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Appendix C: List of Gyro Model Error Sources and Weighting Functions In addition to the above MWD weighting functions the gyro error model introduces a whole new set of error sources and associated weighting functions. The weighting functions can be grouped into those which apply in S tationary survey mode, C ontinuous survey mode or either mode. During a single survey leg a tool made transition between these modes as a function of inclination.
Error Code
Description
SurveyMode Propagation Mode
Weighting Function
MD
Inc
Azimuth
cos 𝐼 𝐺 sin𝐼 𝐺
1
AXYZ-XYB
3-axis: xy accelerometer bias
C/S
S/R
0
0
2
AXYZ-ZB
3-axis: z accelerometer bias
C/S
S
0
0
3 4 5 6 7 8
AXYZ-SF AXYZ-MS
3-axis: accelerometer scale factor error 3-axis: accelerometer misalignment
C/S C/S C/S C/S C/S C/S
S S
0 0 0 0 0 0
1.3 sin I cos I
0 0 0 0 0 0
1
1 𝐺𝑐𝑜𝑠(1 − 𝑘. 𝛾) tan(𝐼 − 𝑘. 𝛾)
AXY-B
2-axis: xy accelerometer bias
S/R
AXY-SF AXY-MS AXY-GB
2-axis: Accelerometer scale factor error 2-axis: Accelerometer misalignment
S S S
1
tan(𝐼 − 𝑘. 𝛾) 𝐺
2-axis: Gravity Bias
𝑠𝑖𝑛𝐴 𝑐𝑜𝑠𝐼 Ωcosϕ
9
GXYZ-XYB1
3-axis, stationary: xy gyro bias 1
S
S/R
0
0
𝑐𝑜𝑠𝐴 Ωcosϕ
10
GXYZ-XYB2
3-axis, stationary: xy gyro bias 2
S
S/R
0
0
11
GXYZ-XYRN
3-axis, stationary: xy gyro random noise
S
R
0
0
√1−𝑠𝑖𝑛 2 𝐴. 𝑠𝑖𝑛 2 𝐼 Ωcosϕ
𝑓.
𝑐𝑜𝑠𝐴 𝑠𝑖𝑛𝐼 Ωcosϕ 𝑐𝑜𝑠𝐴 𝑐𝑜𝑠𝐼 Ωcosϕ 𝑠𝑖𝑛𝐴 𝑐𝑜𝑠 2 𝐼 Ωcosϕ
12
GXYZ-XYG1
3-axis, stationary: xy gyro g-dependent error 1
S
S
0
0
13
GXYZ-XYG2
3-axis, stationary: xy gyro g-dependent error 2
S
S/R
0
0
14
GXYZ-XYG3
3-axis, stationary: xy gyro g-dependent error 3
S
S/R
0
0
𝑠𝑖𝑛𝐴 𝑠𝑖𝑛𝐼 𝑐𝑜𝑠𝐼 Ωcosϕ
15
GXYZ-XYG4
3-axis, stationary: xy gyro g-dependent error 4
S
S
0
0
𝑠𝑖𝑛𝐴 𝑠𝑖𝑛𝐼 Ωcosϕ 𝑠𝑖𝑛𝐴 𝑠𝑖𝑛𝐼 Ωcosϕ 𝑠𝑖𝑛𝐴 𝑠𝑖𝑛 2 𝐼 Ωcosϕ
16
GXYZ-ZB
3-axis, stationary: z gyro bias
S
S
0
0
17
GXYZ-ZRN
3-axis, stationary: z gyro random noise
S
R
0
0
18
GXYZ-ZG1
3-axis, stationary: z gyro g-dependent error 1
S
S/R
0
0
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