E3 ยท Publication Volume 25

Interval Data Models

from, to, point samples and open or closed interval conventions

Learning objectives

  • Explain the decision and evidence boundary for from, to, point samples and open or closed interval conventions.
  • 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 canonical interval contract with boundary and point-event fixtures 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

The model must state what a downhole record supports. An interval observation applies over a measured-depth extent; a point event applies at one path coordinate; a cumulative depth is neither unless its semantics say so. From and to values need a borehole, depth datum, unit, boundary convention, observation type, source identity and validity state. A zero-length interval is not silently reinterpreted as a point sample.

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

Use a canonical half-open convention [from,to) for partition-like interval tables unless a domain requirement states otherwise. Adjacent intervals then meet without double ownership of the shared boundary. Preserve the source convention and record the conversion. Geological boundaries, samples, recovery runs and image segments may share measured-depth coordinates while representing different observation types; they remain in separate typed collections or carry an explicit support type.

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

Represent each interval with immutable source values and canonical numeric boundaries. Attach interval identity, borehole identity, table or observation type, source row identity, depth unit, datum, boundary convention, attributes, quality state and provenance. Point events use a point-support model rather than duplicated from and to. Unknown endpoints remain unknown; an end-of-hole value may constrain validity but must not be inserted as a missing endpoint without evidence.

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 support declares borehole, depth datum and unit. | Reject or quarantine any record that violates this condition and record the exact affected identity. | | Boundary convention is explicit and preserved through conversion. | Evaluate this condition before producing a derived trajectory or interval result. | | Point events and positive-length intervals are distinct types. | Preserve received evidence and create a new version for every correction. | | Unknown boundaries are never filled from convenience. | 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

Canonical interval length is \ell=to-from. A valid ordinary interval requires finite boundaries and \ell>0; a contract that permits zero-length marker intervals must type them separately. The intersection of two half-open intervals has length \ell_{\cap}=\max(0,\min(to_1,to_2)-\max(from_1,from_2)). Equality tests use the declared depth tolerance only for classification; stored evidence is not rounded merely to make boundaries meet.

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 canonical interval contract with boundary and point-event fixtures
a canonical interval contract with boundary and point-event fixtures

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 canonical interval contract with boundary and point-event fixtures into the evolving synthetic drillhole package, rerun all earlier fixtures and record any changed assumption.

Synthetic worked example

A synthetic log contains lithology [0,10], [10,25] under an undocumented closed convention and a marker at 25. The import preserves those source statements, maps the partition to [0,10) and [10,25), and models the marker as a point event. A sample [24,26) overlaps both the final lithology metre and the point location but does not become part of the lithology partition.

  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 canonical interval contract with boundary and point-event fixtures, 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

  • Mixing inclusive and half-open intervals without metadata.
  • Treating a zero-length interval as a valid sample.
  • Using row order as interval identity.
  • Filling a missing endpoint with end of hole.

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 are half-open intervals useful for partitions?
  2. How does a point event differ from a zero-length interval?
  3. Which metadata makes downhole support interpretable?
  4. How is interval intersection length computed?

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