The concept of an ellipse at any point in a drill hole to quantify the possible locations of the point is illustrated with the following example.
Suppose the measured depth is 2500 feet as shown in the sketch and that systematic errors (errors which regularly re-occur and are not compensating) at any survey station are 1° in azimuth, 0.5° in inclination, and 1 part in 500 for measured depth. Further, suppose the inclination and azimuth are thought to be 30° and 90°, respectively.
NORTH A MD sin I
The expected location of the bottom of the drill hole is
The actual location of the bottom of the drill hole could be anywhere within a volume shown as an ellipsoid in the sketch. The dimensions of the ellipsoid are given by the variations of variables of inclination, azimuth, and measured depth. The maximum dimensions of the ellipsoid and consequently the position of uncertainty which is called the "ellipse of uncertainty" are
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