Survey uncertainty depends on the magnitude of each error source, the well geometry, and the correlation between measurements. The terms "systematic" and "random" describe physical error behavior, but ISCWSA also uses them as names for specific propagation modes. The distinction matters when combining uncertainty along a well.
Physical systematic and random errors
A systematic component can remain fixed or change predictably under stated measurement conditions. A residual magnetometer bias that persists during a run is one example. A shared sensor error can nevertheless produce different inclination or azimuth effects as tool attitude changes.
A random component varies unpredictably between repeated measurements. Unpredictability alone does not establish independence: sensor noise can have time correlation. See the JCGM definitions of systematic error and random error.
Vibration and rounding need qualification as examples. Vibration can produce an offset as well as scatter. Quantization error can depend on the input signal rather than behaving as independent noise. See vibration rectification and ADC quantization assumptions.
ISCWSA correlation assumptions
The selected tool model assigns a propagation mode to each error source. These modes specify how the underlying error is assumed to correlate between stations, survey legs, and wells.
| Mode | Correlation represented |
|---|---|
| Random | Independent between survey stations |
| Systematic | Shared across stations within one survey leg; independent between legs |
| Well by well | Shared across survey legs in one well; independent between wells |
| Global | Shared between surveys assigned the same global error source |
A mode is a modeling assumption, not a statement that every physical error with that name behaves identically. Tool configuration and measurement mode can affect the appropriate assignment. See the ISCWSA definition, section 4.7.
Crustal magnetic contributions vary spatially. They do not produce one identical error at every survey in a field. Rev5 represents reference uncertainty using shared and unshared components between wells. The applicable reference records and correlation assumptions determine those components. See the geomagnetic correlation supplement and Main Field Models article.
Combining uncertainty along the well
Within one correlated source, station responses combine before its covariance is calculated. Within a source modeled as random, independent station covariance contributions add. Independent sources then combine through their covariance contributions, including sources with systematic propagation.
Root-sum-square combination therefore applies to independent contributions; it is not exclusive to random sources. Changing well geometry also changes the position response, so the labels alone do not establish steady ellipse growth or rank the sources by importance.
A one-dimensional illustration shows the effect of correlation. For N equal, aligned contributions, each with standard deviation σ:
- Fully correlated contributions have a combined standard deviation of Nσ.
- Independent contributions have a combined standard deviation of √Nσ.
This comparison assumes equal weights and one direction. An actual well has geometry-dependent responses, survey intervals, and multiple error sources.
A defined inclination-bias example
Consider a straight 1,000 m section with a constant 0.1° inclination bias, a correct azimuth, and the same starting position. The endpoint displacement is approximately:
1,000 m × (0.1 × π / 180) = 1.75 m
The small-angle calculation describes the displacement caused by that specified bias. It is not a TD uncertainty ellipse. The error direction depends on inclination and azimuth; an ellipse also requires an uncertainty model and a selected confidence level.
Averaging and measurement noise
Repeated measurements of the same quantity can reduce the random part of the uncertainty when the noise has zero mean and suitable correlation properties. A systematic offset remains in the average.
Different stations along a changing trajectory do not measure one fixed inclination or azimuth. Their uncertainty must propagate through the wellpath calculation. For correlated measurements, the usual independent sample averaging rule is insufficient. See NIST's averaging guidance.
Averaging, suitable filtering, and improved acquisition conditions can reduce some noise without replacing the tool. The signal must remain suitable for the chosen processing, and the remaining uncertainty must account for correlation. See the sensor noise and bandwidth discussion.
Selecting accuracy enhancements
Select improvements from the actual error budget, survey method, and geological target or clearance requirements. A source's propagation label does not establish which improvement matters most.
- IFR1 estimates local crustal contributions unresolved by the global reference.
- IFR2 estimates temporal magnetic variation. Its benefit includes reducing reference terms modeled with random propagation.
- MSA estimates selected sensor parameters when the data make them observable.
Benefits depend on data coverage, quality, observable parameters, and the uncertainty remaining after correction. A service name alone does not establish a smaller ellipse or a cost-effectiveness ranking. For the conditions and residual errors, see the Main Field Models article and Bias vs Scale Factor article.
References
- JCGM: Systematic measurement error and random measurement error.
- ISCWSA (January 2023): Definition of the ISCWSA Error Model, Rev5.13, especially sections 3.1 and 4.7.
- ISCWSA: Application of Partial Correlations Between Geomagnetic Terms.
- NIST: Uncertainty analysis for autocorrelated measurement data.
- Analog Devices: Vibration rectification, ADC quantization, and sensor noise and bandwidth.