Azimuth Accuracy in MWD Without Specifying Magnetic Dip — How Meaningful Is It?
In the specifications of magnetic MWD inclinometers, we often see a simple number:
Azimuth accuracy: ±0.5°
At first glance, everything seems clear.
But there is a simple question:
At what magnetic dip was this accuracy achieved?
And this is far from being a formal question.
For a magnetic inclinometer, azimuth accuracy is directly related to the geometry of the Earth’s magnetic field.
How does a magnetic inclinometer determine azimuth?
A magnetometer measures the Earth’s magnetic field vector F.
Azimuth is not determined from the total magnitude of this vector, but from its horizontal projection.
If:
- F — total magnetic field intensity;
- I — magnetic dip angle;
- H — horizontal component of the magnetic field,
after that:
H = F · cos(I)
Therefore, the greater the magnetic dip, the smaller the horizontal component of the field.
At:
I = 0° → H = F
I = 60° → H = 0.5F
I = 80° → H ≈ 0.17F
I = 85° → H ≈ 0.087F
In other words, at a magnetic dip of 85°, the horizontal component is less than 9% of the total magnetic field.
And this is the component that determines the magnetic azimuth.
Why does the same magnetometer error produce a different azimuth error?
Let us assume that a magnetometer has some absolute error in measuring the magnetic field.
At a small magnetic dip, the horizontal component is sufficiently large, so this error is relatively small compared with it.
But as the magnetic dip increases, the horizontal component decreases.
Therefore, the same measurement error has an increasingly greater effect on the determined azimuth.
As a first approximation:
σAz ≈ σB / H
or:
σAz ≈ σB / (F · cos(I))
Thus, the sensitivity of the azimuth channel to magnetic errors increases approximately as:
1 / cos(I)
As we approach the magnetic pole, where:
I → 90°
the horizontal component approaches zero.
The problem of determining azimuth from the magnetic field becomes increasingly ill-conditioned.
Therefore, “Azimuth accuracy ±0.5°” is not the whole story
Two manufacturers may both state:
Azimuth accuracy: ±0.5°
But if one instrument was tested at a small magnetic dip and the other at a significantly larger one, comparing these two numbers directly is not entirely meaningful.
It is somewhat like specifying the accuracy of a length measurement without stating the conditions under which the measurement was performed.
For an objective assessment of the azimuth channel, it is desirable to know at least:
- magnetic dip at the calibration point;
- total magnetic field intensity;
- calibration conditions;
- tool orientation and inclination;
- preferably, the test methodology and range of conditions covered.
But magnetic dip is also a test of instrument quality
And here, in our opinion, there is an even more interesting point.
Specifying the magnetic dip at which calibration was performed tells us not only the conditions under which the stated accuracy was achieved.
It also provides some information about how demanding the test of the instrument itself was.
A large magnetic dip reduces the horizontal component of the magnetic field and therefore increases the sensitivity of the azimuth channel to various errors, including:
- nonlinearities in the magnetic channel;
- orthogonality errors;
- scale-factor errors;
- residual systematic errors;
- errors in determining axis orientation;
- errors in mathematical processing of the magnetic vector.
In other words, a high magnetic dip can serve as a kind of stress test for the azimuth channel.
If an instrument maintains its specified accuracy under conditions where the horizontal component of the magnetic field is significantly reduced, this is a much more informative result than the same accuracy demonstrated under conditions of a small magnetic dip.
And what about inclinometer laboratories?
This leads to another interesting question.
Why not locate inclinometer laboratories in regions with high magnetic dip?
For testing magnetic MWD inclinometers, this could provide a significant advantage.
Testing under conditions of high magnetic dip creates more demanding conditions for the azimuth channel and can help reveal its real limitations.
It becomes a kind of natural stress test of the design and calibration quality of a magnetic inclinometer.
Of course, a high magnetic dip alone is not sufficient for a complete instrument evaluation. Total field intensity, magnetic anomalies, the quality of the calibration equipment, and other test conditions must also be taken into account.
But as a general principle:
The more demanding the conditions for determining magnetic azimuth, the more information the test can provide about the quality of the channel itself.
So here is a simple question for MWD manufacturers
When a specification says:
Azimuth accuracy: ±0.5°
we would like to ask:
At what magnetic dip?
Because without this information, the stated accuracy is an incomplete specification.
And if a manufacturer additionally shows calibration results obtained at a high magnetic dip, this is more than just a number in a datasheet.
It demonstrates how well the azimuth channel performs under an unfavorable magnetic-field geometry.
Perhaps it is time to specify not only the azimuth accuracy — but also the conditions under which it was achieved.