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TALBOT METHOD, MIN STRAIN ELLIPSOID

The geometry of the strain ellipsoid provides a graphic illustration of the following property of three-dimensional strain; namely that a line will suffer elongation, contraction or retain its length depending on its orientation relative to the principal strain axes. Extended lines will lie in orientations close to the S1 axis whilst contracted lines will define an orientation field centred on the S3 axis.

The transition between these fields of positive and negative extension will be marked by lines with orientations that define the conical surface of on finite elongation, the angular dimensions of which depend on the axial ratio of the strain ellipsoid and the volume change.

Talbot's method states that the shape of the surface of no finite elongation can be estimated stereographically by plotting the orientations of extended and contracted element. Hence from the form of this surface the axial ratios of an ellipsoid can be deduced. Such a method is ideally suited to the analysis of variably oriented line elements. It is found thou that the application of the method to planar data, (e.g. veins which have been folded or boudinaged), is complicated by the fact that such planes should often contain both extended and contracted lines. This problem of deducing the strain ellipsoid from the angular dimensions of the surface of no finite elongation is found to depend on the volume change and is often not diagnostic of a single ellipsoid. Talbot's method offers the potential of calculating tectonic volume changes.

2 2 3

b ={-A[A +4(n/(1-n) }/2

where 2 3

A={(1-n) (1+2n)+([n/m]-1) /(1-n) }

and 2 2

n=cos2 yz and m=cos2 xz

2

1/a= {(b (1-n)+m} /b