Extra notes on numbering lineations (optional)

Corresponding lineations are numbered L1, L2 etc. However, lineations are a little more complicated. First, a single strain may generate more than one lineation. For example, if a bedded unit is folded, and axial plane cleavage is formed, then it's common for there to be both a bedding-cleavage intersection lineation (parallel to the fold hinges) and a stretching lineation (at a high angle to fold hinges). Both of these could theoretically be labelled L1; they would have to be distinguished with letter subscripts (L1i, L1e).

A second problem affects the numbering of lineations. Imagine an area with bedding (S0) and a single cleavage S1 that is deformed and affected by a crenulation cleavage S2. There will now be two intersection lineations formed by:

• the intersection of S2 with S1
• the intersection of S2 with S0

In detailed work these will be distingished as L2/1 and L2/0 (read L-two-on-one and L-two-on-zero).

Folded fabrics show distinctive patterns on the stereographic projections. By now you should be familiar with the pattern that results when a planar fabric is folded by cylindrical folds; poles to the fabric lie on a great circle on the stereoplot. The great circle represents the profile plane of the folds (i.e. the plane with the fold axis as its pole).

What about folded lineations? The results can be a little more complex because they depend on the shape of the strain ellipse in the folded surface. There are two special cases that are easy to deal with.

We consider the case of a lineation (L1) that lies on a foliation (S2) refolded by F2 folds. Assume that the lineation makes an angle α with the F2 fold axis.

• If the folding operates by flexural slip, then the strain ellipse on the S1 surface is always circular. The angle α will be constant regardless of where the lineation lies. Hence all L1 orientations make a constant angle α with F2 and the L1 points will lie on a small circle centred on F2.
• If the folding is by heterogeneous simple shear (flow folding) then the direction of simple shear is a vector (call it V). If we think of the initial lineation direction L1 as a unit vector L then the distorted lineations L_d = L + γV where γ takes variable values depending on the amount of shear. The vector Ld will always lie in the plane common to L and V. This means that all the distorted lineations will lie in a plane - therefore they lie in a great circle that includes the flow direction and the original lineation direction.

Unfortunately for other mechanisms of folding the answer is not so simple, and it is common for folded lineations to lie somewhere between the small circle predicted in the first case and the great circle predicted in the second.