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W 12
W 34
Alternative 1 Alternative 2 Alternative 3
1 0
0 1
sinI
cosI
Alternatives 1 and 2 have their own strengths and weaknesses, whereas Alternative 3 is designed to combine the best of both options and is the preferred calculation option. This is discussed in detail in Appendix B of [2] and in [4].
Revision 2 makes some corrections to the depth error magnitudes.
Revision 3 replaced the remaining 16 toolface dependant weighting functions with 20 new ones, following a method developed for the gyro error model. This removes the need to either include survey toolfaces, or use methods to evaluate at the planning stage which toolfaces might be observed, a process which can give rise to unexpected results. The new terms replace all the existing x and y accelerometer and x and y magnetometer bias and scalefactor terms, for both the standard MWD and MWD with Axial correction cases. The new terms lump together the x and y effects, and the propagation mode varies from either random, where the toolface varies between survey stations and systematic for sliding between survey stations with constant toolface. In practise for MWD the random propagation would normally be considered at the planning stage. The details of revision 3 are dealt with in [5]. Revision 4 brings in lookup tables for the uncertainty in the BGGM model which will change how the error magnitudes are determined for the reference field terms. This revision does not may any changes to the weighting functions. As discussed in section Ap1.2.3 above, the error model assumes that all the errors are Gaussian. However, as detailed in [6] it has come to light that the errors in the global geomagnetic models are in fact, non-Gaussian and are best modelled with a Laplacian distribution which has greater likelihood in the tails of the distribution. This presents some problems in the implementation, especially when varying the number of standard deviations at which to report the output results. The current recommendation is to define in advance the number of standard deviations required for output and then determine the uncertainty in the magnetic model at that confidence level. Divide this value by the number of standard deviation required to g n ‘ qu l n G uss n s nd d d on’ ( l d only h confd nc l l nqu s on) and then use that value as normal in the subsequent calculations.
Although revision 4 has been approved by the ISCWSA, there is still on-going discussion on this point. The appearance of new global magnetic models may lead to further changes in this part of the model.
Ap1.4
Gyro Error Model
Ap1.4.1 Gyro Tool Types and Running Modes Whereas we considered that all MWD tools were essentially the same and comprised three orthogonal accelerometers and three orthogonal accelerometers, there are many different types of gyro survey tool and main different ways of running them in a well. The running modes can broadly be divided into tools which take measurements whilst stationary at regular survey stations and those which run into hole, whilst constantly moving and recording data. Furthermore a gyro tool may include three orthogonal accelerometers and three orthogonal gyros or might only use a subset of sensors. Tools with additional redundant sensors can be reflected in the error magnitudes assigned rather in than in the model mathematics.
So the gyro model covers tools which have:
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