domain that mixes incompatible populations or a revision that overwrites its predecessor. Credibility must come from traceable constraints, explicit rules, reproducible construction, validation evidence and honest uncertainty.

A model is a decision-bounded claim

Begin with six linked statements:

1. Decision: what choice, test or communication task will use the model?
2. Target volume: what horizontal extent, vertical range and time state are represented?
3. Geological objects: which units, contacts, faults, folds, intrusions, alteration zones or mineralisation domains matter?
4. Evidence: which observations constrain each object, and with what spatial support and quality?
5. Construction rules: how are surfaces interpolated, truncated, displaced, joined and converted to volumes?
6. Acceptance limits: which errors, unsupported extrapolations or scenario differences would make the model unsuitable for the decision?

These statements form a model contract. They prevent detail from expanding merely because a tool can display it. They also make review possible: a reviewer can test whether the selected objects, resolution and validation actually address the declared use.

Learning outcomes

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

• distinguish observations, derived constraints, interpretations and presentation geometry;
• define a model purpose, extent, scale, resolution, coordinate reference and acceptance criteria;
• prepare contact, orientation, interval, surface and categorical data without erasing lineage;
• explain the strengths and limits of explicit and implicit construction;
• build a fault and stratigraphic relationship framework before interpolating detailed geometry;
• recognise invalid surfaces, non-manifold meshes, gaps, overlaps, self-intersections and impossible topology;
• define lithological and mineralisation domains from geological continuity rather than convenient shapes;
• construct and compare alternative structural scenarios;
• validate data honouring, topology, volumes, contacts, sections and downstream fitness;
• represent uncertainty as source, location, magnitude, scenario and consequence; and
• version a model so that every adopted change can be reconstructed and reviewed.

Prerequisites and notation

The book assumes familiarity with geological observation, maps and sections, structural geology, drillhole evidence and basic uncertainty. Coordinates are written as vectors \mathbf{x}=(x,y,z) in a declared reference system. A contact surface may be represented explicitly as a mesh S or implicitly as a level set of a scalar field f(\mathbf{x})=c. A geological domain is a subset D_k of the model volume associated with stated geological membership rules.

Symbols are deliberately generic. d(\mathbf{x},S) denotes distance to a surface, \nabla f the gradient of a scalar field, I_k(\mathbf{x}) a domain indicator and U(\mathbf{x}) a spatial uncertainty descriptor. The notation does not prescribe an algorithm. When a method requires stationarity, smoothness, continuity or a particular boundary condition, that assumption must be stated independently of the software that implements it.

Representations and their consequences

A section line, triangulated surface, tetrahedral mesh, voxel grid and block model are not interchangeable pictures of the same thing. Each representation has a topology, resolution, numerical precision and set of permitted operations. A surface mesh can preserve a sharp contact but does not by itself assign the material on either side. A voxel field samples space but may stair-step a narrow feature. A closed solid supports volume and containment queries, provided its boundary is valid and consistently oriented.

The chosen representation should follow the question. Preserve source geometry separately from display simplification. Record whether distances and volumes were calculated from the adopted model or from a decimated derivative. Never infer geological certainty from dense tessellation: many triangles can describe a poorly constrained surface.

Synthetic study volume used in examples

The worked examples use a fictional rectangular volume measuring 1{,}200\,\mathrm{m} east–west, 900\,\mathrm{m} north–south and 700\,\mathrm{m} vertically. It contains four ordered units, one erosional surface, a steep fault and a folded mineralised horizon. Forty-two synthetic drillholes and a synthetic surface map provide incomplete constraints. Coordinates, names and values were invented for teaching and do not correspond to any real property or organisation.

The examples deliberately contain contradictions: duplicate contacts, uncertain orientations, an unclosed mesh, alternative fault offsets and sparse deep control. The objective is not to produce a polished image. It is to show how defects are found, represented and carried into a decision record.

Assessment and completion standard

Completion requires more than drawing a model. For each chapter, the learner should be able to provide a small evidence package containing the input subset, declared rules, construction parameters, validation results, uncertainty statement and interpretation limits. A satisfactory final package includes:

• a model-purpose and acceptance record;
• a source and constraint register;
• a relationship graph for units and structures;
• at least two plausible structural scenarios;
• explicit topology and data-honouring tests;
• a spatial confidence or extrapolation representation;
• a version-to-version change set; and
• a concise statement of what the model does not support.

Core sources

• An inventory of three-dimensional geologic models, defines and compares published 3D geological model purposes, extents, objects and release attributes.
• GeoSciML 4.1, provides a logical model for geological features, observations, boreholes and exchange semantics.
• LoopStructural 1.0, describes explicit and implicit representations, structural frames and time-aware geological relationships.
• GemPy 1.0, presents implicit structural modelling, topology analysis and stochastic approaches.
• PROV-O, supplies a general provenance model for entities, activities, derivation and revision.