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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 +Ö4(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= Ö {(b (1-n)+m} /b
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