Introduction

Deforming a circle into an ellipse clearly demonstrates that the orientations and lengths of lines and the angles between pairs of lines generally change. With suitable material the stretch and angle of shear associated with a line may be determined from measurements made on deformed objects whose original shape or size are known. It may then be possible to determine something of the shape, size and orientation of the strain ellipse. For example, measurement of the deformed shape of an originally spherical oolite yields the shape of the ellipse and its orientation directly. This chapter deals with some additional techniques for extracting two-dimensional strain information from deformed rocks. Many more examples, including some excellent photographs, can be found in the book by Ramsay and Huber (1983). Lisle (1994) gives a good review of more recent developments.

Before describing the full analytical method it will be useful to show that in some situations the shape and orientation of the strain ellipse can be obtained simply and directly using purely graphical means.

Deformed grains

The center points of individual grains in a section through a rock form a grid. In terms of the center-to-center distances the possible geometrical patterns have two end-members. If the distribution is random, the minimum distance between centers is zero and such pattern exhibits clustering. If all the grains are perfectly uniform circles and are closely packed then all distances between centers will be equal in the undeformed state (Fig. 12.1a), and thus are radii of a circle.