Evaluation of 3D positions and the positional accuracy of points within a borehole

The article discusses simple algorithms used for the evaluation of 3D positions of points within a borehole and the accuracy of 3D positions of points within a borehole. The kinds of boreholes discussed are typically from 1500 m to 3000 m deep, and are dug for the purposes of exploration and extraction of oils, gases and geothermal water. The algorithm used to evaluate 3D positions of points within a borehole is based on a gradual application of an approximation of the curve of the borehole between two successive points within the borehole, using a circular arc. The position of the second point belonging to the pair of successive points is calculated based on the chord of the circular arc (the length of the chord, direction angle and inclination angle) between the two points. The algorithm used to evaluate the accuracy of 3D positions is based upon a theory regarding function accuracy developed within the field of mining measurements and geodesy. Both algorithms are easily implemented in spreadsheet programs, as well as visualised and modelled in CAD programs.