Multi-Station Analysis

What MSA estimates

Multi-Station Analysis (MSA) uses measurements from several survey stations to estimate systematic errors in a directional sensor package. These include axis biases, scale-factor errors, and non-orthogonality.

A single station can support checks of gravity magnitude, magnetic field strength, and dip. These checks cannot determine a full calibration. Some sensor errors pass these limits while still causing inclination or azimuth errors.

A calibration applies to an interval where the error pattern is sufficiently stable. Temperature changes, shock, or drift can change that pattern during a run. The analysis must then assess whether one calibration remains suitable.

How sensor errors change the measurements

An ideal three-axis sensor measuring a constant field places every possible orientation on a sphere centred on zero. The following drawings show conceptual projections of that measurement surface.

Bias shifts the surface. Unequal scale factors and non-orthogonal axes can deform it. A rigid rotation preserves the sphere, so field magnitude alone cannot determine every alignment correction.

Real survey stations sample only part of the surface. Similar inclinations or toolfaces can leave parameters coupled or poorly determined. More stations with similar orientations do not necessarily resolve these limits.

How the analysis works

The analysis compares each station with its reference gravity magnitude, magnetic field strength, and dip. The reference values can vary with location, depth, and time.

TALLENTECH uses joint nonlinear estimation with robust residual weighting. The model includes nine basic sensor error terms per triad: three biases, three scale-factor errors, and three non-orthogonality terms. It also supports relative accelerometer–magnetometer alignment and constrained magnetic field-strength and dip offsets.

The selected configuration determines which parameters vary, remain fixed, or use prior constraints. A fitted parameter set is not proof of one uniquely determined physical calibration.

The magnetic reference follows the selected survey-processing source. This can include a main-field model, IFR1, or IFR2. Reference uncertainty remains part of the analysis. Declination is needed to convert magnetic azimuth to true azimuth.

Robust weighting reduces the influence of some large residuals. It does not guarantee detection of every bad measurement. Review the station flags, weights, excluded data, and solver status before accepting a correction.

Before-and-after residuals show agreement with the fitted constraints. Smaller residuals do not, by themselves, prove more accurate inclination or azimuth. Parameter resolution, remaining uncertainty, and independent checks also matter.

Axial accelerometer check shots

Downhole survey stations give MSA little information about the axial accelerometer. Its bias (Gz bias) and scale-factor error are hard to resolve from downhole data, and both affect inclination and TVD.

Surface check shots isolate them. The rig takes surveys with the tool vertical, at 0° and at 180° inclination. The axial accelerometer then reads about +1 g and about −1 g. Half the sum of the two readings gives the bias. Half the difference, compared with local gravity, gives the scale-factor error. MSA solves these check shots separately. It then holds the axial bias and scale-factor error at the measured values when it fits the downhole stations.

The check shots give each tool's actual values, instead of the generic allowance of 0.4 mg (1σ) for the bias. A bias that is not corrected tilts the calculated path. On a horizontal lateral, each 1 mg of bias tilts it by about 0.06°, which moves the well about 3 m vertically over 3,000 m. The bias also reaches dip and azimuth: see how a Gz bias reaches inclination, dip and azimuth.

An illustrative uncertainty comparison

Figure 1 uses TALLENTECH's uncertainty engine and generic error models on the published ISCWSA standard test well #1. It compares reference-model, MSA and check-shot assumptions at a total measured depth of 8,000 m. The displayed 2σ values are uncertainty half-widths.

For the published direction, the IFR1-to-MSA step reduces the lateral half-width from 166.9 m to 86.7 m, about 48%. In the turned N–S case, it changes from 73.9 m to 53.7 m, about 27%. This step changes magnetometer terms only, so the vertical half-width remains 45.3 m.

The last step adds the Gz check shots. In the error model, the allowance for the axial accelerometer bias falls from 0.4 mg to 0.1 mg (1σ), and the allowance for its scale-factor error from 0.05% to 0.04%. The vertical half-width falls to 45.1 m in both directions. In the published direction, which runs nearly magnetic east–west, the lateral half-width also falls slightly, from 86.7 m to 85.7 m: there, an axial bias also moves the long collar azimuth.

That change is small. Uncertainty terms add in quadrature, and BHA sag and tool misalignment dominate this well's vertical uncertainty. Figure 2 shows the terms at TD: the check shots reduce the 2.2 m axial bias term to 0.55 m, and the 22.7 m total (1σ) changes by only about 0.1 m.

The ellipse includes an uncorrected bias only as the 0.4 mg allowance (1σ), combined in quadrature with the other terms. An actual bias does not add in quadrature; it moves the whole well by its full amount. On this well, each 1 mg of axial bias moves the calculated TD about 5.4 m vertically. After sag correction, the vertical total at TD is 13.2 m (1σ), so a bias of that size is a large part of what remains. The check shots measure the bias of each tool, so MSA can remove the shift.

The step changes in Figure 1 are modeled uncertainty changes, not measured correction accuracy. In this example, the MSA step halves selected magnetometer bias and scale-factor terms and reduces the axial interference term.

The benefit depends on the well direction, measurements, reference uncertainty, and remaining errors. A good residual fit alone does not justify a reduced error model. Its use needs applicable quality checks and evidence for the remaining uncertainty.

Correction limits and quality checks

MSA can estimate systematic sensor errors and stable tool-axis magnetic interference patterns. In one run, an axial sensor bias and drillstring interference can contribute to the same fitted offset. The fit does not necessarily separate their causes.

Some configurations can estimate constrained field-strength and dip offsets. They cannot independently establish all reference-field errors. Declination errors need external information. BHA sag and measured-depth errors also need separate treatment.

Referencing, MSA, and sag correction address different errors. Select their combination from the well conditions, available data, and processing requirements.

Poor residual agreement can result from unsuitable reference values, changing sensor errors, bad measurements, or limited measurement geometry. Numerical convergence only means the solver met a stopping condition. Review the fit quality and warnings separately.

Record the accepted correction, its valid interval, input references, solver configuration, and application status. Include the available parameter-resolution and uncertainty information. Keep the basis for any reduced uncertainty model with the definitive survey records.

References

• ISCWSA: Introduction to Wellbore Positioning, Chapter 29 explains multi-station quality checks and measurement-geometry limits.
• Hanak: Assessment of the Validity of Assigning MSA-Variant Error Models to the ISCWSA Test Wells (2014) examines calibration uncertainty and generic-model assumptions.
• ISCWSA error-model documentation provides the current model framework and guidance.