Abstract
A new method is described for finite strain analysis of naturally deformed sub-fabrics of elliptical markers assuming an homogeneous deformation on the scale of the sample. The method is numerical, and relies on derived equations which relate the axial ratios and orientations of elliptical markers to algebraic parameters of finite linear transformations. This treatment provides criteria for the identification in the deformed state of initial random and non-random but symmetric distributions of elliptical markers about the bedding-trace. For these types of deformed fabric, the method allows: 1. (1) numerical evaluation of the finite strain ratio for the plane of section 2. (2) statistical estimation of the error in this determination due to the sample-size of measured markers and the orientation of the section 3. (3) optimal evaluation of the strain ratio in cases where an initial random fabric is identified 4. (4) determination of the pre-tectonic axial ratios and orientations of the elliptical markers relative to the undeformed bedding-trace 5. (5) determination of pre-tectonic compactional strain imposed on a random depositional fabric; and 6. (6) theoretical investigation of the minimum number of measurements required by the method for any specified level of precision in strain determination in relation to various postulated initial distributions of axial ratios and orientations. Some practical applications of the method are described.
Published Version
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