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These distortions: • Can be calculated and understood, but without proper care and well educated workforce, it is easy to make mistakes. • Are non-linear; that is to say, the size of the distortion varies across the projected area are very important component in mapping wellbores. The most important and potentially destructive distortions when projecting geospatial data to a map are scale and orientation, particularly when mapping wellbore positions. Figure 18 shows ‘m c o’ l l x mpl of sc l nd azimuth distortion. This effect happens even at short distances but not so obviously to the eye. The orientation or zmuhch ng swh sc ll dcon g nc . s lu c nb c lcul d nd ppl d o‘ lwold’m su m ns to adjust them to projection north referenced value. Similarly, scale distortion can be applied to survey measurements to represent a scaled distance on the map.
1.3.4 Azimuth Distortion A key point to remember is that the projection central meridian is truly a meridian - there is no azimuth distortion. As one moves away from the central meridian east or west, the other meridians plot on the projection as curved lines that curve towards the nearest pole, whereas grid north lines are parallel to the central meridian. At any given point, the difference in azimuth between the grid north lines and the meridian lines is the convergence angle. On the equator, convergence is generally zero also, and increases as one moves north. Figure 18 shows ‘glob l’ c oon wof h conc p.
Figure 18: The plane surface can be tangent or secant to the ellipsoid. Secant permits the scale distortion to be distributed more evenly and therefore a larger area to be covered per unit distortion.
Figure 19 shows a simple way to verify that the value derived is correct (i.e. that the sign of convergence has been correctly applied). It is important when dealing with convergence to do a coupl of ‘s n y’ ch cks:
Always draw a diagram (Figure 19)
•
• Always check that the software application is applying the correct value, correctly • Always have someone else check that the results agree with supplied results of wellbore location • If you are not sure – find a specialist The formal algorithm is Grid azimuth = True Azimuth – Convergence but many applications do not observe the correct sign. It is better to use True Azimuth = Grid Azimuth ± Convergence α where (per figure 19), α - W s of M, nd α + East of CM in Northern hemisphere and the opposite in Southern hemisphere. In the equation above, use the sign in the diagram, not the sign you get with the software, because some applications use the opposite convention.
Figure 19: Shows two projection zones with Central Meridians, as well as non-central meridians plotted on the projection (curved lines) that converge towards the nearest pole. Two additional grid north lines are shown to the right and left of the figure. Grid north lines are parallel on the projection, creating a grid. Convergence and scale sign distortion vary in a non-linear fashion across the projection, but can be calculated for any given point.
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