Tutorial on the Principle of Borehole Deviation Survey - An Application of the Coordinate Transforms

시추공 공곡 측정의 원리 - 좌표계 변환의 응용

  • Song, Yoonho (Deep Subsurface Research Center, Korea Institute of Geoscience and Mineral Resources)
  • 송윤호 (한국지질자원연구원 심지층연구센터)
  • Received : 2020.07.10
  • Accepted : 2020.10.07
  • Published : 2020.11.30


To share an understanding of trajectory measurement in surveys using borehole, this tutorial summarizes the relevant mathematical principles of the borehole deviation survey based on coordinate transform. For uncased or open holes, calculations of the azimuth-deviation-tool face rotation using three-component accelerometer and magnetometer measurements are summarized. For the steel-cased holes, calculations are based on the time-derivative formula of the coordinate transform matrix; yaw-pitch-roll angles through time are mathematically determined by integrating the threecomponent angular velocity measurements from the gyroscope while also removing the Earth's rotation effect. Sensor and data fusion to increase the accuracy of borehole deviation survey is explained with an example of the method. These principles of borehole deviation surveys can be adapted for attitude estimation in air-borne surveys or for positioning in tunnels where global positioning system (GPS) signals cannot be accessed. Information on the optimization filter that must be incorporated in sensor fusion is introduced to help future research.