E3 ยท Publication Volume 25

Depth Registration across Data Types

core photographs, assays, logs, geophysics and recovery

Learning objectives

  • Explain the decision and evidence boundary for core photographs, assays, logs, geophysics and recovery.
  • Design and implement the relevant drillhole data or algorithm contract without hidden conventions.
  • Separate hard release gates from diagnostics, interpretation and authorised review.
  • Produce a versioned depth-registration map with anchors, uncertainty and residuals from synthetic evidence.

The lesson is complete only when the learner can defend the data model, algorithm, tests and release decision. An attractive trajectory or clean interval table without source evidence and executable invariants remains unverified.

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.

Decision context

Different data streams can use driller depth, recovered-core position, sample depth, image coordinate, tool depth or processed trajectory depth. Registration decides how a coordinate in one stream maps to the borehole reference depth and whether the mapping is sufficiently supported for a stated use. Coincident labels do not prove coincident physical support. Recovery loss, depth resets, cable stretch, image cropping and manual marks can all break a one-to-one mapping.

Write the intended use, consequence of error, required evidence and release authority before selecting a transformation. The same source can be suitable for exploratory display and unsuitable for a released derivative. Fitness is evaluated against a versioned contract and use, not attached permanently to a file.

Core concept

Define each depth axis as a typed coordinate system with datum, unit, direction and acquisition context. Registration consists of evidence-backed anchor pairs and an interpolation model between them. A piecewise-linear map is appropriate only where monotonicity and local correspondence are justified. Discontinuities, unmapped gaps and ambiguous sections remain explicit. The registered derivative points to both source axes and the mapping version.

Keep received observations, accepted evidence views and derived results as distinct objects. This separation allows corrected evidence or a changed method to generate a new result without rewriting history. Every derived coordinate or interval therefore answers both a scientific question and a provenance question.

Algorithm and data model

Store anchor identity, source coordinate, target measured depth, evidence type, reviewer state and uncertainty. Partition the map into monotonic segments; reject reversed anchors unless the source axis legitimately reverses and the contract supports it. Images additionally require pixel-to-length calibration and crop offsets. Interval data are transformed by mapping both boundaries and then checking order, while point events map once with propagated uncertainty.

Define the transformation as a pure, testable operation wherever practical. Parsing, semantic validation, evidence selection, numeric calculation and release evaluation are separate stages. Each stage emits structured output and does not depend on interface state, filename order or an undocumented default.

Constraints and invariants

| Invariant | Executable or review test | | --- | --- | | Every depth axis declares its datum, unit and acquisition context. | Reject or quarantine any record that violates this condition and record the exact affected identity. | | Registration anchors retain evidence and uncertainty. | Evaluate this condition before producing a derived trajectory or interval result. | | Unmapped gaps remain gaps rather than being stretched away. | Preserve received evidence and create a new version for every correction. | | Every derivative identifies the mapping version. | Include the rule identifier, observed value and resolution state in audit output. |

An invariant must survive import, conversion, processing, export and rerun. A failed hard invariant produces no apparently valid substitute. Diagnostic checks remain visible with their threshold, scope and evidence, and require a reviewed rule before they can trigger correction.

Quantitative reasoning

Between anchors (s_0,m_0) and (s_1,m_1), piecewise-linear registration is m(s)=m_0+(s-s_0)(m_1-m_0)/(s_1-s_0). Residuals at independent check points are r_j=m^{observed}_j-m(s_j). Report bias, absolute residuals, maximum gap between anchors and uncertainty bands; do not collapse them into one score. For interval [s_a,s_b), transform both endpoints and preserve the source support link.

Every reported metric includes units, numerator and denominator where applicable, exclusions, comparison policy and evaluation version. Aggregate values are stratified when pooling could hide a local failure. A quantitative diagnostic supports a decision but cannot overrule missing identity, invalid geometry, unresolved conflict or broken lineage.

Evidence and uncertainty

Keep observation uncertainty, interpolation uncertainty, numeric approximation and metadata uncertainty separate. A smooth trajectory can be numerically precise while still poorly constrained between widely spaced stations. An exact interval overlay can still be unfit when a source depth datum is unknown. The assessed result states which uncertainty belongs to the phenomenon, the measurement, the algorithm and the interpretation.

