by Dag Billger, Owner & Business Manager and Duncan McLeod, Owner & Product Manager at Inertial Sensing
Downhole survey instruments rely on a range of sensors to produce data that gives position information about a borehole. One class of sensors that has undergone rapid change over recent years are MEMS gyros and inclinometers.
In the last decade, these have gone from single- and dual-axis systems on a large chip to very small multi-axis, multi-sensor components. These components often include a basic calibration and a basic ‘navigation engine’ that can directly output the heading angles of the system. The natural temptation is to exploit this technology to create a survey gyro. In fact, several such tools have appeared on the market in recent years, but things are not as simple as they seem. These micro IMUs have an ‘off-the-shelf’ navigation performance adequate for simple consumer-grade applications but fall short of the requirements for precision borehole navigation over any significant distance.
Indeed, it is the miniaturization of these components that led to the launch of Inertial Sensing’s 21.6 mm (0.85 in) diameter SlimGyro in January 2015. During the course of the SlimGyro development, it was quickly discovered that the built-in calibration and navigation algorithms could not satisfy the demands of borehole surveying. In parallel with the growing convenience of the miniaturized components, it was necessary to continuously develop and refine the calibration and navigation theory and algorithms. It is clear that a precision survey instrument must be founded on a triad of (1) detailed knowledge of the sensors down to the raw signal behavior, (2) navigation algorithms founded in mathematics and physics, and (3) precision calibration and alignment.
This article outlines the impact on survey results in the absence of proper precision calibration. The aim is to illustrate that, despite the proliferation of easy-to-use miniature components, rigorous individual component calibration is still paramount for obtaining reliable and accurate results.
Temperature calibration
All sensors tend to have a change of output as the tool temperature changes, for the same input. For instance, a gyro may measure 10.0ᵒ/s at 20ᵒC but 10.1ᵒ/s at 25ᵒC for the same turn rate. These small variations have a major impact on the survey results. A calibration of each individual sensor’s response to temperature is required, for both gyros and inclinometers, if precise and repeatable results are to be obtained in the field. This requires sophisticated calibration equipment to rotate and orient the sensors while also setting and maintaining numerous constant temperatures over a required temperature operating range. Multiple temperature test cycles are needed to validate the statistical confidence necessary to qualify or discard a sensor component from use in a system to be delivered.
System alignment
A compact MEMS sensor component is typically comprised of three gyro axes and three inclinometer axes. These are manufactured ‘on the chip’ to be perpendicular to each other, but in practice, there is a wide variation from chip to chip. The variations are between the three gyro axes as a group and the three inclinometer axes as a group, but also as a variation between the triads formed by the gyros and by the inclinometers. Computing and compensating for these small misalignments is a critical stage of calibration to avoid skewed results.
‘Factory’ calibration
What happens if a proper calibration of the IMU component is not performed, or is done inadequately? This is the same as relying on the default ‘factory’ calibrations from the manufacturer. These are usually linear temperature models that are approximately good for an entire class of mass-produced sensor components. Since they are produced in the tens of millions, there is no way that the manufacturer can conduct individual and exact calibration of every individual axis in an IMU. The system alignment is also approximate and assumes that the manufacturing process produces sensor axes that are sufficiently perpendicular. The typical variations are usually noted in the data sheets, with wording like ‘variation of scale factor over temperature’ of 3%, or a ‘cross-axis sensitivity’ of 2%.
A basic improvement to the factory temperature calibration would be to measure the gyro and inclinometer response at room temperature and obtain a gross correction. This shows better performance when the survey tool is tested near room temperature, but quickly degrades as the tool is warmed or cooled in a borehole.
A simple correction to the alignment is to roll the survey tool about its long axis to get a better fix on where the sensors are pointing. But this is insufficient to properly align all the axes and to align the gyros with the inclinometers. Such a gross correction may help in standard situations where the tool is in an inclined borehole and not subject to rotation. But with typical in-hole rotations and/or coming near a vertical section, errors quickly blow up to unacceptable levels.
