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18.2 Covariance
First we have to introduc h d of “co nc ”.
As the name suggests it is a measure of how parameters vary together. Recall that we discussed how height and weight might vary together (correlate) but height and intelligence do not. If we measure the variance of an observation it is simply the square of the deviation but the covariance is the product of the deviations of two parameters. The co nc h lpsus om su h co l onwhchshowsup s “sk w” n h llps .
Figure 78 above shows this, but it is also true in 3D and if we can build up a matrix of covariances in northings, eastings and TVD we can derive an ellipsoid, its dimensions and orientation in 3D space.
In order to build up this matrix we need to know how each error source affects the observations and how the observation error will move the wellpath in North, East and vertically in TVD.
18.1.1 How the errors affect the observations. These error sources are multiple and varied. In the ISCWSA error model there are dozens of error sources. Each will affect a given survey station in different way. For example the accuracy with which we know our magnetic north would be a simple azimuth effect. This will not have any effect on either inclination or measured depth observations. “W gh ng Func ons” usd od mn h ffc ny o souc wllh onM , ncln on nd zmuh respectively. We say that the weighting functions for a compass reference error are (0, 0, 1) i.e. they have no effect on MD, no effect on inclination and a full effect on azimuth. However, a tool misalignment due to a bent housing in the assembly might affect inclination or azimuth depending on the toolface. In this case the weighting function would be (0, cos(Toolface), sin(Toolface)). A drillpipe stretch error would have a weighting function of (1, 0, 0) as you might expect and a BHA sag correction error would have a weight function of (0, 1, 0). The ISCWSA error model SPE paper 67616 (from the ISCWSA website – iscwsa.org) details all the weighting functions for all the error sources.
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