Build an evidence packet containing immutable received records, semantic declarations, validation findings, algorithm inputs and outputs, test results, reviewer decisions and fingerprints. Contradictory evidence remains available. When a required dependency cannot be resolved, return an explicit unknown, conflict or blocked status rather than choosing the most convenient value.

Interfaces and storage

Interfaces transmit identities, units, coordinate and depth references, conventions, value states, versions and lineage beside numeric values. A trajectory exchange includes collar and datum context, accepted station identities, algorithm identity, numerical policy and output coordinates. An interval exchange includes support type, boundary convention and source links. Structured errors identify the record, field, observed value, expected condition and rule.

Store authoritative received evidence separately from reproducible derivatives and disposable views. Indexes, caches and visualisations may improve access but cannot become the only copy of angle conventions, accepted-station decisions or interval lineage. Export round trips verify that identifiers, precision, ordering and missing states survive encoding changes.

Governance and review

Assign responsibilities to roles rather than named organisations or people: evidence custodian, rule author, implementation maintainer, independent validator and release reviewer. A role may propose a correction but cannot erase source evidence. Rule and algorithm changes are reviewed, versioned and evaluated against fixed regression fixtures before they affect a release.

Exceptions are explicit decisions with scope, rationale, evidence, approving role, affected versions and review trigger. They never rewrite a failed rule and never propagate automatically. The host website has no ownership or scientific-authority role in this workflow; it only delivers the tutorial.

Integration checkpoint

a versioned depth-registration map with anchors, uncertainty and residuals
a versioned depth-registration map with anchors, uncertainty and residuals

Read the figure as a reasoning map from preserved evidence through explicit conventions, deterministic calculation, validation and release. Each arrow represents a declared relationship or transformation. Integrate a versioned depth-registration map with anchors, uncertainty and residuals into the evolving synthetic drillhole package, rerun all earlier fixtures and record any changed assumption.

Synthetic worked example

A synthetic core image strip runs from pixel 0 to 2400 and represents recovered core from 50.0 to 55.8 m, while the drilled run extends to 56.0 m. Two photographed depth blocks provide anchors, and a documented 0.2 m loss remains unmapped rather than stretched across the image. An assay interval crossing the loss is linked to the borehole axis but is not assigned fictitious pixels. The mapping report shows anchors, segment equations and the unmapped span.

  1. Preserve the received records and state the intended decision without correction.
  2. Resolve identities, units, conventions and evidence eligibility; mark every unresolved item.
  3. Run the versioned algorithm and tests while retaining intermediate diagnostics.
  4. Issue accept, reject or quarantine and show how an independent reviewer can reproduce it.

Practice task

Implement the chapter artefact against a synthetic fixture containing one normal case, one boundary case, one invalid case and one unresolved-evidence case. Preserve the received fixture. Produce canonical input, validation findings, derivative output, processing manifest and a short release decision.

Acceptance criteria:

  • Every input identity, unit and convention required by the rule is explicit.
  • The implementation is deterministic under stable ordering and the declared numerical policy.
  • No correction overwrites received evidence or turns unknown into a guessed value.
  • All hard failures block the affected derivative and remain machine-readable.
  • A second implementation or reviewer can reproduce the result from the package alone.

Submit a versioned depth-registration map with anchors, uncertainty and residuals, the golden and adversarial fixtures, exact findings and a limitations note. A screenshot is not sufficient evidence because it does not identify the input version, algorithm or rule configuration.

Common failure modes

  • Assuming equal depth labels imply physical alignment.
  • Stretching recovery loss uniformly across an image.
  • Using non-monotonic anchors without an explicit segment model.
  • Transforming an interval midpoint but not its boundaries.

These failures share a pattern: an implicit convenience is substituted for evidence. Diagnose the earliest boundary where the assumption entered, restore the source statement, make the convention or rule explicit, rerun every dependent derivative and supersede rather than overwrite the affected release.

Review questions

  1. Why is each depth stream a separate coordinate axis?
  2. What evidence makes a registration anchor defensible?
  3. How should recovery loss appear in a mapping?
  4. Which diagnostics describe registration quality?

For every answer, identify the governing invariant, the evidence needed to evaluate it, the numerical or semantic policy involved and the correct behaviour when the condition fails.

Sources and further reading