Practical example
All of the above can be rigorously proven mathematically but is far beyond the scope of this article. By using a real survey that exemplifies these effects it can be shown just how bad the problems can be. All of Inertial Sensing’s gyro systems maintain a record of raw sensor data. This means complete access to the unadulterated sensor signals at very high data rates for every survey. It is therefore possible to take surveyed data from any of Inertial Sensing’s gyros and reprocess this under the conditions of interest here.
GoGyro survey
The surveyed hole used as an example is nearly 1900 m (6234 ft) in depth, begins at a near-vertical inclination of -89.5ᵒ, builds about 2ᵒ of inclination at 700 m (2297 ft), and then rapidly built to -78ᵒ inclination over approximately 100 m (328 ft). The azimuth holds at about 240ᵒ in the vertical section and is steered to about 340ᵒ in the inclined section. The surveying was done in late-2022 using a GoGyro in fast continuous surveying mode, with data output processed using 3 m (9.84 ft) station intervals.
The initial data is processed with the normal high-precision calibration that is standard in all Inertial Sensing gyro models, using full temperature calibration and alignment. The resulting azimuths and inclinations are shown in green in Figures 1 and 2 respectively.
Inadequate alignment: oscillations and offsets
By disabling the full alignment calibration for the GoGyro and relying on the manufacturer’s tolerances the results shown in orange are obtained. This reveals the tell-tale of a poor alignment: strong ‘oscillations’ in the angles due to the coning of the sensing axes around the instrument’s physical axis as the tool rolls going down the hole. Each oscillation corresponds to one roll of the tool. In this case, the error caused by the oscillation is about 1ᵒ in the inclination and 5ᵒ in the azimuth! The nature of inertial navigation means that an alignment error of a fraction of a degree can blow up to several degrees in the results. A naive approach would be to try to improve these results by smoothing these oscillations, but this also seriously degrades the results, grossly blunting any true turning and biasing the survey angles.
On top of this, the fractional misalignment error means that a very significant error of 12ᵒ is picked up in the azimuth as it passes near or through vertical. This is mathematically unavoidable. In inclined or horizontal holes, the effect becomes a decreased sensitivity to turns, leading to unusually ‘flattened’ borehole profiles.
Inadequate temperature calibration: offset and drift
Next, the precise temperature calibration is removed, entirely falling back on the manufacturer’s bulk calibration. The effects are shown in Figures 1 and 2 in blue. This adds an additional 9ᵒ of error in the azimuth and 1ᵒ to 2ᵒ in the inclination. Detailed analysis shows that there is also a drift of the results as the temperature changes. Another naive mitigation strategy is to enforce roll on the tool as it traverses the hole to spread the angle error around an ‘average’ value. However, this will in general still be biased and worse, feeds straight back into the misalignment oscillations.
Effect on the final position error
The effect on the final position of the hole is dramatic. Figure 3 shows the coordinates of the borehole reconstructed with standard minimum curvature calculations. The misalignment effect causes an error in the final hole position of ~50 m – or ~164 ft – (2.6% of depth) while the poor temperature calibration adds another ~40 m (~131 ft) for a total of 90 m (295 ft) in error (4.7% of depth).
Conclusion
In recent years, the proliferation of compact inertial measurement units comprising triads of gyro and inclinometer sensors has led to the possibility of making survey instruments without the apparent need for high-precision calibrations. However, by doing so the results from borehole surveys are seriously degraded. Unavoidable problems with uncontrolled oscillations, drift and biases due to inadequate temperature calibration and alignment are introduced.
Attempts to mitigate these problems by using ad-hoc filters on already processed survey angles destroy the detailed profile of the borehole or give unexplainable variations. These attempts smooth and flatten the borehole profile, making it appear more acceptable and severely reducing the dogleg severity. False confidence in the results is created. The final error profile can be grossly affected, being as much as several percent of hole depth.
While each new generation of miniaturized sensor packages brings advantages in instrument design, a proper high-precision calibration in temperature and alignment for each individual tool is absolutely required for precise and reliable survey results.
This is part 1 of a 2-part series. In the next article, we discuss more specific calibration effects.
For more information visit: www.inertialsensing.com
