Introduction

In a number of geological situations structural lines and planes have been rotated from some initial orientation. One of our tasks is to describe such rotations and this can be done with the aid of the stereonet. Every rigid rotation can be defined by an angle and sense of rotation about a specified axis.

The most general case involves rotation about an inclined axis, but we start with the simpler cases of rotations about vertical and horizontal axes. We do this because it is a good way to introduce the techniques of rotations and because a sequence of such rotations is equivalent to a rotation about a single inclined axis. In all cases, the sense of rotation is described as clockwise or anticlockwise when looking along the rotation axis, whether horizontal, inclined or vertical.

Basic techniques

As an aid to visualization consider a turntable (Fig. 6.1). As the base rotates about its axis R through some angle ω the locus of an oblique line L through its center O is a right-circular cone of rotation Angle ϕ between R and L is the semi-vertex angle of this cone. The intersection of this cone with the sphere will, in general, be a small circle, one in the lower and one in the upper hemisphere. There are, however, two limiting cases: if ϕ = 0 the surface degenerates to a line and if ϕ = 90° it becomes a plane.