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An ellipse of uncertainty is formed around the wellbore where the lateral dimension is proportional to the azimuth error and the high side dimension is proportional to the inclination error. If the azimuth was more accurate than the inclination, the ellipse would be thinner across the wellbore. This example is more typical with the azimuth less certain than the inclination, creating an ellipse with a larger lateral dimension. The final shape is like an almond, elliptical in all three orthogonal planes.
Figure 73: Applying normal distribution modelling to a section of the wellbore.
17.4 How can we determine the size and shape?
In reality, this is a complex calculation best left to computer software but a very simple rule of thumb can estimate spatial error from an angular error as follows:
1 degree in angle creates about 2% in distance.
For example; if a line of 1000 m was measured on a bearing of 90 degrees plus or minus 1 degree, the final point would be in error by approximately +/- 2 0m.
Figure 74: Trajectory error calculations.
The correct answer would be closer to 1000 sin (1o) = 17.45m but as a conservative estimate the 2% per 1° rule is easy to calculate.
It is not true that errors are proportional to measured depth. In surveying, systematic (i.e. unchanging) errors propagate in proportion to how far you are from your origin. A compass reference error for example may pull you to the right as you walk away from the origin but will still pull you to the right as you return effectively cancelling out the positional error. A scaling error may underestimate your distance from the origin but equally it will be proportional to the distance and will cancel out on the return. When estimating the likely positional error, we can use this simple fact and the assumption that the dominant errors are systematic. Clearly though, not all errors are. Some errors like
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