E3 ยท Publication Volume 25

Desurvey Methods

tangential, balanced tangential and minimum-curvature methods

Learning objectives

  • Explain the decision and evidence boundary for tangential, balanced tangential and minimum-curvature methods.
  • 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 method-comparison fixture with traceable coordinate increments 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

Choose a trajectory interpolation model that is appropriate for the evidence and intended use, then identify it in every output. Discrete survey stations do not reveal the exact path between stations. Tangential, balanced tangential and minimum-curvature methods impose different geometric assumptions, so two valid implementations can return different coordinates from identical stations. A method change creates a new derived trajectory version and triggers dependent recalculation.

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

The tangential method applies one station direction over an interval and introduces a direction discontinuity at stations. The balanced tangential method averages the endpoint direction vectors before multiplying by course length. The minimum-curvature method scales that average with a ratio factor so the endpoint tangents lie on a circular arc. None of these models proves the physical hole followed that ideal curve; they are deterministic interpolation rules between observations.

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

Implement every method as a pure interval function whose inputs are two canonical stations and whose output is a displacement plus diagnostics. Accumulate intervals in stable measured-depth order from a declared start position. Store method identifier, method version, angular convention, units, numerical policy and input-station fingerprints. Comparison outputs keep per-interval displacement differences so cumulative divergence can be traced to a specific course.

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 | | --- | --- | | The interpolation method and variant are mandatory metadata. | Reject or quarantine any record that violates this condition and record the exact affected identity. | | Inputs use one canonical coordinate and angle convention. | Evaluate this condition before producing a derived trajectory or interval result. | | Method changes create new trajectory versions. | Preserve received evidence and create a new version for every correction. | | Per-course increments remain available for audit. | 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

For course length \Delta MD and endpoint tangents \mathbf{t}_1,\mathbf{t}_2, balanced tangential displacement is \Delta\mathbf{r}_{BT}=\frac{\Delta MD}{2}(\mathbf{t}_1+\mathbf{t}_2). A lower-station tangential implementation uses \Delta\mathbf{r}_{T}=\Delta MD\,\mathbf{t}_2; another tangential convention may use the upper station, so the variant must be named. Minimum curvature multiplies the balanced result by a ratio factor derived from angular separation. Compare both incremental and cumulative coordinates under the same frame.

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 method-comparison fixture with traceable coordinate increments
a method-comparison fixture with traceable coordinate increments

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 method-comparison fixture with traceable coordinate increments into the evolving synthetic drillhole package, rerun all earlier fixtures and record any changed assumption.

Synthetic worked example

A synthetic two-course fixture starts vertical, turns east and then holds direction. The lower-station tangential result moves too much laterally in the first course; the balanced result splits the change between endpoints; the minimum-curvature result follows a smooth arc. The fixture records all three valid model outputs, identifies the selected production rule and proves that switching the rule invalidates downstream interval coordinates.

  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 method-comparison fixture with traceable coordinate increments, 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

  • Calling every implementation desurvey without naming the method.
  • Comparing methods after changing angle conventions.
  • Rounding each course before accumulation.
  • Overwriting a prior trajectory when the method changes.

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. What path assumption does each method impose?
  2. Why can identical stations yield different valid coordinates?
  3. Which metadata makes a trajectory reproducible?
  4. Why should per-course increments be retained?

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