How your main field model shapes the ISCWSA error model

The magnetic reference model supplies values for declination, magnetic dip, and total field. Its uncertainty enters specific terms in the ISCWSA instrument performance model (IPM). A lower reference uncertainty can reduce position uncertainty, but the result also depends on the survey method, well geometry, and other error sources.

The reference also affects the assumed correlation of magnetic errors between wells. That correlation matters when calculating relative position uncertainty for anti-collision. Rev5 separates reference errors into components so that partial correlations can be represented within the existing framework.

For a practical comparison of IGRF, WMM, BGGM, and HDGM, see which magnetic model to drill with. This article explains how the error model uses the selected reference.

Original reference uncertainties

Hugh Williamson's "Accuracy Prediction for Directional Measurement While Drilling" (SPE 67616, December 2000) established the original ISCWSA MWD framework. Each error source has a 1σ magnitude, a weighting function that maps it into depth, inclination, and azimuth errors, and a propagation mode that specifies correlation across survey stations, legs, and wells.

For the original standard six-axis MWD calculation, the magnetic reference terms were a declination uncertainty of 0.36° and a horizontal-field-dependent source magnitude of 5000 deg·nT. The latter has an azimuth weighting proportional to 1/(B·cos dip). Here, B is the total magnetic field strength in nT, and dip is the magnetic dip angle. B·cos dip is the horizontal magnetic field strength. The azimuth effect therefore increases where that horizontal field is weak, often at high magnetic latitudes.

The axial-corrected calculation also depends on reference dip and total field uncertainty. Those dependencies must be represented in its error model; the two standard-method terms do not describe the whole reference budget for every MWD method.

The original global classification assumed a common reference error across wells in the same field. It did not establish that the physical error was identical at every location. Global propagation is a correlation assumption in the model, whose suitability depends on the surveys being compared. See Williamson's paper and the ISCWSA definition, sections 3.1 and 6.2.3.

Temporal uncertainty: Rev4

The Earth's magnetic field changes with daily variation and geomagnetic activity. Surveys taken at different times can therefore experience different errors against a static reference. The random propagation mode represents temporal uncertainty statistically; it does not mean that all physical storm effects are independent between surveys.

Rev4 (March 2015) added random reference terms, including DECR (0.10°) and DBHR (3000 deg·nT), with dip and total-field counterparts for axial correction. These terms contribute to the uncertainty calculation and to field acceptance criteria derived from the error model. A complete QC criterion must also account for the other relevant errors and the selected acceptance limit. The reference terms alone do not define an acceptable survey-to-survey disagreement. See the ISCWSA definition, section 6.3.5.

Rev5 reference components

ISCWSA records approval of Rev5 in October 2019. The definition document records its first Rev5 version in March 2020, although its model history table lists October 2020. These are distinct documentation dates; the approval date is October 2019.

Rev5 divides each reference family into up to seven components:

• -U: the part modeled as uncorrelated between different wells. It propagates well by well, so it remains correlated within a well.
• -OS: omission error in the wavelength band between standard and high-resolution model resolution.
• -OH: omission error in the band between high-resolution and IFR resolution.
• -OI: omission error at wavelengths shorter than IFR resolves.
• -CH / -CI: commission errors within the resolved crustal field of high-resolution and IFR models, respectively.
• -R: the temporal component modeled with random propagation.

These components represent a practical decomposition based on assumptions about the field spectrum and correlations. They are not direct measurements of seven separate errors in an individual well. See the geomagnetic correlation supplement.

The following generic 1σ declination estimates come from the ISCWSA definition, Rev5.13, January 2023. A blank cell means that the term is inactive in that model variant. It does not mean that the corresponding physical error is absent.

Higher-resolution references remove some omission terms and introduce commission terms for the field they resolve. IFR2 also reduces the generic temporal component. The table therefore shows changes in the error budget, rather than a guarantee that every term shrinks at each step.

The same decomposition applies to horizontal-field-dependent reference errors and to the dip and total-field sources used with axial correction. The selected tool model determines the active terms and magnitudes. These generic estimates are defaults, not mandatory performance specifications. The declination table alone is not a complete azimuth uncertainty budget.

Correlation between wells

Williamson's original framework already supported fully correlated error sources. Rev5 makes partial correlation between different reference types practical by separating them into components modeled as either shared or uncorrelated.

