Vectorial Formulation of Direction Cosines for Anisotropic Geologic Structures from Their Geologic Angle Measurements

Abstract

On the basis of vectorial formulation, a series of relatively simple closed-form mathematical equations is presented to determine the direction cosines of the local coordinate axes associated with planar and linear structures in an anisotropic geologic material from their geologic angle measurements (i.e., strike and dip for planar structures and trend and plunge for linear structures). The equations are then applied to calculation of global anisotropic hydraulic conductivity and elastic stiffness tensors with respect to the geographical coordinate axes from their local counterparts with respect to the material symmetry axes.