AVERAGE PROPERTIES OF ELLIPSOIDAL FABRICS - IMPLICATIONS FOR TWO-DIMENSIONAL AND 3-DIMENSIONAL METHODS OF STRAIN ANALYSIS

Many rocks contain ellipsoidal objects (such as pebbles or reduction zones) which display a variety of shapes and orientations. In deformed rocks such objects may be used for strain analysis by using the concept of an average ellipsoid (here called the 'fabric ellipsoid'). Two fabric ellipsoids are defined which are the results of two different algebraic averaging processes. During deformation of ellipsoidal distributions, the fabric ellipsoids change as if they were themselves material ellipsoids, and are therefore of fundamental importance in strain analysis. In most studies to date, such 3-D fabric ellipsoids have been obtained from 2-D average ellipses determined on section planes cut through the rock sample. Previous work has assumed that the average ellipses will approximate to section through a single fabric ellipsoid. I show here that this is not the case as sectioning introduces a systematic bias into the section ellipse data. This bias is distinct from the statistical errors (due to finite sample size and measurement errors) discussed in other work, and must be considered in any method of strain analysis using section planes.