• Geophysics and Geophysical Exploration
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• v.23 no.2
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• pp.89-96
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• 2020

This tutorial summarizes the coordinate transforms for formulating geophysical problems. To ensure mathematical consistency, this discussion begins with the right-hand rule. Further, the concepts of active and passive transforms are introduced. By extending these concepts, the coordinate transform and its inverse between two coordinates are related to the matrix transpose. The yaw-pitch-roll rotation and the azimuth-deviation-tool face rotation transforms are described as the most frequently used schemes, and the relation between the Rodrigues' rotation formula and these two transforms are mathematically explained. The "Gimbal Lock" problem inherent in yaw-pitch-roll rotation is schematically presented and mathematically derived. As a useful tool overcome this problem, the principle and usage of the quaternion is also described.