The correlation supplement gives an ideal example of parallel wells from the same pad sharing a declination error. Complete cancellation in relative position requires matching position-error responses at the compared points. That component still contributes to each well's absolute position uncertainty. It cannot be removed from every collision calculation solely because both wells share a reference.

For two wells expressed in a common coordinate frame, relative covariance is:

Crel = CA + CB − CAB − CABᵀ

CA and CB are the individual-well covariance matrices. CAB is the cross-covariance between the position errors of wells A and B, and CABᵀ is its transpose. If CAB is zero, the result reduces to CA + CB. The correlation correction uses cross-covariance; it is not the subtraction of each well's global variance.

Under the generic Rev5 correlation assumptions, matching global source terms contribute to that cross-covariance. The commission terms must be included along with the omission terms:

• Two IFR1 references: shared -CI and -OI components.
• Two high-resolution references: shared -CH, -OH, and -OI components.
• One IFR1 and one high-resolution reference: shared -OI components.

The -U components are uncorrelated between different wells, but remain correlated within each well. The applicable correlation assumptions and reference records must support the selected terms. See the correlation supplement's software guidance and the definition's relative-positioning equations.

Shared errors do not always reduce relative uncertainty. The two wells can respond in different directions, so correlation can increase or decrease the uncertainty relevant to their separation. The result depends on their geometry and error responses. An updated covariance does not itself set allowable spacing; the applicable clearance rule and acceptance criteria still govern the decision.

Consistent reference records help identify the correct correlation assumptions. Using matching references does not guarantee a smaller relative ellipse or improved clearance.

Location-specific uncertainty

BGS estimates and model mapping

The BGS BGGM error service provides scalable 1σ estimates for a latitude, longitude, and date. The public service splits them into global and random components. BGS states that an upgrade accounting for the correlated and uncorrelated Rev5 components can be requested. The public G/R outputs are therefore not a direct replacement for all the Rev5 sub-terms in the table.

The parameter mapping also matters. The public service does not compute DBHG and DBHR separately; their contributions are included in DECG and DECR. Retaining generic DBH contributions alongside those combined outputs would count that contribution twice. Use the mapping supplied with the selected reference estimates and tool model.

In Beggan et al. (2021), Table 3, location-specific values reduced modeled 1σ lateral semi-major axes at total depth by about 7.8–26% across the three ISCWSA test wells and the reported standard and axial-corrected methods. The broader 5.2–26% range includes a fourth well offshore Brazil. These are comparisons of modeled uncertainty, not measurements of improved field accuracy.

The same study also found increases for some orientations. Near-horizontal east–west drilling with axial correction in the Brazil example increased modeled lateral uncertainty by up to 24%. Location-specific estimates can be larger than generic estimates where the field conditions warrant it.

IFR measurements and estimates

IFR1 uses local vector observations or transformed aeromagnetic or marine survey data to estimate the local crustal field. IFR2 uses observatory data to estimate temporal variation at the wellsite. Both combine measurements and estimates, and both retain uncertainty. Their error models must represent the reference actually supplied. See the BGS description of IFR1 and IFR2.

References

• Williamson, H.S. (2000). Accuracy Prediction for Directional Measurement While Drilling. SPE Drilling & Completion 15(4), SPE 67616.
• ISCWSA (January 2023). Definition of the ISCWSA Error Model, Rev5.13.
• ISCWSA. Application of Partial Correlations Between Geomagnetic Terms. Technical Supplement to MWD Error Model Rev5, linked from the error model documentation.
• Sawaryn, S.J. et al. (2019). Well-Collision-Avoidance Separation Rule. SPE Drilling & Completion 34(01), SPE 187073.
• Grindrod, S.J. et al. (2016). OWSG Standard Survey Tool Error Model Set for Improved Quality and Implementation in Directional Survey Management. SPE/IADC 178843.
• Beggan, C.D., Macmillan, S., Brown, W.J., Grindrod, S.J. (2021). Quantifying Global and Random Uncertainties in High Resolution Global Geomagnetic Field Models Used for Directional Drilling. SPE Drilling & Completion 36(3), SPE 204038.
• British Geological Survey. BGGM model, error service, and parameter definitions.