E3 · Publication Volume 25

Drillhole Trajectories, Interval Data and Quality-Control Algorithms

Develops reproducible algorithms for drillhole trajectories, intervals, compositing and automated quality control.

Purpose and boundary of this book

This book develops reproducible methods for turning collars, directional survey stations and downhole intervals into auditable spatial evidence. It covers coordinate conventions, station semantics, trajectory interpolation, minimum-curvature calculation, survey validation, interval algebra, compositing, cross-stream depth registration, numerical policy and reviewable quality control. It is a methods tutorial, not a product manual.

This is a general, institution-neutral tutorial with no relationship to any company or individual. All borehole identifiers, coordinates, depths, directions, intervals, values and review events in the lesson are synthetic and must not be used for an operational decision.

The website carrying the material acts only as a host. It is not the owner, publisher, scientific authority or subject of the curriculum. Named standards and technical works appear only in source sections to identify evidence used in preparing the tutorial.

Control chain

A defensible drillhole derivative follows one chain: preserve received evidence; resolve identities and conventions; validate stations and intervals; run a named versioned algorithm; retain intermediate diagnostics; link every output to exact inputs; evaluate purpose-specific quality gates; and record the release or quarantine decision.

The chain separates observation from interpolation. A collar and survey station are observations under declared methods. A continuous trajectory is a derived geometric model. A downhole log or sample has measured-depth support. Its three-dimensional position is another derivative obtained by intersecting that support with a selected trajectory version.

Learning outcomes

  • declare drillhole coordinate, angle, depth and datum conventions without ambiguity;
  • model, select and validate directional survey observations;
  • implement tangential, balanced-tangential and minimum-curvature calculations;
  • design interval contracts and exact gap, overlap and intersection algorithms;
  • create support-aware composites that respect domains, missingness and residual policy;
  • register images, assays, logs, geophysics and recovery onto a traceable depth axis;
  • control floating-point comparisons, ordering and canonical output; and
  • combine automated findings, human review and governed exceptions into an auditable release.

Prerequisites, notation and conventions

The tutorial assumes the quantitative foundations of A1, coordinate-reference reasoning from E1 and semantic/provenance principles from E2. It also benefits from the drilling and sampling concepts developed in C6. No particular programming language, database or software product is required.

Unless stated otherwise, lengths use metres, angles in formulas use radians, azimuth is clockwise from declared north, inclination is measured from vertical down, positions use East–North–Up, and downhole intervals are half-open [from,to). MD denotes measured depth along the reference path; TVD denotes vertical depth under a declared datum and sign convention.

Synthetic teaching dataset

All exercises use a synthetic set of boreholes identified SYN-H001 and onward. Coordinates are local and invented. Survey stations include deliberately designed duplicates, angle wraps, wide spacing, invalid order and missing metadata. Interval tables include exact adjacency, small numeric discrepancies, gaps, overlaps, domain boundaries, censored values and recovery loss.

The dataset evolves without overwriting prior evidence. Every correction is a new observation or derivation. Every trajectory, overlay, composite and registration result carries a manifest. When the evidence cannot support a unique answer, the correct output is conflict, unknown or blocked release rather than an invented value.

Learning workflow

Each lesson starts with a decision and ends with an assessed artefact. Learners write the convention or rule first, implement the smallest deterministic transformation, construct golden and adversarial cases, inspect exact findings, and then integrate the result into one evolving drillhole quality package.

A second learner should reproduce the result from the package alone. If success depends on a remembered angle convention, row order, interface default, hidden tolerance or private explanation, the artefact is incomplete.

Evidence architecture and quality gates

Source evidence preserves collars, stations, intervals, files and acquisition context. Semantic evidence declares identities, depth axes, units, coordinate frames, angle conventions and value states. Process evidence records selection, conversion, calculation, overlay, compositing and registration. Decision evidence records findings, review, exceptions and release.

  • All required identities, references, units and conventions resolve.
  • Station and interval invariants pass under versioned rules.
  • Every derivative identifies exact inputs, algorithm, parameters and numerical policy.
  • Support, coordinates and uncertainty remain traceable through transformations.
  • Unresolved hard failures block the affected release regardless of aggregate scores.

Assessment and completion standard

The final assessed package contains a coordinate-convention contract, accepted survey view, at least three desurvey method fixtures, an independently verified minimum-curvature kernel, survey and interval findings, a lossless interval overlay, a domain-aware composite table, a depth-registration map, a numerical policy, golden datasets, run manifests and a release decision.

Acceptance requires deterministic reruns, exact lineage, stable ordering, explicit tolerance policies, conserved interval support, no silent correction and an explainable outcome for every hard finding. A precise blocked result is valid; an apparently complete result produced by guessing metadata is not.

Core sources