A MATHEMATICAL PROCEDURE FOR PROCESSING A VARIETY OF 3D STRUCTURAL GEOLOGY PROBLEMS INCLUDING ROTATIONS
A purely mathematical set of algorithms address the above problems by allowing students to rapidly calculate a correct answer on a computer or calculator. The mathematical method converts orientation data to 3D vectors where the positive X, Y, and Z axes are oriented due east and horizontal, due north and horizontal, and vertically down respectively. Because the desired answer is an orientation only, all orientation vectors are unit length. The directional angles alpha, beta, and gamma made by a vector with the X, Y, and Z axes respectively yield the vector components parallel to the axes by taking the cosine of the angle. The components can then be manipulated by algorithms that use the cross-product and dot-product to determine angular relationships, or process rotations. These algorithms are easily incorporated into spreadsheet applications for instantaneous solution. This allows students to verify answers, or for researchers to quickly process 3D problems in the field (app. dip, 3-point, rotation, etc.) on a calculator without the need for a stereonet or other plotting tools.