Quaternions for Rotations in Paleomagnetism.

Various rotation operations are required in paleomagnetism. These include transformations to the geographic coordinate system, tilt correction, and finding virtual geomagnetic poles. Different methods have been used for each rotation operation—graphical manipulation on stereonet, matrix calculation, and spherical trigonometry—and computer software has been developed based on these methods. Quaternions, which are commonly used in three-dimensional computer graphics, can handle rotations about arbitrary axes and provide a unified description of the various rotation operations in paleomagnetism. The conversion from a sample coordinate system to the geographic coordinate system depends on orientation methods that vary by sample type and laboratory. Traditionally, coordinate transformations have been computed using rotation matrices of Euler angles based on stereonet manipulation, but quaternions can flexibly accommodate samples oriented by different conventions. Tilt correction can be expressed as a single rotation around the strike direction of the formation. Virtual geomagnetic poles can be obtained by a single quaternion rotation instead of complicated spherical trigonometry. Python functions are provided for all of the rotation operations discussed in this paper, so the readers can incorporate these functions into their own programs to perform rotations using quaternions. [ABSTRACT FROM AUTHOR]